ops

The operations collection consists of various default gates and is a work-in-progress, as users start to work with ProjectQ.

projectq.ops.BasicGate()	Base class of all gates.
projectq.ops.SelfInverseGate()	Self-inverse basic gate class.
projectq.ops.BasicRotationGate(angle)	Defines a base class of a rotation gate.
projectq.ops.BasicPhaseGate(angle)	Defines a base class of a phase gate.
projectq.ops.ClassicalInstructionGate()	Classical instruction gate.
projectq.ops.FastForwardingGate()	Base class for classical instruction gates which require a fast-forward through compiler engines that cache / buffer gates.
projectq.ops.BasicMathGate(math_fun)	Base class for all math gates.
projectq.ops.apply_command(cmd)	Apply a command.
projectq.ops.Command(engine, gate, qubits[, …])	Class used as a container to store commands.
projectq.ops.H	Shortcut (instance of) projectq.ops.HGate
projectq.ops.X	Shortcut (instance of) projectq.ops.XGate
projectq.ops.Y	Shortcut (instance of) projectq.ops.YGate
projectq.ops.Z	Shortcut (instance of) projectq.ops.ZGate
projectq.ops.S	Shortcut (instance of) projectq.ops.SGate
projectq.ops.Sdag	Wrapper class allowing to execute the inverse of a gate, even when it does not define one.
projectq.ops.T	Shortcut (instance of) projectq.ops.TGate
projectq.ops.Tdag	Wrapper class allowing to execute the inverse of a gate, even when it does not define one.
projectq.ops.SqrtX	Shortcut (instance of) projectq.ops.SqrtXGate
projectq.ops.Swap	Shortcut (instance of) projectq.ops.SwapGate
projectq.ops.SqrtSwap	Shortcut (instance of) projectq.ops.SqrtSwapGate
projectq.ops.Entangle	Shortcut (instance of) projectq.ops.EntangleGate
projectq.ops.Ph(angle)	Phase gate (global phase)
projectq.ops.Rx(angle)	RotationX gate class
projectq.ops.Ry(angle)	RotationX gate class
projectq.ops.Rz(angle)	RotationZ gate class
projectq.ops.R(angle)	Phase-shift gate (equivalent to Rz up to a global phase)
projectq.ops.FlushGate()	Flush gate (denotes the end of the circuit).
projectq.ops.MeasureGate()	Measurement gate class (for single qubits).
projectq.ops.Allocate	Shortcut (instance of) projectq.ops.AllocateQubitGate
projectq.ops.Deallocate	Shortcut (instance of) projectq.ops.DeallocateQubitGate
projectq.ops.AllocateDirty	Shortcut (instance of) projectq.ops.AllocateDirtyQubitGate
projectq.ops.Barrier	Shortcut (instance of) projectq.ops.BarrierGate
projectq.ops.DaggeredGate(gate)	Wrapper class allowing to execute the inverse of a gate, even when it does not define one.
projectq.ops.ControlledGate(gate[, n])	Controlled version of a gate.
projectq.ops.C(gate[, n])	Return n-controlled version of the provided gate.
projectq.ops.All	Shortcut (instance of) projectq.ops.Tensor
projectq.ops.Tensor(gate)	Wrapper class allowing to apply a (single-qubit) gate to every qubit in a quantum register.
projectq.ops.QFT	Shortcut (instance of) projectq.ops.QFTGate
projectq.ops.QubitOperator([term, coefficient])	A sum of terms acting on qubits, e.g., 0.5 * ‘X0 X5’ + 0.3 * ‘Z1 Z2’.
projectq.ops.CRz(angle)	Shortcut for C(Rz(angle), n=1).
projectq.ops.CNOT	Controlled version of a gate.
projectq.ops.CZ	Controlled version of a gate.
projectq.ops.Toffoli	Controlled version of a gate.
projectq.ops.TimeEvolution(time, hamiltonian)	Gate for time evolution under a Hamiltonian (QubitOperator object).
projectq.ops.UniformlyControlledRy(angles)	Uniformly controlled Ry gate as introduced in arXiv:quant-ph/0312218.
projectq.ops.UniformlyControlledRz(angles)	Uniformly controlled Rz gate as introduced in arXiv:quant-ph/0312218.
projectq.ops.StatePreparation(final_state)	Gate for transforming qubits in state |0> to any desired quantum state.

Module contents

projectq.ops.All

Shortcut (instance of) projectq.ops.Tensor

alias of projectq.ops._metagates.Tensor

class projectq.ops.AllocateDirtyQubitGate

Dirty qubit allocation gate class

get_inverse()

Return the inverse gate.

Standard implementation of get_inverse:

Raises:NotInvertible – inverse is not implemented

class projectq.ops.AllocateQubitGate

Qubit allocation gate class

get_inverse()

Return the inverse gate.

Standard implementation of get_inverse:

Raises:NotInvertible – inverse is not implemented

class projectq.ops.BarrierGate

Barrier gate class

get_inverse()

Return the inverse gate.

Standard implementation of get_inverse:

Raises:NotInvertible – inverse is not implemented

class projectq.ops.BasicGate

Base class of all gates.

__init__()

Initialize a basic gate.

Note

Set interchangeable qubit indices! (gate.interchangeable_qubit_indices)

As an example, consider

ExampleGate | (a,b,c,d,e)

where a and b are interchangeable. Then, call this function as follows:

self.set_interchangeable_qubit_indices([[0,1]])

As another example, consider

ExampleGate2 | (a,b,c,d,e)

where a and b are interchangeable and, in addition, c, d, and e are interchangeable among themselves. Then, call this function as

self.set_interchangeable_qubit_indices([[0,1],[2,3,4]])

__or__(qubits)

Operator| overload which enables the syntax Gate | qubits.

Example

1. Gate | qubit
2. Gate | [qubit0, qubit1]
3. Gate | qureg
4. Gate | (qubit, )
5. Gate | (qureg, qubit)

Parameters:qubits – a Qubit object, a list of Qubit objects, a Qureg object, or a tuple of Qubit or Qureg objects (can be mixed).

generate_command(qubits)

Helper function to generate a command consisting of the gate and the qubits being acted upon.

Parameters:qubits – see BasicGate.make_tuple_of_qureg(qubits) Returns:A Command object containing the gate and the qubits.

get_inverse()

Return the inverse gate.

Standard implementation of get_inverse:

Raises:NotInvertible – inverse is not implemented

get_merged(other)

Return this gate merged with another gate.

Standard implementation of get_merged:

Raises:NotMergeable – merging is not implemented

static make_tuple_of_qureg(qubits)

Convert quantum input of “gate | quantum input” to internal formatting.

A Command object only accepts tuples of Quregs (list of Qubit objects) as qubits input parameter. However, with this function we allow the user to use a more flexible syntax:

1. Gate | qubit
2. Gate | [qubit0, qubit1]
3. Gate | qureg
4. Gate | (qubit, )
5. Gate | (qureg, qubit)

where qubit is a Qubit object and qureg is a Qureg object. This function takes the right hand side of | and transforms it to the correct input parameter of a Command object which is:

1. -> Gate | ([qubit], )
2. -> Gate | ([qubit0, qubit1], )
3. -> Gate | (qureg, )
4. -> Gate | ([qubit], )
5. -> Gate | (qureg, [qubit])

Parameters:qubits – a Qubit object, a list of Qubit objects, a Qureg object, or a tuple of Qubit or Qureg objects (can be mixed). Returns:A tuple containing Qureg (or list of Qubits) objects. Return type:Canonical representation (tuple<qureg>)

class projectq.ops.BasicMathGate(math_fun)

Base class for all math gates.

It allows efficient emulation by providing a mathematical representation which is given by the concrete gate which derives from this base class. The AddConstant gate, for example, registers a function of the form

def add(x):
    return (x+a,)

upon initialization. More generally, the function takes integers as parameters and returns a tuple / list of outputs, each entry corresponding to the function input. As an example, consider out-of-place multiplication, which takes two input registers and adds the result into a third, i.e., (a,b,c) -> (a,b,c+a*b). The corresponding function then is

def multiply(a,b,c)
    return (a,b,c+a*b)

__init__(math_fun)

Initialize a BasicMathGate by providing the mathematical function that it implements.

Parameters:math_fun (function) – Function which takes as many int values as input, as the gate takes registers. For each of these values, it then returns the output (i.e., it returns a list/tuple of output values).

Example

def add(a,b):
    return (a,a+b)
BasicMathGate.__init__(self, add)

If the gate acts on, e.g., fixed point numbers, the number of bits per register is also required in order to describe the action of such a mathematical gate. For this reason, there is

BasicMathGate.get_math_function(qubits)

which can be overwritten by the gate deriving from BasicMathGate.

Example

def get_math_function(self, qubits):
    n = len(qubits[0])
    scal = 2.**n
    def math_fun(a):
        return (int(scal * (math.sin(math.pi * a / scal))),)
    return math_fun

get_math_function(qubits)

Return the math function which corresponds to the action of this math gate, given the input to the gate (a tuple of quantum registers).

Parameters:qubits (tuple<Qureg>) – Qubits to which the math gate is being applied. Returns:Python function describing the action of this gate. (See BasicMathGate.__init__ for an example). Return type:math_fun (function)

class projectq.ops.BasicPhaseGate(angle)

Defines a base class of a phase gate.

A phase gate has a continuous parameter (the angle), labeled ‘angle’ / self.angle. Its inverse is the same gate with the negated argument. Phase gates of the same class can be merged by adding the angles. The continuous parameter is modulo 2 * pi, self.angle is in the interval [0, 2 * pi).

__init__(angle)

Initialize a basic rotation gate.

Parameters:angle (float) – Angle of rotation (saved modulo 2 * pi)

get_inverse()

Return the inverse of this rotation gate (negate the angle, return new object).

get_merged(other)

Return self merged with another gate.

Default implementation handles rotation gate of the same type, where angles are simply added.

Parameters:other – Rotation gate of same type. Raises:NotMergeable – For non-rotation gates or rotation gates of different type. Returns:New object representing the merged gates.

tex_str()

Return the Latex string representation of a BasicPhaseGate.

Returns the class name and the angle as a subscript, i.e.

[CLASSNAME]$_[ANGLE]$

class projectq.ops.BasicQubit(engine, idx)

BasicQubit objects represent qubits.

They have an id and a reference to the owning engine.

__init__(engine, idx)

Initialize a BasicQubit object.

Parameters:

• engine – Owning engine / engine that created the qubit
• idx – Unique index of the qubit referenced by this qubit

class projectq.ops.BasicRotationGate(angle)

Defines a base class of a rotation gate.

A rotation gate has a continuous parameter (the angle), labeled ‘angle’ / self.angle. Its inverse is the same gate with the negated argument. Rotation gates of the same class can be merged by adding the angles. The continuous parameter is modulo 4 * pi, self.angle is in the interval [0, 4 * pi).

__init__(angle)

Initialize a basic rotation gate.

Parameters:angle (float) – Angle of rotation (saved modulo 4 * pi)

get_inverse()

Return the inverse of this rotation gate (negate the angle, return new object).

get_merged(other)

Return self merged with another gate.

Default implementation handles rotation gate of the same type, where angles are simply added.

Parameters:other – Rotation gate of same type. Raises:NotMergeable – For non-rotation gates or rotation gates of different type. Returns:New object representing the merged gates.

tex_str()

Return the Latex string representation of a BasicRotationGate.

Returns the class name and the angle as a subscript, i.e.

[CLASSNAME]$_[ANGLE]$

projectq.ops.C(gate, n=1)

Return n-controlled version of the provided gate.

Parameters:

• gate – Gate to turn into its controlled version
• n – Number of controls (default: 1)

Example

C(NOT) | (c, q) # equivalent to CNOT | (c, q)

projectq.ops.CRz(angle)

Shortcut for C(Rz(angle), n=1).

class projectq.ops.ClassicalInstructionGate

Classical instruction gate.

Base class for all gates which are not quantum gates in the typical sense, e.g., measurement, allocation/deallocation, …

class projectq.ops.Command(engine, gate, qubits, controls=(), tags=())

Class used as a container to store commands. If a gate is applied to qubits, then the gate and qubits are saved in a command object. Qubits are copied into WeakQubitRefs in order to allow early deallocation (would be kept alive otherwise). WeakQubitRef qubits don’t send deallocate gate when destructed.

gate

The gate to execute

qubits

Tuple of qubit lists (e.g. Quregs). Interchangeable qubits are stored in a unique order

control_qubits

The Qureg of control qubits in a unique order

engine

The engine (usually: MainEngine)

tags

The list of tag objects associated with this command (e.g., ComputeTag, UncomputeTag, LoopTag, …). tag objects need to support ==, != (__eq__ and __ne__) for comparison as used in e.g. TagRemover. New tags should always be added to the end of the list. This means that if there are e.g. two LoopTags in a command, tag[0] is from the inner scope while tag[1] is from the other scope as the other scope receives the command after the inner scope LoopEngine and hence adds its LoopTag to the end.

all_qubits

A tuple of control_qubits + qubits

__init__(engine, gate, qubits, controls=(), tags=())

Initialize a Command object.

Note

control qubits (Command.control_qubits) are stored as a list of qubits, and command tags (Command.tags) as a list of tag- objects. All functions within this class also work if WeakQubitRefs are supplied instead of normal Qubit objects (see WeakQubitRef).

Parameters:

• engine (projectq.cengines.BasicEngine) – engine which created the qubit (mostly the MainEngine)
• gate (projectq.ops.Gate) – Gate to be executed
• qubits (tuple[Qureg]) – Tuple of quantum registers (to which the gate is applied)
• controls (Qureg|list[Qubit]) – Qubits that condition the command.
• tags (list[object]) – Tags associated with the command.

add_control_qubits(qubits)

Add (additional) control qubits to this command object.

They are sorted to ensure a canonical order. Also Qubit objects are converted to WeakQubitRef objects to allow garbage collection and thus early deallocation of qubits.

Parameters:qubits (list of Qubit objects) – List of qubits which control this gate, i.e., the gate is only executed if all qubits are in state 1.

all_qubits

Get all qubits (gate and control qubits).

Returns a tuple T where T[0] is a quantum register (a list of WeakQubitRef objects) containing the control qubits and T[1:] contains the quantum registers to which the gate is applied.

control_qubits

Returns Qureg of control qubits.

engine

Return engine to which the qubits belong / on which the gates are executed.

get_inverse()

Get the command object corresponding to the inverse of this command.

Inverts the gate (if possible) and creates a new command object from the result.

Raises:NotInvertible – If the gate does not provide an inverse (see BasicGate.get_inverse)

get_merged(other)

Merge this command with another one and return the merged command object.

Parameters:other – Other command to merge with this one (self) Raises:NotMergeable – if the gates don’t supply a get_merged()-function or can’t be merged for other reasons.

interchangeable_qubit_indices

Return nested list of qubit indices which are interchangeable.

Certain qubits can be interchanged (e.g., the qubit order for a Swap gate). To ensure that only those are sorted when determining the ordering (see _order_qubits), self.interchangeable_qubit_indices is used. .. rubric:: Example

If we can interchange qubits 0,1 and qubits 3,4,5, then this function returns [[0,1],[3,4,5]]

class projectq.ops.ControlledGate(gate, n=1)

Controlled version of a gate.

Note

Use the meta function C() to create a controlled gate

A wrapper class which enables (multi-) controlled gates. It overloads the __or__-operator, using the first qubits provided as control qubits. The n control-qubits need to be the first n qubits. They can be in separate quregs.

Example

ControlledGate(gate, 2) | (qb0, qb2, qb3) # qb0 & qb2 are controls
C(gate, 2) | (qb0, qb2, qb3) # This is much nicer.
C(gate, 2) | ([qb0,qb2], qb3) # Is equivalent

Note

Use C() rather than ControlledGate, i.e.,

C(X, 2) == Toffoli

__init__(gate, n=1)

Initialize a ControlledGate object.

Parameters:

• gate – Gate to wrap.
• n (int) – Number of control qubits.

__or__(qubits)

Apply the controlled gate to qubits, using the first n qubits as controls.

Note: The control qubits can be split across the first quregs.

However, the n-th control qubit needs to be the last qubit in a qureg. The following quregs belong to the gate.

Parameters:qubits (tuple of lists of Qubit objects) – qubits to which to apply the gate.

get_inverse()

Return inverse of a controlled gate, which is the controlled inverse gate.

class projectq.ops.DaggeredGate(gate)

Wrapper class allowing to execute the inverse of a gate, even when it does not define one.

If there is a replacement available, then there is also one for the inverse, namely the replacement function run in reverse, while inverting all gates. This class enables using this emulation automatically.

A DaggeredGate is returned automatically when employing the get_inverse- function on a gate which does not provide a get_inverse() member function.

Example

with Dagger(eng):
    MySpecialGate | qubits

will create a DaggeredGate if MySpecialGate does not implement get_inverse. If there is a decomposition function available, an auto- replacer engine can automatically replace the inverted gate by a call to the decomposition function inside a “with Dagger”-statement.

__init__(gate)

Initialize a DaggeredGate representing the inverse of the gate ‘gate’.

Parameters:gate – Any gate object of which to represent the inverse.

get_inverse()

Return the inverse gate (the inverse of the inverse of a gate is the gate itself).

tex_str()

Return the Latex string representation of a Daggered gate.

class projectq.ops.DeallocateQubitGate

Qubit deallocation gate class

get_inverse()

Return the inverse gate.

Standard implementation of get_inverse:

Raises:NotInvertible – inverse is not implemented

class projectq.ops.EntangleGate

Entangle gate (Hadamard on first qubit, followed by CNOTs applied to all other qubits).

class projectq.ops.FastForwardingGate

Base class for classical instruction gates which require a fast-forward through compiler engines that cache / buffer gates. Examples include Measure and Deallocate, which both should be executed asap, such that Measurement results are available and resources are freed, respectively.

Note

The only requirement is that FlushGate commands run the entire circuit. FastForwardingGate objects can be used but the user cannot expect a measurement result to be available for all back-ends when calling only Measure. E.g., for the IBM Quantum Experience back-end, sending the circuit for each Measure-gate would be too inefficient, which is why a final

is required before the circuit gets sent through the API.

class projectq.ops.FlushGate

Flush gate (denotes the end of the circuit).

Note

All compiler engines (cengines) which cache/buffer gates are obligated to flush and send all gates to the next compiler engine (followed by the flush command).

Note

This gate is sent when calling

eng.flush()

on the MainEngine eng.

class projectq.ops.HGate

Hadamard gate class

class projectq.ops.MeasureGate

Measurement gate class (for single qubits).

__or__(qubits)

Previously (ProjectQ <= v0.3.6) MeasureGate/Measure was allowed to be applied to any number of quantum registers. Now the MeasureGate/Measure is strictly a single qubit gate. In the coming releases the backward compatibility will be removed!

exception projectq.ops.NotInvertible

Exception thrown when trying to invert a gate which is not invertable (or where the inverse is not implemented (yet)).

exception projectq.ops.NotMergeable

Exception thrown when trying to merge two gates which are not mergeable (or where it is not implemented (yet)).

class projectq.ops.Ph(angle)

Phase gate (global phase)

class projectq.ops.QFTGate

Quantum Fourier Transform gate.

class projectq.ops.QubitOperator(term=None, coefficient=1.0)

A sum of terms acting on qubits, e.g., 0.5 * ‘X0 X5’ + 0.3 * ‘Z1 Z2’.

A term is an operator acting on n qubits and can be represented as:

coefficent * local_operator[0] x … x local_operator[n-1]

where x is the tensor product. A local operator is a Pauli operator (‘I’, ‘X’, ‘Y’, or ‘Z’) which acts on one qubit. In math notation a term is, for example, 0.5 * ‘X0 X5’, which means that a Pauli X operator acts on qubit 0 and 5, while the identity operator acts on all other qubits.

A QubitOperator represents a sum of terms acting on qubits and overloads operations for easy manipulation of these objects by the user.

Note for a QubitOperator to be a Hamiltonian which is a hermitian operator, the coefficients of all terms must be real.

hamiltonian = 0.5 * QubitOperator('X0 X5') + 0.3 * QubitOperator('Z0')

Our Simulator takes a hermitian QubitOperator to directly calculate the expectation value (see Simulator.get_expectation_value) of this observable.

A hermitian QubitOperator can also be used as input for the TimeEvolution gate.

If the QubitOperator is unitary, i.e., it contains only one term with a coefficient, whose absolute value is 1, then one can apply it directly to qubits:

eng = projectq.MainEngine()
qureg = eng.allocate_qureg(6)
QubitOperator('X0 X5', 1.j) | qureg  # Applies X to qubit 0 and 5
                                     # with an additional global phase
                                     # of 1.j

terms

dict – key: A term represented by a tuple containing all non-trivial local Pauli operators (‘X’, ‘Y’, or ‘Z’). A non-trivial local Pauli operator is specified by a tuple with the first element being an integer indicating the qubit on which a non-trivial local operator acts and the second element being a string, either ‘X’, ‘Y’, or ‘Z’, indicating which non-trivial Pauli operator acts on that qubit. Examples: ((1, ‘X’),) or ((1, ‘X’), (4,’Z’)) or the identity (). The tuples representing the non-trivial local terms are sorted according to the qubit number they act on, starting from 0. value: Coefficient of this term as a (complex) float

__init__(term=None, coefficient=1.0)

Inits a QubitOperator.

The init function only allows to initialize one term. Additional terms have to be added using += (which is fast) or using + of two QubitOperator objects:

Example

ham = ((QubitOperator('X0 Y3', 0.5)
        + 0.6 * QubitOperator('X0 Y3')))
# Equivalently
ham2 = QubitOperator('X0 Y3', 0.5)
ham2 += 0.6 * QubitOperator('X0 Y3')

Note

Adding terms to QubitOperator is faster using += (as this is done by in-place addition). Specifying the coefficient in the __init__ is faster than by multiplying a QubitOperator with a scalar as calls an out-of-place multiplication.

Parameters:

• coefficient (complex float, optional) – The coefficient of the first term of this QubitOperator. Default is 1.0.
• term (optional, empy tuple, a tuple of tuples, or a string) –
  1. Default is None which means there are no terms in the QubitOperator hence it is the “zero” Operator
  2. An empty tuple means there are no non-trivial Pauli operators acting on the qubits hence only identities with a coefficient (which by default is 1.0).
  3. A sorted tuple of tuples. The first element of each tuple is an integer indicating the qubit on which a non-trivial local operator acts, starting from zero. The second element of each tuple is a string, either ‘X’, ‘Y’ or ‘Z’, indicating which local operator acts on that qubit.
  4. A string of the form ‘X0 Z2 Y5’, indicating an X on qubit 0, Z on qubit 2, and Y on qubit 5. The string should be sorted by the qubit number. ‘’ is the identity.

Raises:

QubitOperatorError – Invalid operators provided to QubitOperator.

__or__(qubits)

Operator| overload which enables the following syntax:

QubitOperator(...) | qureg
QubitOperator(...) | (qureg,)
QubitOperator(...) | qubit
QubitOperator(...) | (qubit,)

Unlike other gates, this gate is only allowed to be applied to one quantum register or one qubit and only if the QubitOperator is unitary, i.e., consists of one term with a coefficient whose absolute values is 1.

Example:

eng = projectq.MainEngine()
qureg = eng.allocate_qureg(6)
QubitOperator('X0 X5', 1.j) | qureg  # Applies X to qubit 0 and 5
                                     # with an additional global
                                     # phase of 1.j

While in the above example the QubitOperator gate is applied to 6 qubits, it only acts non-trivially on the two qubits qureg[0] and qureg[5]. Therefore, the operator| will create a new rescaled QubitOperator, i.e, it sends the equivalent of the following new gate to the MainEngine:

QubitOperator('X0 X1', 1.j) | [qureg[0], qureg[5]]

which is only a two qubit gate.

Parameters:

qubits – one Qubit object, one list of Qubit objects, one Qureg object, or a tuple of the former three cases.

Raises:

• TypeError – If QubitOperator is not unitary or applied to more than one quantum register.
• ValueError – If quantum register does not have enough qubits

compress(abs_tol=1e-12)

Eliminates all terms with coefficients close to zero and removes imaginary parts of coefficients that are close to zero.

Parameters:abs_tol (float) – Absolute tolerance, must be at least 0.0

get_inverse()

Return the inverse gate of a QubitOperator if applied as a gate.

Raises:NotInvertible – Not implemented for QubitOperators which have multiple terms or a coefficient with absolute value not equal to 1.

get_merged(other)

Return this gate merged with another gate.

Standard implementation of get_merged:

Raises:NotMergeable – merging is not possible

isclose(other, rel_tol=1e-12, abs_tol=1e-12)

Returns True if other (QubitOperator) is close to self.

Comparison is done for each term individually. Return True if the difference between each term in self and other is less than the relative tolerance w.r.t. either other or self (symmetric test) or if the difference is less than the absolute tolerance.

Parameters:

• other (QubitOperator) – QubitOperator to compare against.
• rel_tol (float) – Relative tolerance, must be greater than 0.0
• abs_tol (float) – Absolute tolerance, must be at least 0.0

class projectq.ops.R(angle)

Phase-shift gate (equivalent to Rz up to a global phase)

class projectq.ops.Rx(angle)

RotationX gate class

class projectq.ops.Ry(angle)

RotationX gate class

class projectq.ops.Rz(angle)

RotationZ gate class

class projectq.ops.SGate

S gate class

class projectq.ops.SelfInverseGate

Self-inverse basic gate class.

Automatic implementation of the get_inverse-member function for self- inverse gates.

Example

# get_inverse(H) == H, it is a self-inverse gate:
get_inverse(H) | qubit

get_inverse()

Return the inverse gate.

Standard implementation of get_inverse:

Raises:NotInvertible – inverse is not implemented

class projectq.ops.SqrtSwapGate

Square-root Swap gate class

__init__()

Initialize a basic gate.

Note

Set interchangeable qubit indices! (gate.interchangeable_qubit_indices)

As an example, consider

ExampleGate | (a,b,c,d,e)

where a and b are interchangeable. Then, call this function as follows:

self.set_interchangeable_qubit_indices([[0,1]])

As another example, consider

ExampleGate2 | (a,b,c,d,e)

where a and b are interchangeable and, in addition, c, d, and e are interchangeable among themselves. Then, call this function as

self.set_interchangeable_qubit_indices([[0,1],[2,3,4]])

class projectq.ops.SqrtXGate

Square-root X gate class

class projectq.ops.StatePreparation(final_state)

Gate for transforming qubits in state |0> to any desired quantum state.

__init__(final_state)

Initialize StatePreparation gate.

Example

qureg = eng.allocate_qureg(2)
StatePreparation([0.5, -0.5j, -0.5, 0.5]) | qureg

Note

The amplitude of state k is final_state[k]. When the state k is written in binary notation, then qureg[0] denotes the qubit whose state corresponds to the least significant bit of k.

Parameters:final_state (list[complex]) – wavefunction of the desired quantum state. len(final_state) must be 2**len(qureg). Must be normalized!

class projectq.ops.SwapGate

Swap gate class (swaps 2 qubits)

__init__()

Initialize a basic gate.

Note

Set interchangeable qubit indices! (gate.interchangeable_qubit_indices)

As an example, consider

ExampleGate | (a,b,c,d,e)

where a and b are interchangeable. Then, call this function as follows:

self.set_interchangeable_qubit_indices([[0,1]])

As another example, consider

ExampleGate2 | (a,b,c,d,e)

where a and b are interchangeable and, in addition, c, d, and e are interchangeable among themselves. Then, call this function as

self.set_interchangeable_qubit_indices([[0,1],[2,3,4]])

class projectq.ops.TGate

T gate class

class projectq.ops.Tensor(gate)

Wrapper class allowing to apply a (single-qubit) gate to every qubit in a quantum register. Allowed syntax is to supply either a qureg or a tuple which contains only one qureg.

Example

Tensor(H) | x # applies H to every qubit in the list of qubits x
Tensor(H) | (x,) # alternative to be consistent with other syntax

__init__(gate)

Initialize a Tensor object for the gate.

__or__(qubits)

Applies the gate to every qubit in the quantum register qubits.

get_inverse()

Return the inverse of this tensored gate (which is the tensored inverse of the gate).

class projectq.ops.TimeEvolution(time, hamiltonian)

Gate for time evolution under a Hamiltonian (QubitOperator object).

This gate is the unitary time evolution propagator: exp(-i * H * t), where H is the Hamiltonian of the system and t is the time. Note that -i factor is stored implicitely.

Example

wavefunction = eng.allocate_qureg(5)
hamiltonian = 0.5 * QubitOperator("X0 Z1 Y5")
# Apply exp(-i * H * t) to the wavefunction:
TimeEvolution(time=2.0, hamiltonian=hamiltonian) | wavefunction

time

float, int – time t

hamiltonian

QubitOperator – hamiltonaian H

__init__(time, hamiltonian)

Initialize time evolution gate.

Note

The hamiltonian must be hermitian and therefore only terms with real coefficients are allowed. Coefficients are internally converted to float.

Parameters:

• time (float, or int) – time to evolve under (can be negative).
• hamiltonian (QubitOperator) – hamiltonian to evolve under.

Raises:

• TypeError – If time is not a numeric type and hamiltonian is not a QubitOperator.
• NotHermitianOperatorError – If the input hamiltonian is not hermitian (only real coefficients).

__or__(qubits)

Operator| overload which enables the following syntax:

TimeEvolution(...) | qureg
TimeEvolution(...) | (qureg,)
TimeEvolution(...) | qubit
TimeEvolution(...) | (qubit,)

Unlike other gates, this gate is only allowed to be applied to one quantum register or one qubit.

Example:

wavefunction = eng.allocate_qureg(5)
hamiltonian = QubitOperator("X1 Y3", 0.5)
TimeEvolution(time=2.0, hamiltonian=hamiltonian) | wavefunction

While in the above example the TimeEvolution gate is applied to 5 qubits, the hamiltonian of this TimeEvolution gate acts only non-trivially on the two qubits wavefunction[1] and wavefunction[3]. Therefore, the operator| will rescale the indices in the hamiltonian and sends the equivalent of the following new gate to the MainEngine:

h = QubitOperator("X0 Y1", 0.5)
TimeEvolution(2.0, h) | [wavefunction[1], wavefunction[3]]

which is only a two qubit gate.

Parameters:qubits – one Qubit object, one list of Qubit objects, one Qureg object, or a tuple of the former three cases.

get_inverse()

Return the inverse gate.

get_merged(other)

Return self merged with another TimeEvolution gate if possible.

Two TimeEvolution gates are merged if:

1. both have the same terms
2. the proportionality factor for each of the terms must have relative error <= 1e-9 compared to the proportionality factors of the other terms.

Note

While one could merge gates for which both hamiltonians commute, we are not doing this as in general the resulting gate would have to be decomposed again.

Note

We are not comparing if terms are proportional to each other with an absolute tolerance. It is up to the user to remove terms close to zero because we cannot choose a suitable absolute error which works for everyone. Use, e.g., a decomposition rule for that.

Parameters:other – TimeEvolution gate Raises:NotMergeable – If the other gate is not a TimeEvolution gate or hamiltonians are not suitable for merging. Returns:New TimeEvolution gate equivalent to the two merged gates.

class projectq.ops.UniformlyControlledRy(angles)

Uniformly controlled Ry gate as introduced in arXiv:quant-ph/0312218.

This is an n-qubit gate. There are n-1 control qubits and one target qubit. This gate applies Ry(angles(k)) to the target qubit if the n-1 control qubits are in the classical state k. As there are 2^(n-1) classical states for the control qubits, this gate requires 2^(n-1) (potentially different) angle parameters.

Example

controls = eng.allocate_qureg(2) target = eng.allocate_qubit() UniformlyControlledRy(angles=[0.1, 0.2, 0.3, 0.4]) | (controls, target)

Note

The first quantum register contains the control qubits. When converting the classical state k of the control qubits to an integer, we define controls[0] to be the least significant (qu)bit. controls can also be an empty list in which case the gate corresponds to an Ry.

Parameters:angles (list[float]) – Rotation angles. Ry(angles[k]) is applied conditioned on the control qubits being in state k.

__init__(angles)

Initialize a basic gate.

Note

Set interchangeable qubit indices! (gate.interchangeable_qubit_indices)

As an example, consider

ExampleGate | (a,b,c,d,e)

where a and b are interchangeable. Then, call this function as follows:

self.set_interchangeable_qubit_indices([[0,1]])

As another example, consider

ExampleGate2 | (a,b,c,d,e)

where a and b are interchangeable and, in addition, c, d, and e are interchangeable among themselves. Then, call this function as

self.set_interchangeable_qubit_indices([[0,1],[2,3,4]])

get_inverse()

Return the inverse gate.

Standard implementation of get_inverse:

Raises:NotInvertible – inverse is not implemented

get_merged(other)

Return this gate merged with another gate.

Standard implementation of get_merged:

Raises:NotMergeable – merging is not implemented

class projectq.ops.UniformlyControlledRz(angles)

Uniformly controlled Rz gate as introduced in arXiv:quant-ph/0312218.

This is an n-qubit gate. There are n-1 control qubits and one target qubit. This gate applies Rz(angles(k)) to the target qubit if the n-1 control qubits are in the classical state k. As there are 2^(n-1) classical states for the control qubits, this gate requires 2^(n-1) (potentially different) angle parameters.

Example

controls = eng.allocate_qureg(2) target = eng.allocate_qubit() UniformlyControlledRz(angles=[0.1, 0.2, 0.3, 0.4]) | (controls, target)

Note

The first quantum register are the contains qubits. When converting the classical state k of the control qubits to an integer, we define controls[0] to be the least significant (qu)bit. controls can also be an empty list in which case the gate corresponds to an Rz.

Parameters:angles (list[float]) – Rotation angles. Rz(angles[k]) is applied conditioned on the control qubits being in state k.

__init__(angles)

Initialize a basic gate.

Note

Set interchangeable qubit indices! (gate.interchangeable_qubit_indices)

As an example, consider

ExampleGate | (a,b,c,d,e)

where a and b are interchangeable. Then, call this function as follows:

self.set_interchangeable_qubit_indices([[0,1]])

As another example, consider

ExampleGate2 | (a,b,c,d,e)

where a and b are interchangeable and, in addition, c, d, and e are interchangeable among themselves. Then, call this function as

self.set_interchangeable_qubit_indices([[0,1],[2,3,4]])

get_inverse()

Return the inverse gate.

Standard implementation of get_inverse:

Raises:NotInvertible – inverse is not implemented

get_merged(other)

Return this gate merged with another gate.

Standard implementation of get_merged:

Raises:NotMergeable – merging is not implemented

class projectq.ops.XGate

Pauli-X gate class

class projectq.ops.YGate

Pauli-Y gate class

class projectq.ops.ZGate

Pauli-Z gate class

projectq.ops.apply_command(cmd)

Apply a command.

Extracts the qubits-owning (target) engine from the Command object and sends the Command to it.

Parameters:cmd (Command) – Command to apply

projectq.ops.get_inverse(gate)

Return the inverse of a gate.

Tries to call gate.get_inverse and, upon failure, creates a DaggeredGate instead.

Parameters:gate – Gate of which to get the inverse

Example

get_inverse(H) # returns a Hadamard gate (HGate object)