Safe Haskell  None 

Language  Haskell2010 
 The Circ monad
 Basic types
 Basic gates
 Other circuitbuilding functions
 Notation for controls
 Signed items
 Comments and labelling
 Hierarchical circuits
 Block structure
 Operations on circuits
 Circuit transformers
 Automatic circuit generation from classical code
 Example
 General lifting functions
 Liftings of specific constants
 List operations
 Other operations
 Extended quantum data types
This is the main export module for Quipper, collecting everything that Quipper applications need. This is Quipper's "public" interface.
 data Circ a
 data Qubit
 data Bit
 type Qulist = [Qubit]
 type Bitlist = [Bit]
 type Timestep = Double
 qnot :: Qubit > Circ Qubit
 hadamard :: Qubit > Circ Qubit
 gate_H :: Qubit > Circ Qubit
 gate_X :: Qubit > Circ Qubit
 gate_Y :: Qubit > Circ Qubit
 gate_Z :: Qubit > Circ Qubit
 gate_S :: Qubit > Circ Qubit
 gate_S_inv :: Qubit > Circ Qubit
 gate_T :: Qubit > Circ Qubit
 gate_T_inv :: Qubit > Circ Qubit
 gate_E :: Qubit > Circ Qubit
 gate_E_inv :: Qubit > Circ Qubit
 gate_omega :: Qubit > Circ Qubit
 gate_V :: Qubit > Circ Qubit
 gate_V_inv :: Qubit > Circ Qubit
 expZt :: Timestep > Qubit > Circ Qubit
 rGate :: Int > Qubit > Circ Qubit
 gate_W :: Qubit > Qubit > Circ (Qubit, Qubit)
 gate_iX :: Qubit > Circ Qubit
 gate_iX_inv :: Qubit > Circ Qubit
 global_phase :: Double > Circ ()
 global_phase_anchored :: QCData qc => Double > qc > Circ ()
 qmultinot :: QData qa => qa > Circ qa
 cnot :: Bit > Circ Bit
 swap :: QCData qc => qc > qc > Circ (qc, qc)
 qnot_at :: Qubit > Circ ()
 hadamard_at :: Qubit > Circ ()
 gate_H_at :: Qubit > Circ ()
 gate_X_at :: Qubit > Circ ()
 gate_Y_at :: Qubit > Circ ()
 gate_Z_at :: Qubit > Circ ()
 gate_S_at :: Qubit > Circ ()
 gate_S_inv_at :: Qubit > Circ ()
 gate_T_at :: Qubit > Circ ()
 gate_T_inv_at :: Qubit > Circ ()
 gate_E_at :: Qubit > Circ ()
 gate_E_inv_at :: Qubit > Circ ()
 gate_omega_at :: Qubit > Circ ()
 gate_V_at :: Qubit > Circ ()
 gate_V_inv_at :: Qubit > Circ ()
 expZt_at :: Timestep > Qubit > Circ ()
 rGate_at :: Int > Qubit > Circ ()
 gate_W_at :: Qubit > Qubit > Circ ()
 gate_iX_at :: Qubit > Circ ()
 gate_iX_inv_at :: Qubit > Circ ()
 qmultinot_at :: QData qa => qa > Circ ()
 cnot_at :: Bit > Circ ()
 swap_at :: QCData qc => qc > qc > Circ ()
 qinit :: QShape ba qa ca => ba > Circ qa
 qterm :: QShape ba qa ca => ba > qa > Circ ()
 qdiscard :: QData qa => qa > Circ ()
 cinit :: QShape ba qa ca => ba > Circ ca
 cterm :: QShape ba qa ca => ba > ca > Circ ()
 cdiscard :: CData ca => ca > Circ ()
 qc_init :: QCData qc => BType qc > Circ qc
 qc_init_with_shape :: QCData qc => qc > BType qc > Circ qc
 qc_term :: QCData qc => BType qc > qc > Circ ()
 qc_discard :: QCData qc => qc > Circ ()
 measure :: QShape ba qa ca => qa > Circ ca
 prepare :: QShape ba qa ca => ca > Circ qa
 qc_measure :: QCData qc => qc > Circ (QCType Bit Bit qc)
 qc_prepare :: QCData qc => qc > Circ (QCType Qubit Qubit qc)
 cgate_xor :: [Bit] > Circ Bit
 cgate_eq :: Bit > Bit > Circ Bit
 cgate_not :: Bit > Circ Bit
 cgate_and :: [Bit] > Circ Bit
 cgate_or :: [Bit] > Circ Bit
 cgate_if :: CData ca => Bit > ca > ca > Circ ca
 circ_if :: CData ca => Bit > Circ ca > Circ ca > Circ ca
 named_gate :: QData qa => String > qa > Circ qa
 named_gate_at :: QData qa => String > qa > Circ ()
 named_rotation :: QData qa => String > Timestep > qa > Circ qa
 named_rotation_at :: QData qa => String > Timestep > qa > Circ ()
 extended_named_gate :: (QData qa, QData qb) => String > qa > qb > Circ qa
 extended_named_gate_at :: (QData qa, QData qb) => String > qa > qb > Circ ()
 dynamic_lift :: QShape ba qa ca => ca > Circ ba
 qinit_plusminus :: Bool > Circ Qubit
 qinit_of_char :: Char > Circ Qubit
 qinit_of_string :: String > Circ [Qubit]
 map_hadamard :: QData qa => qa > Circ qa
 map_hadamard_at :: QData qa => qa > Circ ()
 controlled_not :: QCData qc => qc > qc > Circ (qc, qc)
 controlled_not_at :: QCData qc => qc > qc > Circ ()
 bool_controlled_not :: QCData qc => qc > BType qc > Circ qc
 bool_controlled_not_at :: QCData qc => qc > BType qc > Circ ()
 qc_copy :: QCData qc => qc > Circ qc
 qc_uncopy :: QCData qc => qc > qc > Circ ()
 qc_copy_fun :: QCData qc => qc > Circ (qc, qc)
 qc_uncopy_fun :: QCData qc => qc > qc > Circ qc
 mapUnary :: QData qa => (Qubit > Circ Qubit) > qa > Circ qa
 mapBinary :: QData qa => (Qubit > Qubit > Circ (Qubit, Qubit)) > qa > qa > Circ (qa, qa)
 mapBinary_c :: QShape ba qa ca => (Qubit > Bit > Circ (Qubit, Bit)) > qa > ca > Circ (qa, ca)
 qc_mapBinary :: QCData qc => (Qubit > Qubit > Circ (Qubit, Qubit)) > (Bit > Bit > Circ (Bit, Bit)) > qc > qc > Circ (qc, qc)
 class ControlSource a where
 data ControlList
 (.&&.) :: (ControlSource a, ControlSource b) => a > b > ControlList
 (.==.) :: QCData qc => qc > BType qc > ControlList
 (./=.) :: QCLeaf q => q > Bool > ControlList
 controlled :: ControlSource c => Circ a > c > Circ a
 data Signed a = Signed a Bool
 from_signed :: Signed a > a
 get_sign :: Signed a > Bool
 comment :: String > Circ ()
 label :: Labelable qa labels => qa > labels > Circ ()
 comment_with_label :: Labelable qa labels => String > qa > labels > Circ ()
 without_comments :: Circ a > Circ a
 class Labelable a s
 box :: (QCData qa, QCData qb, QCurry qa_qb qa qb) => String > qa_qb > qa_qb
 nbox :: QCData qa => String > Integer > (qa > Circ qa) > qa > Circ qa
 box_loopM :: (Integral int, QCData qa) => String > int > qa > (qa > Circ qa) > Circ qa
 loopM_boxed_if :: (Integral int, QCData qa) => Bool > String > int > qa > (qa > Circ qa) > Circ qa
 with_ancilla :: (Qubit > Circ a) > Circ a
 with_ancilla_list :: Int > (Qulist > Circ a) > Circ a
 with_ancilla_init :: QShape a qa ca => a > (qa > Circ b) > Circ b
 with_computed_fun :: (QCData x, QCData y) => x > (x > Circ y) > (y > Circ (y, b)) > Circ (x, b)
 with_computed :: QCData x => Circ x > (x > Circ b) > Circ b
 with_basis_change :: Circ () > Circ b > Circ b
 with_controls :: ControlSource c => c > Circ a > Circ a
 with_classical_control :: QCData qa => Bit > String > qa > (qa > Circ qa) > Circ qa
 without_controls :: Circ a > Circ a
 without_controls_if :: NoControlFlag > Circ a > Circ a
 for :: Monad m => Int > Int > Int > (Int > m ()) > m ()
 endfor :: Monad m => m ()
 foreach :: Monad m => [a] > (a > m b) > m ()
 loop :: (Eq int, Num int) => int > t > (t > t) > t
 loop_with_index :: (Eq int, Num int) => int > t > (int > t > t) > t
 loopM :: (Eq int, Num int, Monad m) => int > t > (t > m t) > m t
 loop_with_indexM :: (Eq int, Num int, Monad m) => int > t > (int > t > m t) > m t
 reverse_generic :: (QCData x, QCData y, TupleOrUnary xt x, QCurry x_y x y, Curry x_y_xt x (y > Circ xt)) => x_y > x_y_xt
 reverse_simple :: (QCData_Simple x, QCData y, TupleOrUnary xt x, QCurry x_y x y) => x_y > y > Circ xt
 reverse_generic_endo :: (QCData x, TupleOrUnary xt x, QCurry x_xt x xt) => x_xt > x_xt
 reverse_generic_imp :: (QCData x, QCurry x__ x ()) => x__ > x__
 reverse_generic_curried :: (QCData x, QCData y, TupleOrUnary xt x, Tuple yt y, QCurry x_yt x yt, QCurry y_xt y xt, Curry x_y_xt x y_xt) => x_yt > x_y_xt
 reverse_simple_curried :: (QCData_Simple x, QCData y, TupleOrUnary xt x, Tuple yt y, QCurry x_yt x yt, QCurry y_xt y xt) => x_yt > y_xt
 reverse_endo_if :: (QCData x, TupleOrUnary xt x, QCurry x_xt x xt) => Bool > x_xt > x_xt
 reverse_imp_if :: (QCData qa, QCurry fun qa ()) => Bool > fun > fun
 data Format
 = EPS
  PS
  ASCII
  Preview
  GateCount
  CustomStyle FormatStyle
 data FormatStyle = FormatStyle {
 renderformat :: RenderFormat
 backgroundcolor :: Color
 foregroundcolor :: Color
 linewidth :: Double
 coffs :: Double
 dotradius :: Double
 oplusradius :: Double
 xoff :: Double
 gatepad :: Double
 gateheight :: Double
 crossradius :: Double
 stringbase :: Double
 barwidth :: Double
 barheight :: Double
 dwidth :: Double
 dheight :: Double
 maxgatelabelwidth :: Double
 maxlabelwidth :: Double
 maxnumberwidth :: Double
 gatefont :: Font
 commentfont :: Font
 commentcolor :: Color
 labelfont :: Font
 labelcolor :: Color
 numberfont :: Font
 numbercolor :: Color
 subroutineshape :: Bool
 format_enum :: [(String, Format)]
 print_unary :: QCData qa => Format > (qa > Circ b) > qa > IO ()
 print_generic :: (QCData qa, QCurry qfun qa b, Curry fun qa (IO ())) => Format > qfun > fun
 print_simple :: (QCData qa, QCurry qfun qa b, Curry fun qa (IO ()), QCData_Simple qa) => Format > qfun > IO ()
 print_of_document :: Format > Document a > IO a
 print_of_document_custom :: Custom > Format > Document a > IO a
 classical_to_cnot :: (QCData qa, QCData qb, QCurry qfun qa qb) => qfun > qfun
 classical_to_quantum :: (QCData qa, QCData qb, QCurry qfun qa qb, QCurry qfun' (QType qa) (QType qb)) => qfun > qfun'
 classical_to_reversible :: (QCData qa, QCData qb) => (qa > Circ qb) > (qa, qb) > Circ (qa, qb)
 type Transformer m a b = forall x. T_Gate m a b x > x
 data T_Gate m a b x
 = T_QGate String Int Int InverseFlag NoControlFlag (([a] > [a] > Ctrls a b > m ([a], [a], Ctrls a b)) > x)
  T_QRot String Int Int InverseFlag Timestep NoControlFlag (([a] > [a] > Ctrls a b > m ([a], [a], Ctrls a b)) > x)
  T_GPhase Double NoControlFlag (([B_Endpoint a b] > Ctrls a b > m (Ctrls a b)) > x)
  T_CNot NoControlFlag ((b > Ctrls a b > m (b, Ctrls a b)) > x)
  T_CGate String NoControlFlag (([b] > m (b, [b])) > x)
  T_CGateInv String NoControlFlag ((b > [b] > m [b]) > x)
  T_CSwap NoControlFlag ((b > b > Ctrls a b > m (b, b, Ctrls a b)) > x)
  T_QPrep NoControlFlag ((b > m a) > x)
  T_QUnprep NoControlFlag ((a > m b) > x)
  T_QInit Bool NoControlFlag (m a > x)
  T_CInit Bool NoControlFlag (m b > x)
  T_QTerm Bool NoControlFlag ((a > m ()) > x)
  T_CTerm Bool NoControlFlag ((b > m ()) > x)
  T_QMeas ((a > m b) > x)
  T_QDiscard ((a > m ()) > x)
  T_CDiscard ((b > m ()) > x)
  T_DTerm Bool ((b > m ()) > x)
  T_Subroutine BoxId InverseFlag NoControlFlag ControllableFlag [Wire] Arity [Wire] Arity RepeatFlag ((Namespace > [B_Endpoint a b] > Ctrls a b > m ([B_Endpoint a b], Ctrls a b)) > x)
  T_Comment String InverseFlag (([(B_Endpoint a b, String)] > m ()) > x)
 identity_transformer :: Transformer Circ Qubit Bit
 transform_generic :: (QCData x, QCData y, QCurry qfun x y) => Transformer Circ Qubit Bit > qfun > qfun
 transform_generic_shape :: (QCData x, QCData y, QCurry qfun x y, Curry qfun' x' (m y'), Curry qfun'' x qfun', x' ~ QCType a b x, y' ~ QCType a b y, Monad m) => Transformer m a b > qfun > qfun''
 type InverseFlag = Bool
 type NoControlFlag = Bool
 data B_Endpoint a b
 = Endpoint_Qubit a
  Endpoint_Bit b
 type Endpoint = B_Endpoint Qubit Bit
 type Ctrls a b = [Signed (B_Endpoint a b)]
 module Quipper.CircLifting
 decToMonad :: String > Q [Dec] > Q [Dec]
 expToMonad :: String > Q Exp > Q Exp
 template_symb_colon_ :: Monad m => m (a > m ([a] > m [a]))
 template_symb_obracket_symb_cbracket_ :: Monad m => m [a]
 template_init :: Monad m => m ([a] > m [a])
 template_last :: Monad m => m ([a] > m a)
 template_symb_plus_symb_plus_ :: Monad m => m ([a] > m ([a] > m [a]))
 template_zip3 :: Monad m => m ([a] > m ([b] > m ([c] > m [(a, b, c)])))
 template_foldl :: Monad m => m ((a > m (b > m a)) > m (a > m ([b] > m a)))
 template_reverse :: Monad m => m ([a] > m [a])
 template_zipWith :: Monad m => m ((a > m (b > m c)) > m ([a] > m ([b] > m [c])))
 template_fold_right_zip :: Monad m => m (((a, b, c) > m (a, d)) > m ((a, [b], [c]) > m (a, [d])))
 template_symb_dollar_ :: Monad m => m ((a > m b) > m (a > m b))
 template_error :: Monad m => m (String > m a)
 template_snd :: Monad m => m ((a, b) > m b)
 class (QData qa, CType qa ~ ca, BType qa ~ ba) => QShape ba qa ca  ba > qa, qa > ca, ca > ba
 class (qa ~ QType (CType qa), qa ~ QTypeB (BType qa), qa ~ QCType Qubit Bool qa, qa ~ QType qa, QCData qa, QCData (CType qa)) => QData qa
 class (QData (QType ca), CType (QType ca) ~ ca) => CData ca
 class (QData (QTypeB ba), BType (QTypeB ba) ~ ba) => BData ba
 class (Labelable qc String, Typeable qc, Show qc, Show (LType qc), qc ~ QCType Qubit Bit qc, CType (QType qc) ~ CType qc, BType (CType qc) ~ BType qc, QCType Int Bool (CType qc) ~ BType qc) => QCData qc
 class (QCData qc, QData (QType qc)) => QCDataPlus qc
 bit :: Bit
 qubit :: Qubit
 qshape :: QData qa => BType qa > qa
 qc_false :: QCData qc => qc > BType qc
 class QCData qc => QEq qc where
 class (QEq qa, QData qa) => QOrd qa where
 q_lt :: QOrd qa => qa > qa > Circ (qa, qa, Qubit)
 q_gt :: QOrd qa => qa > qa > Circ (qa, qa, Qubit)
 q_le :: QOrd qa => qa > qa > Circ (qa, qa, Qubit)
 q_ge :: QOrd qa => qa > qa > Circ (qa, qa, Qubit)
The Circ monad
The Circ
monad encapsulates the type of quantum operations. For
example, a quantum operation that inputs two Qubit
s and outputs a
Qubit
and a Bit
has the following type:
(Qubit, Qubit) > Circ (Qubit, Bit)
Monad Circ Source #  
Functor Circ Source #  
Applicative Circ Source #  
QCurry (Circ b) () b Source #  
CircLiftingUnpack (Circ [a]) (Circ [a]) Source #  
CircLiftingUnpack (Circ ()) (Circ ()) Source #  
CircLiftingUnpack (Circ (a, b)) (Circ (a, b)) Source #  
CircLiftingUnpack (Circ (a, b, c)) (Circ (a, b, c)) Source #  
CircLiftingUnpack (Circ (a, b, c, d)) (Circ (a, b, c, d)) Source #  
CircLiftingUnpack (Circ (a, b, c, d, e)) (Circ (a, b, c, d, e)) Source #  
CircLiftingUnpack (Circ (a, b, c, d, e, f)) (Circ (a, b, c, d, e, f)) Source #  
CircLiftingUnpack (Circ (a, b, c, d, e, f, g)) (Circ (a, b, c, d, e, f, g)) Source #  
CircLiftingUnpack (Circ Qubit) (Circ Qubit) Source #  
CircLiftingUnpack (Circ b) b' => CircLiftingUnpack (Circ (a > Circ b)) (a > b') Source #  
Basic types
The type of qubits.
Eq Qubit Source #  
Ord Qubit Source #  
Show Qubit Source #  
ControlSource Qubit Source #  
QCLeaf Qubit Source #  
SimpleType Qubit Source #  
QCData Qubit Source #  
Labelable Qubit String Source #  
ControlSource (Signed Qubit) Source #  
CircLiftingUnpack (Circ Qubit) (Circ Qubit) Source #  
type QCType x y Qubit Source #  
The type of runtime classical bits (i.e., boolean wires in a circuit).
Basic gates
This section contains various elementary gates that can be used as building blocks for constructing circuits.
type Timestep = Double Source #
A time step is a small floating point number used as a parameter to certain gates, such as rotation gates or the [exp −iZt] gate.
Reversible gates in functional style
The gates in this section are in "functional" style, which means
that they return something. For example, the qnot
gate consumes a
Qubit
, performs an operation, and outputs a new Qubit
. The
gates should be used like this:
output < qnot input
or, for a binary gate:
(out0, out1) < gate_W in0 in1
For each of these gates, we also provide a version in imperative style, see Reversible gates in imperative style below.
gate_E :: Qubit > Circ Qubit Source #
Apply a Clifford E = HS[sup 3]ω[sup 3] gate.
[image E.png]
This gate is the unique Clifford operator with the properties E³ = I, EXE⁻¹ = Y, EYE⁻¹ = Z, and EZE⁻¹ = X. It is a convenient gate for calculations. For example, every Clifford operator can be uniquely written of the form
 E[sup a]X[sup b]S[sup c]ω[sup d],
where a, b, c, and d are taken modulo 3, 2, 4, and 8, respectively.
gate_V :: Qubit > Circ Qubit Source #
Apply a V = √X gate. This is by definition the following gate (see also Nielsen and Chuang, p.182):
[image V.png]
expZt :: Timestep > Qubit > Circ Qubit Source #
Apply an [exp −iZt] gate. The timestep t is a parameter.
rGate :: Int > Qubit > Circ Qubit Source #
Apply a rotation by angle 2πi/2[sup n] about the zaxis.
[image rGate.png]
gate_W :: Qubit > Qubit > Circ (Qubit, Qubit) Source #
Apply a W gate. The W gate is selfinverse and diagonalizes the SWAP gate.
[image W.png]
The arguments are such that
gate_W 0〉 0〉 = 00〉 gate_W 0〉 1〉 = (01〉+10〉) / √2 gate_W 1〉 0〉 = (01〉10〉) / √2 gate_W 1〉 1〉 = 11〉.
In circuit diagrams, W[sub 1] denotes the "left" qubit, and W[sub 2] denotes the "right" qubit.
gate_iX :: Qubit > Circ Qubit Source #
Apply an iX gate. This gate is used similarly to the Pauli X gate, but with two advantages:
 the doublycontrolled iX gate can be implemented in the Clifford+T gate base with Tcount 4 (the doublycontrolled X gate requires Tcount 7);
 the iXgate has determinant 1, and therefore an ntimes controlled iX gate can be implemented in the Clifford+T gate base with no ancillas.
In particular, the iX gate can be used to implement an additional control with Tcount 8, like this:
[image iX.png]
global_phase :: Double > Circ () Source #
Apply a global phase change [exp iπt], where typically t ∈ [0,2]. This gate is uninteresting if not controlled; however, it has nontrivial effect if it is used as a controlled gate.
global_phase_anchored :: QCData qc => Double > qc > Circ () Source #
Like global_phase
, except the gate is also "anchored" at a
qubit, a bit, or more generally at some quantum data. The anchor
is only used as a hint for graphical display. The gate, which is a
zeroqubit gate, will potentially be displayed near the anchor(s).
swap :: QCData qc => qc > qc > Circ (qc, qc) Source #
Apply a swap gate to two qubits. More generally, apply swap gates to every corresponding pair of qubits in two pieces of quantum data.
Reversible gates in imperative style
The gates in this section are in "imperative" style, which means that they operate on a qubit "in place" and do not return anything. The gates should be used like this:
qnot_at q
or, for a binary gate:
gate_W_at q0 q1
For each of these gates, we also provide a version in functional style, see Reversible gates in functional style above.
hadamard_at :: Qubit > Circ () Source #
Apply a Hadamard gate.
gate_S_inv_at :: Qubit > Circ () Source #
Apply the inverse of an Sgate.
gate_T_inv_at :: Qubit > Circ () Source #
Apply the inverse of a Tgate.
gate_E_at :: Qubit > Circ () Source #
Apply a Clifford E = HS[sup 3]ω[sup 3] gate.
[image E.png]
This gate is the unique Clifford operator with the properties E³ = I, EXE⁻¹ = Y, EYE⁻¹ = Z, and EZE⁻¹ = X. It is a convenient gate for calculations. For example, every Clifford operator can be uniquely written of the form
 E[sup a]X[sup b]S[sup c]ω[sup d],
where a, b, c, and d are taken modulo 3, 2, 4, and 8, respectively.
gate_E_inv_at :: Qubit > Circ () Source #
Apply the inverse of an Egate.
gate_omega_at :: Qubit > Circ () Source #
Apply the scalar ω = [exp iπ/4], as a singlequbit gate.
gate_V_at :: Qubit > Circ () Source #
Apply a V = √X gate. This is by definition the following gate (see also Nielsen and Chuang, p.182):
[image V.png]
gate_V_inv_at :: Qubit > Circ () Source #
Apply the inverse of a Vgate.
expZt_at :: Timestep > Qubit > Circ () Source #
Apply an [exp −iZt] gate. The timestep t is a parameter.
rGate_at :: Int > Qubit > Circ () Source #
Apply a rotation by angle 2πi/2[sup n] about the zaxis.
[image rGate.png]
gate_W_at :: Qubit > Qubit > Circ () Source #
Apply a W gate. The W gate is selfinverse and diagonalizes the SWAP gate.
[image W.png]
The arguments are such that
gate_W 0〉 0〉 = 00〉 gate_W 0〉 1〉 = (01〉+10〉) / √2 gate_W 1〉 0〉 = (01〉10〉) / √2 gate_W 1〉 1〉 = 11〉.
In circuit diagrams, W[sub 1] denotes the "left" qubit, and W[sub 2] denotes the "right" qubit.
gate_iX_at :: Qubit > Circ () Source #
Apply an iX gate. This gate is used similarly to the Pauli X gate, but with two advantages:
 the doublycontrolled iX gate can be implemented in the Clifford+T gate base with Tcount 4 (the doublycontrolled X gate requires Tcount 7);
 the iXgate has determinant 1, and therefore an ntimes controlled iX gate can be implemented in the Clifford+T gate base with no ancillas.
In particular, the iX gate can be used to implement an additional control with Tcount 8, like this:
[image iX.png]
gate_iX_inv_at :: Qubit > Circ () Source #
Apply a −iX gate. This is the inverse of gate_iX_at
.
qmultinot_at :: QData qa => qa > Circ () Source #
Negate all qubits in a quantum data structure.
swap_at :: QCData qc => qc > qc > Circ () Source #
Apply a swap gate to two qubits. More generally, apply swap gates to every corresponding pair of qubits in two pieces of quantum data.
Gates for state preparation and termination
qinit :: QShape ba qa ca => ba > Circ qa Source #
Initialize a qubit from a boolean parameter. More generally, initialize a data structure of qubits from a corresponding data structure of boolean parameters. Examples:
q < qinit False (q0, q1) < qinit (True, False) [q0, q1, q2] < qinit [True, False, True]
qterm :: QShape ba qa ca => ba > qa > Circ () Source #
Terminate a qubit, asserting its state to equal the boolean parameter. More generally, terminate a data structure of qubits, asserting that their state is as given by a data structure of booleans parameters. Examples:
qterm False q qterm (False, False) (q0, q1) qterm [False, False, False] [q0, q1, q2]
In some cases, it is permissible for some aspect of the parameter's shape to be underspecified, e.g., a longer than necessary list, or an integer of indeterminate length. It is therefore possible, for example, to write:
qterm 17 qa  when qa :: QDInt, qterm [False..] qa  when qa :: [Qubit].
The rules for when a boolean argument can be "promoted" in this way are specific to each individual data type.
qdiscard :: QData qa => qa > Circ () Source #
Discard a qubit, ignoring its state. This can leave the quantum system in a mixed state, so is not a reversible operation. More generally, discard all the qubits in a quantum data structure. Examples:
qdiscard q qdiscard (q0, q1) qdiscard [q0, q1, q2]
cterm :: QShape ba qa ca => ba > ca > Circ () Source #
Terminate a Bit
, asserting its state to equal the given
Bool
. More generally, terminate a data structure of Bits,
asserting that their state is as given by a data structure of
Bools. Examples:
cterm False b cterm (False, False) (b0, b1) cterm [False, False, False] [b0, b1, b2]
In some cases, it is permissible for some aspect of the parameter's shape to be underspecified, e.g., a longer than necessary list, or an integer of indeterminate length. It is therefore possible, for example, to write:
cterm 17 ca  when ca :: CInt, cterm [False..] ca  when ca :: [Bit].
The rules for when a boolean argument can be "promoted" in this way are specific to each individual data type.
cdiscard :: CData ca => ca > Circ () Source #
Discard a Bit
, ignoring its state. This can leave the system in
a mixed state, so is not a reversible operation. More generally,
discard all the Bits in a data structure. Examples:
cdiscard b cdiscard (b0, b1) cdiscard [b0, b1, b2]
qc_init :: QCData qc => BType qc > Circ qc Source #
Heterogeneous version of qinit
. Please note that the type of
the result of this function cannot be inferred from the type of the
argument. For example,
x < qc_init False
is ambiguous, unless it can be inferred from the context whether
x is a Bit
or a Qubit
. If the type cannot be inferred from
the context, it needs to be stated explicitly, like this:
x < qc_init False :: Circ Qubit
Alternatively, qc_init_with_shape
can be used to fix a specific
type.
qc_init_with_shape :: QCData qc => qc > BType qc > Circ qc Source #
A version of qc_init
that uses a shape type parameter. The
first argument is the shape type parameter, and the second argument
is a data structure containing boolean initializers. The shape type
argument determines which booleans are used to initialize qubits,
and which ones are used to initialize classical bits.
Example:
(x,y) < qc_init_with_shape (bit,[qubit]) (True, [False,True])
This will assign to x a classical bit initialized to 1, and to y a list of two qubits initialized to 0〉 and 1〉, respectively.
qc_measure :: QCData qc => qc > Circ (QCType Bit Bit qc) Source #
Heterogeneous version of measure
. Given a heterogeneous data
structure, measure all of its qubits, and leave any classical bits
unchanged.
qc_prepare :: QCData qc => qc > Circ (QCType Qubit Qubit qc) Source #
Heterogeneous version of prepare
. Given a heterogeneous data
structure, prepare qubits from all classical bits, and leave any
qubits unchanged.
Gates for classical circuits
The gates in this section are for constructing classical circuits. None of these gates alter or discard their inputs; each gate produces a new wire holding the output of the gate.
cgate_eq :: Bit > Bit > Circ Bit Source #
Test equality of two bits, and return True
iff they are equal.
cgate_if :: CData ca => Bit > ca > ca > Circ ca Source #
If a is True
, return a copy of b, else return a copy of
c. Here b and c can be any data structures consisting of
Bits, but b and c must be of the same type and shape (for
example, if they are lists, they must be of equal
length). Examples:
output < cgate_if a b c (out0, out1) < cgate_if a (b0, b1) (c0, c1) [out0, out1, out2] < cgate_if a [b0, b1, b2] [c0, c1, c2]
circ_if :: CData ca => Bit > Circ ca > Circ ca > Circ ca Source #
circ_if
is an ifthenelse function for classical circuits.
It is a wrapper around cgate_if
, intended to be used like this:
result < circ_if <<<condition>>> ( <<thenpart>>> )( <<<elsepart>>> )
Unlike cgate_if
, this is a metaoperation, i.e., the bodies of
the "then" and "else" parts can be circuit building
operations.
What makes this different from the usual boolean "ifthenelse"
is that the condition is of type Bit
, i.e., it is only known at
circuit execution time. Therefore the generated circuit contains
both the "then" and "else" parts, suitably
controlled. Precondition: the "then" and "else" parts must be
of the same type and shape.
Userdefined gates
named_gate :: QData qa => String > qa > Circ qa Source #
Define a new functionalstyle gate of the given name. Usage:
my_unary_gate :: Qubit > Circ Qubit my_unary_gate = named_gate "Q"
my_binary_gate :: (Qubit, Qubit) > Circ (Qubit, Qubit) my_binary_gate = named_gate "R"
This defines a new unary gate and a new binary gate, which will be rendered as Q and R, respectively, in circuit diagrams.
named_gate_at :: QData qa => String > qa > Circ () Source #
Define a new imperativestyle gate of the given name. Usage:
my_unary_gate_at :: Qubit > Circ () my_unary_gate_at = named_gate_at "Q"
my_binary_gate_at :: (Qubit, Qubit) > Circ () my_binary_gate_at = named_gate_at "R"
This defines a new unary gate and a new binary gate, which will be rendered as Q and R, respectively, in circuit diagrams.
named_rotation :: QData qa => String > Timestep > qa > Circ qa Source #
Define a new functionalstyle gate of the given name, and parameterized by a realvalued parameter. This is typically used for rotations or phase gates that are parameterized by an angle. The name can contain '%' as a place holder for the parameter. Usage:
my_unary_gate :: Qubit > Circ Qubit my_unary_gate = named_rotation "exp(i%Z)" 0.123
my_binary_gate :: TimeStep > (Qubit, Qubit) > Circ (Qubit, Qubit) my_binary_gate t = named_rotation "Q(%)" t
named_rotation_at :: QData qa => String > Timestep > qa > Circ () Source #
Define a new imperativestyle gate of the given name, and parameterized by a realvalued parameter. This is typically used for rotations or phase gates that are parameterized by an angle. The name can contain '%' as a place holder for the parameter. Usage:
my_unary_gate_at :: Qubit > Circ () my_unary_gate_at = named_rotation "exp(i%Z)" 0.123
my_binary_gate_at :: TimeStep > (Qubit, Qubit) > Circ () my_binary_gate_at t = named_rotation "Q(%)" t
extended_named_gate :: (QData qa, QData qb) => String > qa > qb > Circ qa Source #
Define a new functionalstyle gate of the given name. Like
named_gate
, except that the generated gate is extended with
"generalized controls". The generalized controls are additional
inputs to the gate that are guaranteed not to be modified if they
are in a computational basis state. They are rendered in a special
way in circuit diagrams. Usage:
my_new_gate :: (Qubit,Qubit) > Qubit > Circ (Qubit,Qubit) my_new_gate = extended_named_gate "Q"
This defines a new gate with name Q, two inputs, and one generalized input.
extended_named_gate_at :: (QData qa, QData qb) => String > qa > qb > Circ () Source #
Like extended_named_gate
, except defines an imperative style gate.
Usage:
my_new_gate_at :: (Qubit,Qubit) > Qubit > Circ () my_new_gate_at = extended_named_gate_at "Q"
This defines a new gate with name Q, two inputs, and one generalized input.
Dynamic lifting
dynamic_lift :: QShape ba qa ca => ca > Circ ba Source #
Convert a Bit
(boolean circuit output) to a Bool
(boolean
parameter). More generally, convert a data structure of Bits to a
corresponding data structure of Bools.
For use in algorithms that require the output of a measurement to be used as a circuitgeneration parameter. This is the case, for example, for sieving methods, and also for some iterative algorithms.
Note that this is not a gate, but a metaoperation. The input consists of classical circuit endpoints (whose values are known at circuit execution time), and the output is a boolean parameter (whose value is known at circuit generation time).
The use of this operation implies an interleaving between circuit
execution and circuit generation. It is therefore a (physically)
expensive operation and should be used sparingly. Using the
dynamic_lift
operation interrupts the batch mode operation of the
quantum device (where circuits are generated ahead of time), and
forces interactive operation (the quantum device must wait for the
next portion of the circuit to be generated). This operation is
especially expensive if the current circuit contains unmeasured
qubits; in this case, the qubits must be preserved while the
quantum device remains on standby.
Also note that this operation is not supported in all contexts. It is an error, for example, to use this operation in a circuit that is going to be reversed, or in the body of a boxed subroutine. Also, not all output devices (such as circuit viewers) support this operation.
Other circuitbuilding functions
qinit_of_char :: Char > Circ Qubit Source #
Generate a new qubit initialized to one of 0〉, 1〉, +〉, −〉, depending on a character c which is '0', '1', '+', or ''.
qinit_of_string :: String > Circ [Qubit] Source #
Generate a list of qubits initialized to a sequence of 0〉, 1〉, +〉, −〉, defined by a string argument e.g. "00+0+++".
map_hadamard :: QData qa => qa > Circ qa Source #
Apply a Hadamard gate to every qubit in a quantum data structure.
map_hadamard_at :: QData qa => qa > Circ () Source #
Imperative version of map_hadamard
.
controlled_not :: QCData qc => qc > qc > Circ (qc, qc) Source #
Apply a controllednot gate to every corresponding pair of quantum or classical bits in two pieces of QCData. The first argument is the target and the second the (positive) control.
For now, we require both pieces of QCData to have the same type, i.e., classical bits can be controlled only by classical bits and quantum bits can be controlled only by quantum bits.
Example:
((a',b'), (x,y)) < controlled_not (a,b) (x,y)
is equivalent to
a' < qnot a `controlled` x b' < qnot b `controlled` y
controlled_not_at :: QCData qc => qc > qc > Circ () Source #
Imperative version of controlled_not
. Apply a controllednot
gate to every corresponding pair of quantum or classical bits in
two pieces of QCData. The first argument is the target and the
second the (positive) control.
bool_controlled_not :: QCData qc => qc > BType qc > Circ qc Source #
A version of controlled_not
where the control consists of
boolean data. Example:
bool_controlled_not (q, r, s) (True, True, False)
negates q and r, but not s.
bool_controlled_not_at :: QCData qc => qc > BType qc > Circ () Source #
A version of controlled_not_at
where the control consists of
boolean data. Example:
bool_controlled_not_at (q, r, s) (True, True, False)
negates q and r, but not s.
qc_copy :: QCData qc => qc > Circ qc Source #
Create a fresh copy of a piece of quantum data. Note: copying is
performed via a controllednot operation, and is not cloning. This
is similar to qc_copy_fun
, except it returns only the copy, and not
the original.
qc_uncopy :: QCData qc => qc > qc > Circ () Source #
"Uncopy" a piece of quantum data; i.e. terminate copy,
assuming it's a copy of orig. This is the inverse of
qc_copy
, in the sense that the following sequence of
instructions behaves like the identity function:
b < qc_copy a qc_uncopy a b
qc_copy_fun :: QCData qc => qc > Circ (qc, qc) Source #
Initialize a new piece of quantum data, as a copy of a given piece. Returns both the original and the copy.
qc_uncopy_fun :: QCData qc => qc > qc > Circ qc Source #
Given two pieces of quantum data, assumed equal (w.r.t. the
computational basis), terminate the second piece (and return the
first, unmodified). This is the inverse of qc_copy_fun
, in the sense
that the following sequence of instructions behaves like the
identity function:
(orig, copy) < qc_copy_fun orig orig < qc_uncopy_fun orig copy
mapUnary :: QData qa => (Qubit > Circ Qubit) > qa > Circ qa Source #
Map a single qubit gate across every qubit in the data structure.
mapBinary :: QData qa => (Qubit > Qubit > Circ (Qubit, Qubit)) > qa > qa > Circ (qa, qa) Source #
Map a binary gate across every corresponding pair of qubits in two quantum data structures of equal shape.
mapBinary_c :: QShape ba qa ca => (Qubit > Bit > Circ (Qubit, Bit)) > qa > ca > Circ (qa, ca) Source #
Like mapBinary
, except the second data structure is classical.
qc_mapBinary :: QCData qc => (Qubit > Qubit > Circ (Qubit, Qubit)) > (Bit > Bit > Circ (Bit, Bit)) > qc > qc > Circ (qc, qc) Source #
Heterogeneous version of mapBinary
. Map a binary gate f
across every corresponding pair of qubits, and a binary gate g
across every corresponding pair of bits, in two quantum data
structures of equal shape.
Notation for controls
Some gates can be controlled by a condition involving one of more "control" qubits and/or classical bits at circuit execution time. Such gates can also be controlled by boolean conditions that are known at circuit generation time (in which case the gate will not be generated when the control condition is false). This section provides a convenient and flexible syntax for specifying controls.
In Quipper, controls can be written in a way that is reminiscent of (a restricted set of) ordinary boolean expressions. Here are some examples:
q1 .==. 0 .&&. q2 .==. 1 for Qubits q1, q2
q .&&. p means q .==. 1 .&&. p .==. 1
qx .==. 5 for a QDInt qx
q1 .==. 0 .&&. z <= 7 combines quantum and classical controls
q ./=. b the negation of q .==. b; here b is a boolean.
[p,q,r,s] a list of positive controls
[(p, True), (q, False), (r, False), (s, True)] a list of positive and negative controls
Among these infix operators, (.&&.)
binds more weakly than
(.==.)
, (./=.)
.
Controls can be attached to a gate by means of the infix
operator controlled
:
gate `controlled` <<controls>>
class ControlSource a where Source #
A "control source" is anything that can be used as a control on
a gate. The most common way to construct a control source is by
using the .==.
, ./=.
, and .&&.
operators. In addition,
we provide the following instances:
Bool
. A boolean condition that is known at circuit generation time can be used as a control, which is then either trivial (the gate is generated) or inconsistent (the gate is not generated).Wire
. This includes the typeBit
(for a classical executiontime control) andQubit
(for a quantum control). A wire can be used as a shorthand notation for a positive control on that wire.ControlList
. A control list is Quipper's internal representation of a control condition, and is trivially a control source. A list of control sources can be used as a control source.
to_control :: a > ControlList Source #
Convert a condition to a control.
data ControlList Source #
A ControlList
is Quipper's internal representation of the type
of conjunctive controls, i.e., controls that can be constructed
using the .==.
, ./=.
, and .&&.
operators.
(.&&.) :: (ControlSource a, ControlSource b) => a > b > ControlList infixr 3 Source #
This is an infix operator to concatenate two controls, forming their logical conjunction.
(.==.) :: QCData qc => qc > BType qc > ControlList infix 4 Source #
(qx .==. x)
: a control which is true just if quantum data qx is in the specified state x.
controlled :: ControlSource c => Circ a > c > Circ a infixl 2 Source #
An infix operator to apply the given controls to a gate:
gate `controlled` <<controls>>
It also works with functionalstyle gates:
result < gate `controlled` <<controls>>
The infix operator is left associative, so it can be applied multiple times:
result < gate `controlled` <<controls1>> `controlled` <<controls2>>
The latter is equivalent to
result < gate `controlled` <<controls1>> .&&. <<controls2>>
Signed items
A signed item of type a. Signed
x True
represents a
positive item, and Signed
x False
represents a negative item.
When used with wires in a circuit, a positive sign is used to represent a positive control, i.e., a filled dot, and a negative sign is used to represent a negative control, i.e., an empty dot.
Show a => Show (Signed a) Source #  
ControlSource (Signed Wire) Source #  
ControlSource (Signed Bit) Source #  
ControlSource (Signed Qubit) Source #  
QCData a => QCData (Signed a) Source #  
Labelable a String => Labelable (Signed a) String Source #  
Labelable a String => Labelable (Signed a) (Signed String) Source #  
type QCType x y (Signed a) Source #  
type QTypeB (Signed a) Source #  
from_signed :: Signed a > a Source #
Extract the underlying item of a signed item.
Comments and labelling
comment :: String > Circ () Source #
Insert a comment in the circuit. This is not a gate, and has no effect, except to mark a spot in the circuit. How the comment is displayed depends on the printing backend.
label :: Labelable qa labels => qa > labels > Circ () Source #
Label qubits in the circuit. This is not a gate, and has no effect, except to make the circuit more readable. How the labels are displayed depends on the printing backend. This can take several different forms. Examples:
Label q as q
and r as r
:
label (q,r) ("q", "r")
Label a, b, and c as a
, b
, and c
, respectively:
label [a,b,c] ["a", "b", "c"]
Label q as x[0]
and r as x[1]
:
label (q,r) "x"
Label a, b, and c as x[0]
, x[1]
, x[2]
:
label [a,b,c] "x"
without_comments :: Circ a > Circ a Source #
Disable labels and comments for a block of code. The intended usage is like this:
without_comments $ do { <<<code block>>> }
This is sometimes useful in situations where code is being reused, for example when one function is implemented in terms of another, but should not inherit comments from it. It is also useful in the definition of recursive function, where a comment should only be applied at the outermost level. Finally, it can be used to suppress comments from parts of circuits for presentation purposes.
Labelable
a s means that a is a data structure that can
be labelled with the format s. A "format" is a string, or a
data structure with strings at the leaves.
Hierarchical circuits
box :: (QCData qa, QCData qb, QCurry qa_qb qa qb) => String > qa_qb > qa_qb Source #
A generic interface for wrapping a circuitgenerating function into a boxed and named subroutine. This takes a name and a circuitgenerating function, and returns a new circuitgenerating function of the same type, but which inserts a boxed subroutine instead of the actual body of the subroutine.
It is intended to be used like this:
somefunc :: Qubit > Circ Qubit somefunc a = do ... somefunc_boxed :: Qubit > Circ Qubit somefunc_boxed = box "somefunc" somefunc
Here, the type of somefunc
is just an example; this could indeed
be a function with any number and type of arguments, as long as the
arguments and return type are quantum data.
It is also possible to inline the box
operator directly, in which
case it should be done like this:
somefunc :: Qubit > Circ Qubit somefunc = box "somefunc" $ \a > do ...
Note: The box
operator wraps around a complete function,
including all of its arguments. It would be incorrect to apply the
box
operator after some quantum variables have already been
defined. Thus, the following is incorrect:
incorrect_somefunc :: Qubit > Circ Qubit incorrect_somefunc a = box "somefunc" $ do ...
It is the user's responsibility not to use the same name for
different subroutines. If box
is called more than once with the
same name and shape of input, Quipper assumes, without checking,
that they are subsequent calls to the same subroutine.
The type of the box
operator is overloaded and quite difficult to
read. It can have for example the following types:
box :: String > (Qubit > Circ Qubit) > (Qubit > Circ Qubit) box :: String > (QDInt > QDInt > Circ (QDInt,QDInt,QDInt)) > (QDInt > QDInt > Circ (QDInt,QDInt,QDInt))
nbox :: QCData qa => String > Integer > (qa > Circ qa) > qa > Circ qa Source #
A version of box
with iteration. The second argument is an
iteration count.
This can only be applied to functions of a single argument, where the input and output types are the same.
box_loopM :: (Integral int, QCData qa) => String > int > qa > (qa > Circ qa) > Circ qa Source #
loopM_boxed_if :: (Integral int, QCData qa) => Bool > String > int > qa > (qa > Circ qa) > Circ qa Source #
A version of loopM
that will be boxed conditionally on a
boolean condition. Typical usage:
loopM_boxed_if (s > 1) "name" s x $ \x > do <<<body>>> return x
Block structure
The following are higherorder functions that provide a way to structure quantum programs into blocks. A block can contain local ancillas or local controls.
Ancillas
The use of the with_ancilla
family of operators is
preferable to using qinit
and qterm
directly. In particular, it
is possible to add controls to a block created with one of the
with_ancilla
family of operators, whereas qinit
and qterm
,
when used individually, cannot be controlled.
with_ancilla :: (Qubit > Circ a) > Circ a Source #
Convenient wrapper around qinit
and qterm
. This can be used
to introduce an ancilla with a local scope, like this:
with_ancilla $ \h > do { <<<code block using ancilla h>>> }
The ancilla will be initialized to 0〉 at the beginning of the block, and it is the programmer's responsibility to ensure that it will be returned to state 0〉 at the end of the block.
A block created with with_ancilla
is controllable, provided that
the body is controllable.
with_ancilla_list :: Int > (Qulist > Circ a) > Circ a Source #
Like with_ancilla
, but creates a list of n ancillas, all
initialized to 0〉. Usage:
with_ancilla_list n $ \a > do { <<<code block using list of ancillas a>>> }
with_ancilla_init :: QShape a qa ca => a > (qa > Circ b) > Circ b Source #
Execute a block with local ancillas. Opens a block, initializing an ancilla with a specified classical value, and terminates it with the same value when the block closes. Note: it is the programmer's responsibility to return the ancilla to its original state at the end of the enclosed block. Usage:
with_ancilla_init True $ \a > do { <<<code block using ancilla a initialized to True>>> }
with_ancilla_init [True,False,True] $ \a > do { <<<code block using list of ancillas a initialized to [True,False,True]>>> }
Automatic uncomputing
with_computed_fun :: (QCData x, QCData y) => x > (x > Circ y) > (y > Circ (y, b)) > Circ (x, b) Source #
: computes x' := f(x); then computes g(x'), which should be organized as a pair (x',y); then uncomputes x' back to x, and returns (x,y).with_computed_fun
x f g
Important subtlety in usage: all quantum data referenced in f, even as controls, must be explicitly bound and returned by f, or the reversing may rebind it incorrectly. g, on the other hand, can safely refer to anything that is in scope outside the with_computed_fun
.
with_computed :: QCData x => Circ x > (x > Circ b) > Circ b Source #
: performs computation
(with result x), then performs code x, and finally performs
the reverse of computation, for example like this:with_computed
computation code
[image with_computed.png]
Both computation and code may refer to any qubits that exist in the current environment, and they may also create new qubits. computation may produce arbitrary garbage in addition to its output.
This is a very general but relatively unsafe operation. It is the user's responsibility to ensure that the computation can indeed be undone. In particular, if computation contains any initializations, then code must ensure that the corresponding assertions will be satisfied in computation[sup −1].
Related more specialized, but potentially safer, operations are:
with_basis_change
, which is likewith_computed
, but assumes that computation is unitary, andclassical_to_reversible
, which assumes that computation is classical (or pseudoclassical), and code is a simple copybycontrollednot operation.
with_basis_change :: Circ () > Circ b > Circ b Source #
: performs a basis change,
then the code, then the inverse of the basis change. Both
basischange and code are in imperative style. It is the user's
responsibility to ensure that the image of code is contained in
the image of basischange, or else there will be unmet assertions
or runtime errors. Usage:with_basis_change
basischange code
with_basis_change basischange $ do <<<code>>> where basischange = do <<<gates>>>
Controls
with_controls :: ControlSource c => c > Circ a > Circ a Source #
A syntax for "if"style (classical and quantum) controls. This can be used as follows:
gate1 with_controls <<controls>> $ do { gate2 gate3 } gate4
The specified controls will be applied to gate2 and gate3. It is an error to specify a control for a gate that cannot be controlled (such as measurement).
with_classical_control :: QCData qa => Bit > String > qa > (qa > Circ qa) > Circ qa Source #
Classical control on a function with same shape of input and output: if the control bit is true the function is fired, otherwise the identity map is used. Note: the constraint on the types is dynamically checked.
without_controls :: Circ a > Circ a Source #
Apply a block of gates while temporarily suspending the
application of controls. This can be used to omit controls on
gates where they are known to be unnecessary. This is a relatively
lowlevel function and should not normally be called directly by
user code. Instead, it is safer to use a higherlevel function such
as with_basis_change
. However, the without_controls
operator is
useful in certain situations, e.g., it can be used to preserve the
NoControlFlag
when defining transformers.
Usage:
without_controls $ do <<code block>>
or:
without_controls (gate)
Note that all controls specified in the surrounding code are
disabled within the without_controls
block. This is even true if
the without_controls
block appears in a subroutine, and the
subroutine is later called in a controlled context. On the other
hand, it is possible to specify controls inside the
without_controls
block. Consider this example:
my_subcircuit = do gate1 without_controls $ do { gate2 gate3 `controlled` <<controls1>> } gate4 my_circuit = do my_subcircuit `controlled` <<controls2>>
In this example, controls 1 will be applied to gate 3, controls 2 will be applied to gates 1 and 4, and no controls will be applied to gate 2.
without_controls_if :: NoControlFlag > Circ a > Circ a Source #
Apply without_controls
if NoControlFlag
is True
, otherwise
do nothing.
Loops
for :: Monad m => Int > Int > Int > (Int > m ()) > m () Source #
A "for" loop. Counts from a to b in increments of s.
Standard notation:
for i = a to b by s do commands end for
Our notation:
for a b s $ \i > do commands endfor
endfor :: Monad m => m () Source #
Mark the end of a "for"loop. This command actually does nothing, but can be used to make the loop look prettier.
foreach :: Monad m => [a] > (a > m b) > m () Source #
Iterate a parameter over a list of values. It can be used as follows:
foreach [1,2,3,4] $ \n > do <<<loop body depending on the parameter n>>> endfor
The loop body will get executed once for each n ∈ {1,2,3,4}.
loop :: (Eq int, Num int) => int > t > (t > t) > t Source #
Iterate a function n times. Example:
loop 3 x f = f (f (f x))
loop_with_index :: (Eq int, Num int) => int > t > (int > t > t) > t Source #
Like loop
, but also pass a loop counter to the function being
iterated. Example:
loop_with_index 3 x f = f 2 (f 1 (f 0 x))
loopM :: (Eq int, Num int, Monad m) => int > t > (t > m t) > m t Source #
Monadic version of loop
.
loop_with_indexM :: (Eq int, Num int, Monad m) => int > t > (int > t > m t) > m t Source #
Monadic version of loop_with_index
. Thus,
loop_with_indexM 3 x0 f
will do the following:
do x1 < f 0 x0 x2 < f 1 x1 x3 < f 2 x2 return x3
Operations on circuits
Reversing
reverse_generic :: (QCData x, QCData y, TupleOrUnary xt x, QCurry x_y x y, Curry x_y_xt x (y > Circ xt)) => x_y > x_y_xt Source #
Reverse a circuitgenerating function. The reversed function requires a shape parameter, given as the input type of the original function.
The type of this highly overloaded function is quite difficult to read. It can have for example the following types:
reverse_generic :: (QCData x, QCData y) => (x > Circ y) > x > (y > Circ x) reverse_generic :: (QCData x, QCData y, QCData z) => (x > y > Circ z) > x > y > (z > Circ (x,y))
reverse_simple :: (QCData_Simple x, QCData y, TupleOrUnary xt x, QCurry x_y x y) => x_y > y > Circ xt Source #
Like reverse_generic
, but only works at simple types, and
therefore requires no shape parameters. Typical type instances:
reverse_simple :: (QCData_Simple x, QCData y) => (x > Circ y) > (y > Circ x) reverse_simple :: (QCData_Simple x, QCData_Simple y, QCData z) => (x > y > Circ z) > (z > Circ (x,y))
reverse_generic_endo :: (QCData x, TupleOrUnary xt x, QCurry x_xt x xt) => x_xt > x_xt Source #
Like reverse_generic
, but specialized to endomorphic circuits,
i.e., circuits where the input and output have the same type (modulo
possibly currying) and shape. In this case, unlike reverse_generic
,
no additional shape parameter is required, and the reversed function
is curried if the original function was. Typical type instances:
reverse_generic_endo :: (QCData x) => (x > Circ x) > (x > Circ x) reverse_generic_endo :: (QCData x, QCData y) => (x > y > Circ (x,y)) > (x > y > Circ (x,y))
reverse_generic_imp :: (QCData x, QCurry x__ x ()) => x__ > x__ Source #
Like reverse_generic_endo
, but applies to endomorphic circuits
expressed in "imperative" style. Typical type instances:
reverse_generic_endo :: (QCData x) => (x > Circ ()) > (x > Circ ()) reverse_generic_endo :: (QCData x, QCData y) => (x > y > Circ ()) > (x > y > Circ ())
reverse_generic_curried :: (QCData x, QCData y, TupleOrUnary xt x, Tuple yt y, QCurry x_yt x yt, QCurry y_xt y xt, Curry x_y_xt x y_xt) => x_yt > x_y_xt Source #
Like reverse_generic
, but takes functions whose output is a
tuple, and curries the reversed function. Differs from
reverse_generic
in an example such as:
f :: (x > y > Circ (z,w)) reverse_generic f :: x > y > ((z,w) > Circ (x,y)) reverse_generic_curried f :: x > y > (z > w > Circ (x,y))
Note: the output must be a ntuple, where n = 0 or n ≥
2. Applying this to a circuit whose output is a nontuple type is a
type error; in this case, reverse_generic
should be used.
reverse_simple_curried :: (QCData_Simple x, QCData y, TupleOrUnary xt x, Tuple yt y, QCurry x_yt x yt, QCurry y_xt y xt) => x_yt > y_xt Source #
Like reverse_simple
, but takes functions whose output is a
tuple, and curries the reversed function. Typical type instance:
reverse_simple_curried :: (QCData_Simple x, QCData y, QCData z) => (x > Circ (y,z)) > (y > z > Circ x)
Note: the output must be a ntuple, where n = 0 or n ≥
2. Applying this to a circuit whose output is a nontuple type is a
type error; in this case, reverse_generic
should be used.
reverse_endo_if :: (QCData x, TupleOrUnary xt x, QCurry x_xt x xt) => Bool > x_xt > x_xt Source #
Conditional version of reverse_generic_endo
. Invert the
endomorphic quantum circuit if the boolean is true; otherwise,
insert the noninverted circuit.
reverse_imp_if :: (QCData qa, QCurry fun qa ()) => Bool > fun > fun Source #
Conditional version of reverse_generic_imp
. Invert the
imperative style quantum circuit if the boolean is true; otherwise,
insert the noninverted circuit.
Printing
Available output formats.
EPS  Encapsulated PostScript graphics. 
Portable Document Format. One circuit per page.  
PS  PostScript. One circuit per page. 
ASCII  A textual representation of circuits. 
Preview  Don't print anything, but preview directly on screen (requires the external program acroread). 
GateCount  Print statistics on gate counts. 
CustomStyle FormatStyle 
data FormatStyle Source #
A data type that holds all the customizable parameters.
FormatStyle  

format_enum :: [(String, Format)] Source #
A mapping from lowercase strings (to be used, e.g., with command line options) to available formats.
print_unary :: QCData qa => Format > (qa > Circ b) > qa > IO () Source #
Print a circuit generating function to the specified format; this requires a shape parameter.
print_generic :: (QCData qa, QCurry qfun qa b, Curry fun qa (IO ())) => Format > qfun > fun Source #
Print a circuit generating function to the specified
format. Unlike print_unary
, this can be applied to a
circuitgenerating function in curried form with n arguments, for
any n >= 0. It then requires n shape parameters.
The type of this heavily overloaded function is difficult to read. In more readable form, it has all of the following types:
print_generic :: Format > Circ qa > IO () print_generic :: (QCData qa) => Format > (qa > Circ qb) > a > IO () print_generic :: (QCData qa, QCData qb) => Format > (qa > qb > Circ qc) > a > b > IO ()
and so forth.
print_simple :: (QCData qa, QCurry qfun qa b, Curry fun qa (IO ()), QCData_Simple qa) => Format > qfun > IO () Source #
Like print_generic
, but only works at simple types, and
therefore requires no shape parameters.
print_of_document :: Format > Document a > IO a Source #
print_of_document_custom :: Custom > Format > Document a > IO a Source #
Like print_of_document
, but also takes a Custom
data
structure.
Classical circuits
classical_to_cnot :: (QCData qa, QCData qb, QCurry qfun qa qb) => qfun > qfun Source #
Translate all classical gates in a circuit into equivalent controllednot gates.
The type of this overloaded function is difficult to read. In more readable form, it has all of the following types:
classical_to_cnot :: (QCData qa) => Circ qa > Circ qa classical_to_cnot :: (QCData qa, QCData qb) => (qa > Circ qb) > (qa > Circ qb) classical_to_cnot :: (QCData qa, QCData qb, QCData qc) => (qa > qb > Circ qc) > (qa > qb > Circ qc)
and so forth.
classical_to_quantum :: (QCData qa, QCData qb, QCurry qfun qa qb, QCurry qfun' (QType qa) (QType qb)) => qfun > qfun' Source #
Replace all classical gates in a circuit by equivalent quantum gates.
The type of this overloaded function is difficult to read. In more readable form, it has all of the following types:
classical_to_quantum :: (QCData qa) => Circ qa > Circ (QType qa) classical_to_quantum :: (QCData qa, QCData qb) => (qa > Circ qb) > (QType qa > Circ (QType qb)) classical_to_quantum :: (QCData qa, QCData qb, QCData qc) => (qa > qb > Circ qc) > (QType qa > QType qb > Circ (QType qc))
and so forth.
Ancilla uncomputation
classical_to_reversible :: (QCData qa, QCData qb) => (qa > Circ qb) > (qa, qb) > Circ (qa, qb) Source #
Generic function for turning a classical (or pseudoclassical)
circuit into a reversible circuit. The input is a classical boolean
function x ↦ f(x), given as a not necessarily reversible
circuit (however, the circuit should be onetoone, i.e., no
"garbage" should be explicitly erased). The output is the
corresponding reversible function (x,y) ↦ (x,y ⊕
f(x)). qa and qb can be any quantum data types. The
function classical_to_reversible
does not itself change
classical bits to qubits; use classical_to_quantum
for that.
Circuit transformers
Transformers are a very general way of defining mappings over circuits. Possible uses of this include:
 gate transformations, where a whole circuit is transformed by replacing each kind of gate with another gate or circuit;
 error correcting codes, where a whole circuit is transformed replacing each qubit by some fixed number of qubits, and each gate by a circuit; and
 simulations, where a whole circuit is mapped to a semantic function by specifying a semantic function for each gate.
The interface is designed to allow the programmer to specify new transformers easily. To define a specific transformation, the programmer has to specify only three pieces of information:
 Types a=⟦Qubit⟧ and b=⟦Bit⟧, to serve as semantic domains.
 A monad m. This is to allow translations to have side effects if desired; one can use the identity monad otherwise.
 For every gate G, a corresponding semantic function ⟦G⟧. The type of this function depends on what kind of gate G is. For example:
If G :: Qubit > Circ Qubit, then ⟦G⟧ :: a > m a. If G :: (Qubit, Bit) > Circ (Bit, Bit), then ⟦G⟧ :: (a, b) > m (b, b).
The programmer provides this information by defining a function of
type Transformer
m a b, see below. Once a
particular transformer has been defined, it can then be applied to
entire circuits. For example, for a circuit with 1 inputs and 2
outputs:
If C :: Qubit > (Qubit, Qubit), then ⟦C⟧ :: a > m (a, a).
Userdefinable transformers
type Transformer m a b = forall x. T_Gate m a b x > x Source #
A circuit transformer is specified by defining a function of type
Transformer
m a b. This involves specifying a monad m,
semantic domains a=⟦Qubit⟧ and b=⟦Bit⟧, and a semantic function
for each gate, like this:
my_transformer :: Transformer m a b my_transformer (T_Gate1 <parameters> f) = f $ <semantic function for gate 1> my_transformer (T_Gate2 <parameters> f) = f $ <semantic function for gate 2> my_transformer (T_Gate3 <parameters> f) = f $ <semantic function for gate 3> ...
The type T_Gate
is used to define case distinctions over gates
in the definition of transformers. For each kind of gate X, it
contains a constructor of the form (T_X f)
. Here, X identifies
the gate, and f is a higherorder function to pass the
translation of X to.
Predefined transformers
identity_transformer :: Transformer Circ Qubit Bit Source #
The identity transformer. This just maps a lowlevel circuits to the corresponding circuitgenerating function. It can also be used as a building block in other transformers, to define "catchall" clauses for gates that don't need to be transformed.
An example transformer
The following is a short but complete example of how to write and use a simple transformer. As usual, we start by importing Quipper:
import Quipper
We will write a transformer called sample_transformer
, which maps
every swap gate to a sequence of three controllednot gates, and
leaves all other gates unchanged. For convenience, Quipper
predefines an identity_transformer
, which can be used as a
catchall clause to take care of all the gates that don't need to
be rewritten.
mytransformer :: Transformer Circ Qubit Bit mytransformer (T_QGate "swap" 2 0 _ ncf f) = f $ \[q0, q1] [] ctrls > do without_controls_if ncf $ do with_controls ctrls $ do qnot_at q0 `controlled` q1 qnot_at q1 `controlled` q0 qnot_at q0 `controlled` q1 return ([q0, q1], [], ctrls) mytransformer g = identity_transformer g
Note how Quipper syntax has been used to define the replacement
circuit new_swap
, consisting of three controllednot gates. Also,
since the original swap gate may have been controlled, we have
added the additional controls with a with_controls
operator. Finally, the without_controls_if
operator ensures that
if the NoControlFlag
is set on the original swap gate, then it
will also be set on the replacement circuit.
To try this out, we define some random circuit using swap gates:
mycirc a b c d = do swap_at a b hadamard_at b swap_at b c `controlled` [a, d] hadamard_at c swap_at c d
To apply the transformer to this circuit, we use the generic
operator transform_generic
:
mycirc2 = transform_generic mytransformer mycirc
Finally, we use a main
function to display the original circuit
and then the transformed one:
main = do print_simple Preview mycirc print_simple Preview mycirc2
Applying transformers to circuits
transform_generic :: (QCData x, QCData y, QCurry qfun x y) => Transformer Circ Qubit Bit > qfun > qfun Source #
Apply the given transformer to a circuit. Unlike
transform_unary
, this function can be applied to a
circuitgenerating function in curried form with n arguments, for
any n ≥ 0.
The type of this heavily overloaded function is difficult to read. In more readable form, it has all of the following types:
transform_generic :: (QCData x) => Transformer Circ Qubit Bit > Circ x > Circ x transform_generic :: (QCData x, QCData y) => Transformer Circ Qubit Bit > (x > Circ y) > (x > Circ y) transform_generic :: (QCData x, QCData y, QCData z) => Transformer Circ Qubit Bit > (x > y > Circ z) > (x > y > Circ z)
and so forth.
transform_generic_shape :: (QCData x, QCData y, QCurry qfun x y, Curry qfun' x' (m y'), Curry qfun'' x qfun', x' ~ QCType a b x, y' ~ QCType a b y, Monad m) => Transformer m a b > qfun > qfun'' Source #
Like transform_generic
, but applies to arbitrary transformers
of type
Transformer m a b
instead of the special case
Transformer Circ Qubit Bit.
This requires an additional shape argument.
The type of this heavily overloaded function is difficult to read. In more readable form, it has all of the following types:
transform_generic :: (QCData x) => Transformer m a b > Circ x > m (QCData a b x) transform_generic :: (QCData x, QCData y) => Transformer m a b > (x > Circ y) > x > (QCData a b x > m (QCData a b y)) transform_generic :: (QCData x, QCData y, QCData z) => Transformer m a b > (x > y > Circ z) > x > y > (QCData a b x > QCData a b y > m (QCData a b z))
and so forth.
Auxiliary type definitions
type InverseFlag = Bool Source #
A flag that, if True
, indicates that the gate is inverted.
type NoControlFlag = Bool Source #
A flag that, if True
, indicates that the gate is controllable,
but any further controls on the gate should be ignored. This is
used, e.g., for circuits consisting of a basis change, some
operation, and the inverse basis change. When controlling such a
circuit, it is sufficient to control the middle operation, so the
gates belonging to the basis change and its inverse will have the
NoControlFlag set.
data B_Endpoint a b Source #
An endpoint is either a qubit or a bit. In a transformer,
we have ⟦Endpoint Qubit Bit⟧ = ⟦Qubit⟧ + ⟦Bit⟧. The type Endpoint
a b is the same as Either
a b, but we use more suggestive
field names.
(Eq b, Eq a) => Eq (B_Endpoint a b) Source #  
(Ord b, Ord a) => Ord (B_Endpoint a b) Source #  
(Show b, Show a) => Show (B_Endpoint a b) Source #  
(QCData a, QCData b) => QCData (B_Endpoint a b) Source #  
(Labelable a String, Labelable b String) => Labelable (B_Endpoint a b) String Source #  
(Labelable a s, Labelable b t) => Labelable (B_Endpoint a b) (B_Endpoint s t) Source #  
type QCType x y (B_Endpoint a b) Source #  
type QTypeB (B_Endpoint a b) Source #  
type Ctrls a b = [Signed (B_Endpoint a b)] Source #
A list of signed values of type ⟦Endpoint⟧. This type is an abbreviation defined for convenience.
Automatic circuit generation from classical code
The following two modules provide functions that are useful for automatic circuit generation from classical code. Please see Quipper.CircLifting for a more detailed explanation of how to use this feature.
module Quipper.CircLifting
Example
We give an example to illustrate what is meant by "lifting" a term to a monad. Consider the expression
f = \g x > g x x,
which has type
f :: (a > a > b) > (a > b).
We can lift this to the IO
monad by
 converting the expression to an abstract syntax tree, using the
special Template Haskell notation [nobr
[ ... ]
];  applying the
expToMonad
function;  converting the resulting abstract syntax tree back to a term,
using the special Template Haskell notation [nobr
$( ... )
].
This allows us to write the following:
f' = $( expToMonad "IO" [ \g x > g x x ] ),
which has type
f' :: IO ((a > IO (a > IO b)) > IO (a > IO b)),
and is in fact equivalent to
f'' = return $ \g > return $ \x > do h < g x y < h x return y
General lifting functions
decToMonad :: String > Q [Dec] > Q [Dec] Source #
Lift a list of declarations. The first argument is the name of the monad to lift into.
expToMonad :: String > Q Exp > Q Exp Source #
Lift an expression. The first argument is the name of the monad to lift into.
Liftings of specific constants
List operations
template_symb_colon_ :: Monad m => m (a > m ([a] > m [a])) Source #
Lifted version of '(:)' :: a > [a] > [a]
.
template_symb_obracket_symb_cbracket_ :: Monad m => m [a] Source #
Lifted version of '[]' :: [a]
.
template_init :: Monad m => m ([a] > m [a]) Source #
Lifted version of
.init
:: [a] > [a]
template_last :: Monad m => m ([a] > m a) Source #
Lifted version of
.last
:: [a] > [a]
template_symb_plus_symb_plus_ :: Monad m => m ([a] > m ([a] > m [a])) Source #
Lifted version of '(++)' :: [a] > [a] > [a]
.
template_zip3 :: Monad m => m ([a] > m ([b] > m ([c] > m [(a, b, c)]))) Source #
Lifted version of zip3
.
template_foldl :: Monad m => m ((a > m (b > m a)) > m (a > m ([b] > m a))) Source #
lifted version of foldl
template_reverse :: Monad m => m ([a] > m [a]) Source #
lifted version of reverse
template_zipWith :: Monad m => m ((a > m (b > m c)) > m ([a] > m ([b] > m [c]))) Source #
lifted version of zipWith
template_fold_right_zip :: Monad m => m (((a, b, c) > m (a, d)) > m ((a, [b], [c]) > m (a, [d]))) Source #
Lifted version of fold_right_zip
Other operations
template_symb_dollar_ :: Monad m => m ((a > m b) > m (a > m b)) Source #
Lifted version of the combinator $
.
template_error :: Monad m => m (String > m a) Source #
template_snd :: Monad m => m ((a, b) > m b) Source #
Lifted version of snd
:: (a,b) > b
Extended quantum data types
Homogeneous quantum data types
class (QData qa, CType qa ~ ca, BType qa ~ ba) => QShape ba qa ca  ba > qa, qa > ca, ca > ba Source #
The QShape
class allows the definition of generic functions that
can operate on quantum data of any "shape", for example, nested
tuples or lists of qubits.
In general, there are three kinds of data: quantum inputs (such as
Qubit
), classical inputs (such as Bit
), and classical
parameters (such as Bool
). For example, a Qubit
can be
initialized from a Bool
; a Qubit
can be measured, resulting in
a Bit
, etc. For this reason, the type class QShape
establishes a
relation between three types:
qa
 A data structure having
Qubit
at the leaves. ca
 A data structure of the same shape as
qa
, havingBit
at the leaves. ba
 A data structure of the same shape as
qa
, havingBool
at the leaves.
Some functions input a classical parameter for the sole purpose of establishing the "shape" of a piece of data. The shape refers to qualities of a data structure, such as the length of a list, which are not uniquely determined by the type. For example, two different lists of length 5 have the same shape. When performing a generic operation, such as reversing a circuit, it is often necessary to specify the shape of the inputs, but not the actual inputs.
In the common case where one only needs to declare one of the types
qa, ca, or ba, one of the simpler type classes QData
,
CData
, or BData
can be used.
class (qa ~ QType (CType qa), qa ~ QTypeB (BType qa), qa ~ QCType Qubit Bool qa, qa ~ QType qa, QCData qa, QCData (CType qa)) => QData qa Source #
Heterogeneous quantum data types
class (Labelable qc String, Typeable qc, Show qc, Show (LType qc), qc ~ QCType Qubit Bit qc, CType (QType qc) ~ CType qc, BType (CType qc) ~ BType qc, QCType Int Bool (CType qc) ~ BType qc) => QCData qc Source #
The QCData
type class contains heterogeneous data types built
up from leaves of type Qubit
and Bit
. It is the basis for
several generic operations that apply to classical and quantum
data, such as copying, transformers, simulation, and heterogeneous
versions of qterm and qdiscard.
QCData
and QData
are interrelated, in the sense that the
following implications hold:
QData qa implies QCData qa CData ca implies QCData ca
Implications in the converse direction also hold whenever qc is a fixed known type:
QCData qc implies QData (QType qc) QCData qc implies CData (CType qc) QCData qc implies BData (BType qc)
However, the type checker cannot prove the above implication in the
case where qc is a type variable; for this, the more flexible
(but more computationally expensive) QCDataPlus
class can be used.
class (QCData qc, QData (QType qc)) => QCDataPlus qc Source #
The QCDataPlus
type class is almost identical to QCData
,
except that it contains one additional piece of information that
allows the type checker to prove the implications
QCDataPlus qc implies QShape (BType qc) (QType qc) (CType qc) QCDataPlus qc implies QData (QType qc) QCDataPlus qc implies CData (CType qc) QCDataPlus qc implies BData (BType qc)
This is sometimes useful, for example, in the context of a function
that inputs a QCData
, measures all the qubits, and returns a
CData
. However, the additional information for the type checker
comes at a price, which is drastically increased compilation time.
Therefore QCDataPlus
should only be used when QCData
is
insufficient.
Shaperelated operations
Some Quipper functions, such as print_generic
, require a
shape parameter. A shape parameter is a parameter passed to a
function for the sole purpose of specifying the type or size of
some data structure, without actually specifying any data.
Example: given a circuit
circuit :: ([Qubit], Bit) > Circ Qubit,
the command
print_generic Preview circuit ([qubit,qubit,qubit], bit)
tells Quipper to preview the circuit for a problem size of 3 qubits and 1 bit.
A dummy term of type Bit
. It can be used in shape parameters
(e.g., qc_init
), as well as shape type parameters (e.g.,
qcdata_mapM
).
A dummy term of type Qubit
. It can be used in shape parameters
(e.g., qc_init
), as well as shape type parameters (e.g.,
qcdata_mapM
).
qshape :: QData qa => BType qa > qa Source #
Return a quantum data structure of the given boolean shape, with
every leaf initialized to the undefined dummy value qubit
.
qc_false :: QCData qc => qc > BType qc Source #
Return a boolean data structure of the given shape, with every
leaf initialized to False
.
Quantum type classes
Haskell provides many convenient type classes: Eq
, Ord
, Num
, etc.
Quipper provides quantum analogues of some of these.
For instance, Haskell’s
has the methodEq
a
(==) :: a > a > Bool.
Correspondingly, our
has a methodQEq
a qa ca
q_is_equal :: qa > qa > Circ (qa,qa,Qubit).
Similarly, where Haskell’s Num
class has methods +
, *
, signum
,
the class QNum
has q_add
, q_mult
, q_signum
, and so on.
(QNum
is defined in QuipperLib.Arith.)
All quantum type classes assume (a) that their instance types are
QCData
, and (b) that the corresponding classical parameter types
are instances of the corresponding Haskell type classes.
Quantum type classes are designed to work well with the automatic circuit generation of Quipper.CircLifting: the methods of Haskell’s standard type classes are translated into their quantum analogues, where available.
class QCData qc => QEq qc where Source #
This is a quantum analogue of Haskell’s Eq
type class. Default
implementations are provided; by default, equality is bitwise
equality of the underlying data structure. However, specific
instances can provide custom implementations. In this case,
q_is_equal
is a minimal complete definition.
q_is_equal :: qc > qc > Circ (qc, qc, Qubit) Source #
Test for equality.
q_is_not_equal :: qc > qc > Circ (qc, qc, Qubit) Source #
Test for inequality.
class (QEq qa, QData qa) => QOrd qa where Source #
This is a quantum analogue of Haskell's Ord
type class. Its
purpose is to define a total ordering on each of its instances. The
functions in this class are assumed dirty in the sense that they do
not uncompute ancillas, and some of the inputs may be returned as
outputs. The functions are also assumed to be nonlinear safe,
i.e., they apply no gates to their inputs except as control
sources. Minimal complete definition: q_less
or q_greater
. The default
implementations of q_max
and q_min
assume that both arguments
are of the same shape (for example, numbers of the same length).
q_less :: qa > qa > Circ Qubit Source #
Test for less than.
q_greater :: qa > qa > Circ Qubit Source #
Test for greater than.
q_leq :: qa > qa > Circ Qubit Source #
Test for less than or equal.
q_geq :: qa > qa > Circ Qubit Source #
Test for greater than or equal.
q_max :: qa > qa > Circ qa Source #
Compute the maximum of two values.
q_min :: qa > qa > Circ qa Source #
Compute the minimum of two values.