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qiskit.quantum_info.Chi

class Chi(data, input_dims=None, output_dims=None)[소스]

Pauli basis Chi-matrix representation of a quantum channel.

The Chi-matrix representation of an \(n\)-qubit quantum channel \(\mathcal{E}\) is a matrix \(\chi\) such that the evolution of a DensityMatrix \(\rho\) is given by

\[\mathcal{E}(ρ) = \sum_{i, j} \chi_{i,j} P_i ρ P_j\]

where \([P_0, P_1, ..., P_{4^{n}-1}]\) is the \(n\)-qubit Pauli basis in lexicographic order. It is related to the Choi representation by a change of basis of the Choi-matrix into the Pauli basis.

See reference [1] for further details.

참조

  1. C.J. Wood, J.D. Biamonte, D.G. Cory, Tensor networks and graphical calculus for open quantum systems, Quant. Inf. Comp. 15, 0579-0811 (2015). arXiv:1111.6950 [quant-ph]

Initialize a quantum channel Chi-matrix operator.

매개변수
  • (QuantumCircuit or (data) – Instruction or BaseOperator or matrix): data to initialize superoperator.

  • input_dims (tuple) – the input subsystem dimensions. [Default: None]

  • output_dims (tuple) – the output subsystem dimensions. [Default: None]

예외

QiskitError – if input data is not an N-qubit channel or cannot be initialized as a Chi-matrix.

Additional Information:

If the input or output dimensions are None, they will be automatically determined from the input data. The Chi matrix representation is only valid for N-qubit channels.

__init__(data, input_dims=None, output_dims=None)[소스]

Initialize a quantum channel Chi-matrix operator.

매개변수
  • (QuantumCircuit or (data) – Instruction or BaseOperator or matrix): data to initialize superoperator.

  • input_dims (tuple) – the input subsystem dimensions. [Default: None]

  • output_dims (tuple) – the output subsystem dimensions. [Default: None]

예외

QiskitError – if input data is not an N-qubit channel or cannot be initialized as a Chi-matrix.

Additional Information:

If the input or output dimensions are None, they will be automatically determined from the input data. The Chi matrix representation is only valid for N-qubit channels.

Methods

__init__(data[, input_dims, output_dims])

Initialize a quantum channel Chi-matrix operator.

add(other)

Return the linear operator self + other.

adjoint()

Return the adjoint of the operator.

compose(other[, qargs, front])

Return the composed quantum channel self @ other.

conjugate()

Return the conjugate of the QuantumChannel.

copy()

Make a deep copy of current operator.

dot(other[, qargs])

Return the right multiplied operator self * other.

expand(other)

Return the tensor product channel other ⊗ self.

input_dims([qargs])

Return tuple of input dimension for specified subsystems.

is_cp([atol, rtol])

Test if Choi-matrix is completely-positive (CP)

is_cptp([atol, rtol])

Return True if completely-positive trace-preserving (CPTP).

is_tp([atol, rtol])

Test if a channel is completely-positive (CP)

is_unitary([atol, rtol])

Return True if QuantumChannel is a unitary channel.

multiply(other)

Return the linear operator other * self.

output_dims([qargs])

Return tuple of output dimension for specified subsystems.

power(n)

The matrix power of the channel.

reshape([input_dims, output_dims])

Return a shallow copy with reshaped input and output subsystem dimensions.

set_atol(value)

Set the class default absolute tolerance parameter for float comparisons.

set_rtol(value)

Set the class default relative tolerance parameter for float comparisons.

subtract(other)

Return the linear operator self - other.

tensor(other)

Return the tensor product channel self ⊗ other.

to_instruction()

Convert to a Kraus or UnitaryGate circuit instruction.

to_operator()

Try to convert channel to a unitary representation Operator.

transpose()

Return the transpose of the QuantumChannel.

Attributes

atol

The default absolute tolerance parameter for float comparisons.

data

Return data.

dim

Return tuple (input_shape, output_shape).

num_qubits

Return the number of qubits if a N-qubit operator or None otherwise.

qargs

Return the qargs for the operator.

rtol

The relative tolerance parameter for float comparisons.

add(other)

Return the linear operator self + other.

DEPRECATED: use operator + other instead.

매개변수

other (BaseOperator) – an operator object.

반환값

the operator self + other.

반환 형식

BaseOperator

adjoint()

Return the adjoint of the operator.

property atol

The default absolute tolerance parameter for float comparisons.

compose(other, qargs=None, front=False)[소스]

Return the composed quantum channel self @ other.

매개변수
  • other (QuantumChannel) – a quantum channel.

  • qargs (list or None) – a list of subsystem positions to apply other on. If None apply on all subsystems [default: None].

  • front (bool) – If True compose using right operator multiplication, instead of left multiplication [default: False].

반환값

The quantum channel self @ other.

반환 형식

Chi

예외

QiskitError – if other has incompatible dimensions.

Additional Information:

Composition (@) is defined as left matrix multiplication for SuperOp matrices. That is that A @ B is equal to B * A. Setting front=True returns right matrix multiplication A * B and is equivalent to the dot() method.

conjugate()[소스]

Return the conjugate of the QuantumChannel.

copy()

Make a deep copy of current operator.

property data

Return data.

property dim

Return tuple (input_shape, output_shape).

dot(other, qargs=None)

Return the right multiplied operator self * other.

매개변수
  • other (BaseOperator) – an operator object.

  • qargs (list or None) – a list of subsystem positions to apply other on. If None apply on all subsystems [default: None].

반환값

The operator self * other.

반환 형식

BaseOperator

예외

QiskitError – if other cannot be converted to an operator, or has incompatible dimensions for specified subsystems.

expand(other)[소스]

Return the tensor product channel other ⊗ self.

매개변수

other (QuantumChannel) – a quantum channel.

반환값

the tensor product channel other ⊗ self as a Chi object.

반환 형식

Chi

예외

QiskitError – if other is not a QuantumChannel subclass.

input_dims(qargs=None)

Return tuple of input dimension for specified subsystems.

is_cp(atol=None, rtol=None)

Test if Choi-matrix is completely-positive (CP)

is_cptp(atol=None, rtol=None)

Return True if completely-positive trace-preserving (CPTP).

is_tp(atol=None, rtol=None)

Test if a channel is completely-positive (CP)

is_unitary(atol=None, rtol=None)

Return True if QuantumChannel is a unitary channel.

multiply(other)

Return the linear operator other * self.

DEPRECATED: use other * operator instead.

매개변수

other (complex) – a complex number.

반환값

the linear operator other * self.

반환 형식

BaseOperator

예외

NotImplementedError – if subclass does not support multiplication.

property num_qubits

Return the number of qubits if a N-qubit operator or None otherwise.

output_dims(qargs=None)

Return tuple of output dimension for specified subsystems.

power(n)[소스]

The matrix power of the channel.

매개변수

n (int) – compute the matrix power of the superoperator matrix.

반환값

the matrix power of the SuperOp converted to a Chi channel.

반환 형식

Chi

예외

QiskitError – if the input and output dimensions of the QuantumChannel are not equal, or the power is not an integer.

property qargs

Return the qargs for the operator.

reshape(input_dims=None, output_dims=None)

Return a shallow copy with reshaped input and output subsystem dimensions.

Arg:
input_dims (None or tuple): new subsystem input dimensions.

If None the original input dims will be preserved [Default: None].

output_dims (None or tuple): new subsystem output dimensions.

If None the original output dims will be preserved [Default: None].

반환값

returns self with reshaped input and output dimensions.

반환 형식

BaseOperator

예외

QiskitError – if combined size of all subsystem input dimension or subsystem output dimensions is not constant.

property rtol

The relative tolerance parameter for float comparisons.

classmethod set_atol(value)

Set the class default absolute tolerance parameter for float comparisons.

DEPRECATED: use operator.atol = value instead

classmethod set_rtol(value)

Set the class default relative tolerance parameter for float comparisons.

DEPRECATED: use operator.rtol = value instead

subtract(other)

Return the linear operator self - other.

DEPRECATED: use operator - other instead.

매개변수

other (BaseOperator) – an operator object.

반환값

the operator self - other.

반환 형식

BaseOperator

tensor(other)[소스]

Return the tensor product channel self ⊗ other.

매개변수

other (QuantumChannel) – a quantum channel.

반환값

the tensor product channel self ⊗ other as a Chi object.

반환 형식

Chi

예외

QiskitError – if other is not a QuantumChannel subclass.

to_instruction()

Convert to a Kraus or UnitaryGate circuit instruction.

If the channel is unitary it will be added as a unitary gate, otherwise it will be added as a kraus simulator instruction.

반환값

A kraus instruction for the channel.

반환 형식

qiskit.circuit.Instruction

예외

QiskitError – if input data is not an N-qubit CPTP quantum channel.

to_operator()

Try to convert channel to a unitary representation Operator.

transpose()[소스]

Return the transpose of the QuantumChannel.

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