Circuit

Circuit class used for the simulations.

The circuit is defined as a list of layers, and each layer is a list of Instructions, i.e. a list [QCOperation, sites]. This structure ensures a simplified analysis of which operations could be executed in parallel. Furthermore, we point out a couple of further important elements of the class:

• qregisters: the quantum registers are a way of keeping track of

  “temporary” qubits, that can be added and removed at will. With the class methods add_qregister() and remove_qregister() it is possible to apply such operations. Then, when you apply an operation you can always specify to which register you are referring, without having to worry about the indexing. In particular, qubits in the same register are naturally ordered from left to right. So, if you want to apply a not gate to the left-most qubit of the register a1 you will have to call qcirc.x(0, ‘a1’), since the left-most has index 0 for the register ‘a1’;

• cregisters: the classical registers, where you store the information of

  projective mesurements happened previously on the system and their probability. So, the position idx of the cregister will hold the tuple (meas_result, meas_prob. Each operation can be conditioned on the value of a classical register. By calling the method inspect_cregister(creg, idx)() where creg is the name of your classical register, you can have access to the value of the bit at the index idx. If idx=None instead, the full register is treated as the binary representation of a decimal number, and that decimal number is given by the function. Remember to add the classical registers you need beforehand, using add_cregister(): the quantum circuit start without any of them!

To add operations to the circuit there are three main ways:

• the add(), to append the operation at the end of the circuit

• some methods to apply widely-used operations to the circuit with a simplified

  notation.

• the insert() method, to insert an operation at any given layer of the circuit.

  However, this method is dangerous and is not recommended.

The str_repr() is meant to give a way to visualize the circuit, but is not needed for the functioning of the class, and it is still under development.

class qmatchatea.circuit.circuit.Qcircuit(num_sites, local_dim=2)

Class used to represent a quantum circuit in the qmatchatea library. Each layer of the circuit is a list containing instructions, i.e. lists [QCOperation, sites].

• When iterating over the class the iterators returns the layers.

• Iterating over the layer returns the instructions, with all permutations of indexes already taken care of, based on the quantum registers.

This means that, once you obtain the operation, you simply need to apply it on the defined sites of the mps, without further complexity.

However, you should not run it by yourself, it is preferred to use the QcMps.run_from_qcirc().

Parameters

num_sites: int

Number of sites in the circuit

local_dim: int, optional

Local dimension of the single site. Default to 2.

add(operation, sites, register='default')

Add an operation to the circuit

Parameters

operationQCOperation

Operation to be added to the

sitesinteger of array-like of integers

Qubits to which the operation is applied

registerstr or array of str

Register to which the operations are applied. Default are both to default.

add_cregister(name, num_bits)

Add a classical register with name name and length num_bits

Parameters

namestr

Name of the classical register

num_bitsint

Number of bits the register can store

add_qregister(new_register, positions, reference_register='default')

Add a new register to the circuit, in a specific positions. The positions is the index of the link where the site will be added, so 0 is attached to the left, num_sites is attached to the right. An intermediate number attaches it in the middle. This link number is taken with respect to the reference register.

This function is a simple loop over add_site, but we expect it to be a very useful function in runtime

Parameters

new_registerstr

Name of the register that will track the index of the new site

positionsarray-like of ints

Index of the link where the new site should be added in the register

reference_register: str

Register with respect to which the position is taken. Default to ‘default’.

add_site(new_register, position, reference_register='default')

Add a site to the circuit, in a specific position. The position is the index of the link where the site will be added, so 0 is attached to the left, num_sites is attached to the right. An intermediate number attaches it in the middle.

Parameters

new_registerstr

Name of the register that will track the index of the new site

positionint

Index of the link where the new site should be added in the register

reference_register: str

Register with respect to which the position is taken. Default to ‘default’.

cp(theta, pos, qreg='default', c_if=<qmatchatea.circuit.operations.ClassicalCondition object>)

Apply a controlled phase gate in the position pos in the qregisters qreg. pos should be an array, qreg should be an array if the qubits are in different qregisters

Parameters

thetafloat

Rotation angle for controlled phase gate

poslist of two ints

Index, relative to the quantum register, where you want to apply the operation

qreglist of str, str or None, optional

Quantum registers where you want to apply the operation. If only a str is provided, the program assumes you want to apply the gate inside the same quantum register. If a list of two strings is provided, the gate is applied between different quantum registers. If None, the “raw index” is considered, i.e. without taking into account the quantum register reindexing. Default to ‘default’.

c_ifClassicalCondition, optional

Classical condition to be checked for applying the operation on the simulation.

property cregisters

Return the full list of classical registers

cx(pos, qreg='default', c_if=<qmatchatea.circuit.operations.ClassicalCondition object>)

Apply a controlled not gate in the position pos in the qregisters qreg. pos should be an array, qreg should be an array if the qubits are in different qregisters

Parameters

poslist of two ints

Index, relative to the quantum register, where you want to apply the operation

qreglist of str, str or None, optional

Quantum registers where you want to apply the operation. If only a str is provided, the program assumes you want to apply the gate inside the same quantum register. If a list of two strings is provided, the gate is applied between different quantum registers. If None, the “raw index” is considered, i.e. without taking into account the quantum register reindexing. Default to ‘default’.

c_ifClassicalCondition, optional

Classical condition to be checked for applying the operation on the simulation.

cz(pos, qreg='default', c_if=<qmatchatea.circuit.operations.ClassicalCondition object>)

Apply a controlled z gate in the position pos in the qregisters qreg. pos should be an array, qreg should be an array if the qubits are in different qregisters

Parameters

poslist of two ints

Index, relative to the quantum register, where you want to apply the operation

qreglist of str, str or None, optional

Quantum registers where you want to apply the operation. If only a str is provided, the program assumes you want to apply the gate inside the same quantum register. If a list of two strings is provided, the gate is applied between different quantum registers. If None, the “raw index” is considered, i.e. without taking into account the quantum register reindexing. Default to ‘default’.

c_ifClassicalCondition, optional

Classical condition to be checked for applying the operation on the simulation.

fill_qcoperators(operators)

Fill the QCoperators dictionary with all the operators in the Qcircuit

Parameters

operators: QCOperators

operators class to fill

classmethod from_qiskit(qc)

Initialize the Qcircuit class from a qiskit quantum circuit

Parameters

qcQuantumCircuit

qiskit QuantumCircuit that will initialize the Qcircuit

gate(gate, pos, name='op', qreg='default', c_if=<qmatchatea.circuit.operations.ClassicalCondition object>)

Apply a matrix to the circuit. The dimensions of the matrix should be consistent with the number of qubits to which it should be applied

Parameters

gatenp.ndarray

gate matrix

posint or array-like of ints

Indexes of the sites to which it should be applied

namestr, optional

Unique identifier of the gate. Default to ‘op’

qregstr or array-like of str, optional

qregister to which the gate should be applied

h(pos, qreg='default', c_if=<qmatchatea.circuit.operations.ClassicalCondition object>)

Apply a hadamard gate in the position pos in the qregister qreg

Parameters

posint

Index, relative to the quantum register, where you want to apply the operation

qregstr or None, optional

Quantum register where you want to apply the operation. If None, the “raw index” is considered, i.e. without taking into account the quantum register reindexing. Default to ‘default’

c_ifClassicalCondition, optional

Classical condition to be checked for applying the operation on the simulation.

insert(operation, sites, layer, register='default', inlayer=True)

Insert an operation after a specific layer on the sites If inlayer is True simply add it into the layer without checking if an operation is already there, otherwise check for the operation and insert a new layer

Parameters

operationQCOperation

Operation to be added to the

sitesint of array-like of integers

Qubits to which the operation is applied

layer: int

integer identifying the layer after which we want to insert the operation

registerstr or array of str

Register to which the operations are applied. Default are both to default.

inlayer: bool, optional

If False, and the position in the layer is already occupied, add a new layer. Otherwise add it to that layer nevertheless. Default to True.

inspect_cregister(register, idx=None)

Retrieve the decimal value of the binary number stored in the classical register register if idx=None, otherwise it returns the value of the bit at position idx

Parameters

registerstr

Name of the classical register

idxint, optional

Index of the bit you want to recover. If None, you will recover the decimal representation of the full register. Default to None.

property local_dim

Local dimension property

measure_observables(name, observables, operators, qreg=None, c_if=<qmatchatea.circuit.operations.ClassicalCondition object>)

Perform a measurement step of all the observables defined in the observable parameter.

Parameters

namestr

Name of the observables step

observables: TNObservables

Observables to be measured at this step

operators: QCOperators

Class containing the operators present in the Observables

qregstr or None, optional

Quantum register where the observables should be measured. If None, they are measured on the FULL circuit, regardless of the registers

c_ifClassicalCondition, optional

Classical condition to be checked for applying the operation on the simulation

measure_projective(pos, cl_idx, qreg='default', creg='default', selected_output=None, c_if=<qmatchatea.circuit.operations.ClassicalCondition object>)

Apply a projective measurement in the position pos in the qregister qreg. You can choose the output of the measure. The result is stored in the classical qregister creg at index cl_idx

Parameters

posint

Index, relative to the quantum register, where you want to apply the operation

cl_idxint

Index of the classical register where to store the result of the measurement

qregstr or None, optional

Quantum register where you want to apply the operation. If None, the “raw index” is considered, i.e. without taking into account the quantum register reindexing. Default to ‘default’

cregisterstr, optional

Classical register where the result of the measurement is stored. Default to ‘default’

selected_outputint, optional

Output selected a priori. Default to None.

c_ifClassicalCondition, optional

Classical condition to be checked for applying the operation on the simulation.

modify_cregister(value, name, idx)

Modify the value of a measured bit in the classical register

Parameters

valuetuple of (int, float)

Value of the measured qubit to be saved in the classical register and of the probability of that outcome

namestr

Name of the classical register

idxint

Index of the bit where to save value

property num_classical_sites

Number of classical sites, i.e. bits

property num_layers

Number of layers in the circuit

property num_qubits

Number of sites property, with another name for simplicity of interfaces

property num_sites

Number of sites property

p(theta, pos, qreg='default', c_if=<qmatchatea.circuit.operations.ClassicalCondition object>)

Apply a Phase gate in the position pos in the qregister qreg with a phase theta

Parameters

thetafloat

Rotation angle for the phase gate

posint

Index, relative to the quantum register, where you want to apply the operation

qregstr or None, optional

Quantum register where you want to apply the operation. If None, the “raw index” is considered, i.e. without taking into account the quantum register reindexing. Default to ‘default’

c_ifClassicalCondition, optional

Classical condition to be checked for applying the operation on the simulation.

remove_qregister(register)

Remove a register from the circuit.

Parameters

registerstr

Name of the register to be removed

remove_site(register, position)

Remove a site from the circuit. The site to be removed is identified by its register and the position in the register.

Parameters

registerstr

Name of the register where the site to remove is

positionint

Index of the site to remove

renormalize(c_if=<qmatchatea.circuit.operations.ClassicalCondition object>)

Renormalize the state

Parameters

c_ifClassicalCondition, optional

Classical condition to be checked for applying the operation on the simulation

s(pos, qreg='default', c_if=<qmatchatea.circuit.operations.ClassicalCondition object>)

Apply a S gate in the position pos in the qregister qreg

Parameters

posint

Index, relative to the quantum register, where you want to apply the operation

qregstr or None, optional

Quantum register where you want to apply the operation. If None, the “raw index” is considered, i.e. without taking into account the quantum register reindexing. Default to ‘default’

c_ifClassicalCondition, optional

Classical condition to be checked for applying the operation on the simulation.

sadg(pos, qreg='default', c_if=<qmatchatea.circuit.operations.ClassicalCondition object>)

Apply the adjoint of an S gate in the position pos in the qregister qreg

Parameters

posint

Index, relative to the quantum register, where you want to apply the operation

qregstr or None, optional

Quantum register where you want to apply the operation. If None, the “raw index” is considered, i.e. without taking into account the quantum register reindexing. Default to ‘default’

c_ifClassicalCondition, optional

Classical condition to be checked for applying the operation on the simulation.

str_repr()

Get the string representation of the circuit

swap(pos, qreg='default', c_if=<qmatchatea.circuit.operations.ClassicalCondition object>)

Apply a swap gate in the position pos in the qregisters qreg. pos should be an array, qreg should be an array if the qubits are in different qregisters

Parameters

poslist of two ints

Index, relative to the quantum register, where you want to apply the operation

qreglist of str, str or None, optional

Quantum registers where you want to apply the operation. If only a str is provided, the program assumes you want to apply the gate inside the same quantum register. If a list of two strings is provided, the gate is applied between different quantum registers. If None, the “raw index” is considered, i.e. without taking into account the quantum register reindexing. Default to ‘default’.

c_ifClassicalCondition, optional

Classical condition to be checked for applying the operation on the simulation.

t(pos, qreg='default', c_if=<qmatchatea.circuit.operations.ClassicalCondition object>)

Apply a T gate in the position pos in the qregister qreg

Parameters

posint

Index, relative to the quantum register, where you want to apply the operation

qregstr or None, optional

Quantum register where you want to apply the operation. If None, the “raw index” is considered, i.e. without taking into account the quantum register reindexing. Default to ‘default’

c_ifClassicalCondition, optional

Classical condition to be checked for applying the operation on the simulation.

tadg(pos, qreg='default', c_if=<qmatchatea.circuit.operations.ClassicalCondition object>)

Apply the adjoint of an T gate in the position pos in the qregister qreg

Parameters

posint

Index, relative to the quantum register, where you want to apply the operation

qregstr or None, optional

Quantum register where you want to apply the operation. If None, the “raw index” is considered, i.e. without taking into account the quantum register reindexing. Default to ‘default’

c_ifClassicalCondition, optional

Classical condition to be checked for applying the operation on the simulation.

to_matrix(sparse=False, max_qubit_equivalent=20, qiskit_order=True)

Return the matrix representation of the circuit. It is a unitary matrix if no noise/non-unitary matrix has been applied. Notice that this computation scales as \(d^{2n}\), where \(d\) is the local dimension of the single degree of freedom and \(n\) the number of sites. Furthermore, the function is not optimized and might take long.

Parameters

sparsebool, optional

If True, return a csr sparse matrix instead of a numpy array. Default to False.

max_qubit_equivalent: int, optional

Maximum number of qubit sites the MPS can have and still be transformed into a matrix. If the number of sites is greater, it will throw an exception. Default to 20.

qiskit_orderbool, optional

If True, return the matrix using qiskit ordering. Default to True.

Returns

matrixnp.ndarray or sp.csr_matrix

Numpy array or sparse matrix representing the system unitary

write(dest, id_mapping)

Write on file (originally written for the Fortran simulator), with the correct formatting

Parameters

dest: str or filehandle

If str, write on that file. Otherwise, write using that filehandle

id_mapping: dict

Mapping from the operator name to the operator id

x(pos, qreg='default', c_if=<qmatchatea.circuit.operations.ClassicalCondition object>)

Apply a x gate in the position pos in the qregister qreg

Parameters

posint

Index, relative to the quantum register, where you want to apply the operation

qregstr or None, optional

Quantum register where you want to apply the operation. If None, the “raw index” is considered, i.e. without taking into account the quantum register reindexing. Default to ‘default’

c_ifClassicalCondition, optional

Classical condition to be checked for applying the operation on the simulation.

y(pos, qreg='default', c_if=<qmatchatea.circuit.operations.ClassicalCondition object>)

Apply a y gate in the position pos in the qregister qreg

Parameters

posint

Index, relative to the quantum register, where you want to apply the operation

qregstr or None, optional

Quantum register where you want to apply the operation. If None, the “raw index” is considered, i.e. without taking into account the quantum register reindexing. Default to ‘default’

c_ifClassicalCondition, optional

Classical condition to be checked for applying the operation on the simulation.

z(pos, qreg='default', c_if=<qmatchatea.circuit.operations.ClassicalCondition object>)

Apply a z gate in the position pos in the qregister qreg

Parameters

posint

Index, relative to the quantum register, where you want to apply the operation

qregstr or None, optional

Quantum register where you want to apply the operation. If None, the “raw index” is considered, i.e. without taking into account the quantum register reindexing. Default to ‘default’

c_ifClassicalCondition, optional

Classical condition to be checked for applying the operation on the simulation.