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Source code for qiskit.quantum_info.states.statevector

# This code is part of Qiskit.
#
# (C) Copyright IBM 2017, 2019.
#
# This code is licensed under the Apache License, Version 2.0. You may
# obtain a copy of this license in the LICENSE.txt file in the root directory
# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.
#
# Any modifications or derivative works of this code must retain this
# copyright notice, and modified files need to carry a notice indicating
# that they have been altered from the originals.

"""
Statevector quantum state class.
"""

import copy
import re
import warnings
from numbers import Number

import numpy as np

from qiskit.circuit.quantumcircuit import QuantumCircuit
from qiskit.circuit.instruction import Instruction
from qiskit.exceptions import QiskitError
from qiskit.quantum_info.states.quantum_state import QuantumState
from qiskit.quantum_info.operators.operator import Operator
from qiskit.quantum_info.operators.predicates import matrix_equal


[docs]class Statevector(QuantumState): """Statevector class"""
[docs] def __init__(self, data, dims=None): """Initialize a statevector object. Args: data (vector_like): a complex statevector. dims (int or tuple or list): Optional. The subsystem dimension of the state (See additional information). Raises: QiskitError: if input data is not valid. Additional Information: The ``dims`` kwarg can be None, an integer, or an iterable of integers. * ``Iterable`` -- the subsystem dimensions are the values in the list with the total number of subsystems given by the length of the list. * ``Int`` or ``None`` -- the length of the input vector specifies the total dimension of the density matrix. If it is a power of two the state will be initialized as an N-qubit state. If it is not a power of two the state will have a single d-dimensional subsystem. """ if isinstance(data, (list, np.ndarray)): # Finally we check if the input is a raw vector in either a # python list or numpy array format. self._data = np.asarray(data, dtype=complex) elif isinstance(data, Statevector): self._data = data._data if dims is None: dims = data._dims elif isinstance(data, Operator): # We allow conversion of column-vector operators to Statevectors input_dim, _ = data.dim if input_dim != 1: raise QiskitError("Input Operator is not a column-vector.") self._data = np.ravel(data.data) else: raise QiskitError("Invalid input data format for Statevector") # Check that the input is a numpy vector or column-vector numpy # matrix. If it is a column-vector matrix reshape to a vector. ndim = self._data.ndim shape = self._data.shape if ndim != 1: if ndim == 2 and shape[1] == 1: self._data = np.reshape(self._data, shape[0]) elif ndim != 2 or shape[1] != 1: raise QiskitError("Invalid input: not a vector or column-vector.") super().__init__(self._automatic_dims(dims, shape[0]))
def __eq__(self, other): return super().__eq__(other) and np.allclose( self._data, other._data, rtol=self.rtol, atol=self.atol) def __repr__(self): prefix = 'Statevector(' pad = len(prefix) * ' ' return '{}{},\n{}dims={})'.format( prefix, np.array2string( self.data, separator=', ', prefix=prefix), pad, self._dims) @property def data(self): """Return data.""" return self._data
[docs] def is_valid(self, atol=None, rtol=None): """Return True if a Statevector has norm 1.""" if atol is None: atol = self.atol if rtol is None: rtol = self.rtol norm = np.linalg.norm(self.data) return np.allclose(norm, 1, rtol=rtol, atol=atol)
[docs] def to_operator(self): """Convert state to a rank-1 projector operator""" mat = np.outer(self.data, np.conj(self.data)) return Operator(mat, input_dims=self.dims(), output_dims=self.dims())
[docs] def conjugate(self): """Return the conjugate of the operator.""" return Statevector(np.conj(self.data), dims=self.dims())
[docs] def trace(self): """Return the trace of the quantum state as a density matrix.""" return np.sum(np.abs(self.data) ** 2)
[docs] def purity(self): """Return the purity of the quantum state.""" # For a valid statevector the purity is always 1, however if we simply # have an arbitrary vector (not correctly normalized) then the # purity is equivalent to the trace squared: # P(|psi>) = Tr[|psi><psi|psi><psi|] = |<psi|psi>|^2 return self.trace() ** 2
[docs] def tensor(self, other): """Return the tensor product state self ⊗ other. Args: other (Statevector): a quantum state object. Returns: Statevector: the tensor product operator self ⊗ other. Raises: QiskitError: if other is not a quantum state. """ if not isinstance(other, Statevector): other = Statevector(other) dims = other.dims() + self.dims() data = np.kron(self._data, other._data) return Statevector(data, dims)
[docs] def expand(self, other): """Return the tensor product state other ⊗ self. Args: other (Statevector): a quantum state object. Returns: Statevector: the tensor product state other ⊗ self. Raises: QiskitError: if other is not a quantum state. """ if not isinstance(other, Statevector): other = Statevector(other) dims = self.dims() + other.dims() data = np.kron(other._data, self._data) return Statevector(data, dims)
def _add(self, other): """Return the linear combination self + other. Args: other (Statevector): a quantum state object. Returns: Statevector: the linear combination self + other. Raises: QiskitError: if other is not a quantum state, or has incompatible dimensions. """ if not isinstance(other, Statevector): other = Statevector(other) if self.dim != other.dim: raise QiskitError("other Statevector has different dimensions.") return Statevector(self.data + other.data, self.dims()) def _multiply(self, other): """Return the scalar multiplied state self * other. Args: other (complex): a complex number. Returns: Statevector: the scalar multiplied state other * self. Raises: QiskitError: if other is not a valid complex number. """ if not isinstance(other, Number): raise QiskitError("other is not a number") return Statevector(other * self.data, self.dims())
[docs] def evolve(self, other, qargs=None): """Evolve a quantum state by the operator. Args: other (Operator): The operator to evolve by. qargs (list): a list of Statevector subsystem positions to apply the operator on. Returns: Statevector: the output quantum state. Raises: QiskitError: if the operator dimension does not match the specified Statevector subsystem dimensions. """ if qargs is None: qargs = getattr(other, 'qargs', None) # Get return vector ret = copy.copy(self) # Evolution by a circuit or instruction if isinstance(other, QuantumCircuit): other = other.to_instruction() if isinstance(other, Instruction): if self.num_qubits is None: raise QiskitError("Cannot apply QuantumCircuit to non-qubit Statevector.") return self._evolve_instruction(ret, other, qargs=qargs) # Evolution by an Operator if not isinstance(other, Operator): other = Operator(other) # check dimension if self.dims(qargs) != other.input_dims(): raise QiskitError( "Operator input dimensions are not equal to statevector subsystem dimensions." ) return Statevector._evolve_operator(ret, other, qargs=qargs)
[docs] def equiv(self, other, rtol=None, atol=None): """Return True if statevectors are equivalent up to global phase. Args: other (Statevector): a statevector object. rtol (float): relative tolerance value for comparison. atol (float): absolute tolerance value for comparison. Returns: bool: True if statevectors are equivalent up to global phase. """ if not isinstance(other, Statevector): try: other = Statevector(other) except QiskitError: return False if self.dim != other.dim: return False if atol is None: atol = self.atol if rtol is None: rtol = self.rtol return matrix_equal(self.data, other.data, ignore_phase=True, rtol=rtol, atol=atol)
[docs] def expectation_value(self, oper, qargs=None): """Compute the expectation value of an operator. Args: oper (Operator): an operator to evaluate expval of. qargs (None or list): subsystems to apply operator on. Returns: complex: the expectation value. """ val = self.evolve(oper, qargs=qargs) conj = self.conjugate() return np.dot(conj.data, val.data)
[docs] def probabilities(self, qargs=None, decimals=None): """Return the subsystem measurement probability vector. Measurement probabilities are with respect to measurement in the computation (diagonal) basis. Args: qargs (None or list): subsystems to return probabilities for, if None return for all subsystems (Default: None). decimals (None or int): the number of decimal places to round values. If None no rounding is done (Default: None). Returns: np.array: The Numpy vector array of probabilities. Examples: Consider a 2-qubit product state :math:`|\\psi\\rangle=|+\\rangle\\otimes|0\\rangle`. .. jupyter-execute:: from qiskit.quantum_info import Statevector psi = Statevector.from_label('+0') # Probabilities for measuring both qubits probs = psi.probabilities() print('probs: {}'.format(probs)) # Probabilities for measuring only qubit-0 probs_qubit_0 = psi.probabilities([0]) print('Qubit-0 probs: {}'.format(probs_qubit_0)) # Probabilities for measuring only qubit-1 probs_qubit_1 = psi.probabilities([1]) print('Qubit-1 probs: {}'.format(probs_qubit_1)) We can also permute the order of qubits in the ``qargs`` list to change the qubit position in the probabilities output .. jupyter-execute:: from qiskit.quantum_info import Statevector psi = Statevector.from_label('+0') # Probabilities for measuring both qubits probs = psi.probabilities([0, 1]) print('probs: {}'.format(probs)) # Probabilities for measuring both qubits # but swapping qubits 0 and 1 in output probs_swapped = psi.probabilities([1, 0]) print('Swapped probs: {}'.format(probs_swapped)) """ probs = self._subsystem_probabilities( np.abs(self.data) ** 2, self._dims, qargs=qargs) if decimals is not None: probs = probs.round(decimals=decimals) return probs
[docs] def reset(self, qargs=None): """Reset state or subsystems to the 0-state. Args: qargs (list or None): subsystems to reset, if None all subsystems will be reset to their 0-state (Default: None). Returns: Statevector: the reset state. Additional Information: If all subsystems are reset this will return the ground state on all subsystems. If only a some subsystems are reset this function will perform a measurement on those subsystems and evolve the subsystems so that the collapsed post-measurement states are rotated to the 0-state. The RNG seed for this sampling can be set using the :meth:`seed` method. """ if qargs is None: # Resetting all qubits does not require sampling or RNG state = np.zeros(self._dim, dtype=complex) state[0] = 1 return Statevector(state, dims=self._dims) # Sample a single measurement outcome dims = self.dims(qargs) probs = self.probabilities(qargs) sample = self._rng.choice(len(probs), p=probs, size=1) # Convert to projector for state update proj = np.zeros(len(probs), dtype=complex) proj[sample] = 1 / np.sqrt(probs[sample]) # Rotate outcome to 0 reset = np.eye(len(probs)) reset[0, 0] = 0 reset[sample, sample] = 0 reset[0, sample] = 1 # compose with reset projection reset = np.dot(reset, np.diag(proj)) return self.evolve( Operator(reset, input_dims=dims, output_dims=dims), qargs=qargs)
[docs] def to_counts(self): """Returns the statevector as a counts dict of probabilities. DEPRECATED: use :meth:`probabilities_dict` instead. Returns: dict: Counts of probabilities. """ warnings.warn( 'The `Statevector.to_counts` method is deprecated as of 0.13.0,' ' and will be removed no earlier than 3 months after that ' 'release date. You should use the `Statevector.probabilities_dict`' ' method instead.', DeprecationWarning, stacklevel=2) return self.probabilities_dict()
[docs] @classmethod def from_label(cls, label): """Return a tensor product of Pauli X,Y,Z eigenstates. .. list-table:: Single-qubit state labels :header-rows: 1 * - Label - Statevector * - ``"0"`` - :math:`[1, 0]` * - ``"1"`` - :math:`[0, 1]` * - ``"+"`` - :math:`[1 / \\sqrt{2}, 1 / \\sqrt{2}]` * - ``"-"`` - :math:`[1 / \\sqrt{2}, -1 / \\sqrt{2}]` * - ``"r"`` - :math:`[1 / \\sqrt{2}, i / \\sqrt{2}]` * - ``"l"`` - :math:`[1 / \\sqrt{2}, -i / \\sqrt{2}]` Args: label (string): a eigenstate string ket label (see table for allowed values). Returns: Statevector: The N-qubit basis state density matrix. Raises: QiskitError: if the label contains invalid characters, or the length of the label is larger than an explicitly specified num_qubits. """ # Check label is valid if re.match(r'^[01rl\-+]+$', label) is None: raise QiskitError('Label contains invalid characters.') # We can prepare Z-eigenstates by converting the computational # basis bit-string to an integer and preparing that unit vector # However, for X-basis states, we will prepare a Z-eigenstate first # then apply Hadamard gates to rotate 0 and 1s to + and -. z_label = label xy_states = False if re.match('^[01]+$', label) is None: # We have X or Y eigenstates so replace +,r with 0 and # -,l with 1 and prepare the corresponding Z state xy_states = True z_label = z_label.replace('+', '0') z_label = z_label.replace('r', '0') z_label = z_label.replace('-', '1') z_label = z_label.replace('l', '1') # Initialize Z eigenstate vector num_qubits = len(label) data = np.zeros(1 << num_qubits, dtype=complex) pos = int(z_label, 2) data[pos] = 1 state = Statevector(data) if xy_states: # Apply hadamards to all qubits in X eigenstates x_mat = np.array([[1, 1], [1, -1]], dtype=complex) / np.sqrt(2) # Apply S.H to qubits in Y eigenstates y_mat = np.dot(np.diag([1, 1j]), x_mat) for qubit, char in enumerate(reversed(label)): if char in ['+', '-']: state = state.evolve(x_mat, qargs=[qubit]) elif char in ['r', 'l']: state = state.evolve(y_mat, qargs=[qubit]) return state
[docs] @staticmethod def from_int(i, dims): """Return a computational basis statevector. Args: i (int): the basis state element. dims (int or tuple or list): The subsystem dimensions of the statevector (See additional information). Returns: Statevector: The computational basis state :math:`|i\\rangle`. Additional Information: The ``dims`` kwarg can be an integer or an iterable of integers. * ``Iterable`` -- the subsystem dimensions are the values in the list with the total number of subsystems given by the length of the list. * ``Int`` -- the integer specifies the total dimension of the state. If it is a power of two the state will be initialized as an N-qubit state. If it is not a power of two the state will have a single d-dimensional subsystem. """ size = np.product(dims) state = np.zeros(size, dtype=complex) state[i] = 1.0 return Statevector(state, dims=dims)
[docs] @classmethod def from_instruction(cls, instruction): """Return the output statevector of an instruction. The statevector is initialized in the state :math:`|{0,\\ldots,0}\\rangle` of the same number of qubits as the input instruction or circuit, evolved by the input instruction, and the output statevector returned. Args: instruction (qiskit.circuit.Instruction or QuantumCircuit): instruction or circuit Returns: Statevector: The final statevector. Raises: QiskitError: if the instruction contains invalid instructions for the statevector simulation. """ # Convert circuit to an instruction if isinstance(instruction, QuantumCircuit): instruction = instruction.to_instruction() # Initialize an the statevector in the all |0> state init = np.zeros(2 ** instruction.num_qubits, dtype=complex) init[0] = 1.0 vec = Statevector(init, dims=instruction.num_qubits * (2,)) return Statevector._evolve_instruction(vec, instruction)
[docs] def to_dict(self, decimals=None): r"""Convert the statevector to dictionary form. This dictionary representation uses a Ket-like notation where the dictionary keys are qudit strings for the subsystem basis vectors. If any subsystem has a dimension greater than 10 comma delimiters are inserted between integers so that subsystems can be distinguished. Args: decimals (None or int): the number of decimal places to round values. If None no rounding is done (Default: None). Returns: dict: the dictionary form of the Statevector. Example: The ket-form of a 2-qubit statevector :math:`|\psi\rangle = |-\rangle\otimes |0\rangle` .. jupyter-execute:: from qiskit.quantum_info import Statevector psi = Statevector.from_label('-0') print(psi.to_dict()) For non-qubit subsystems the integer range can go from 0 to 9. For example in a qutrit system .. jupyter-execute:: import numpy as np from qiskit.quantum_info import Statevector vec = np.zeros(9) vec[0] = 1 / np.sqrt(2) vec[-1] = 1 / np.sqrt(2) psi = Statevector(vec, dims=(3, 3)) print(psi.to_dict()) For large subsystem dimensions delimeters are required. The following example is for a 20-dimensional system consisting of a qubit and 10-dimensional qudit. .. jupyter-execute:: import numpy as np from qiskit.quantum_info import Statevector vec = np.zeros(2 * 10) vec[0] = 1 / np.sqrt(2) vec[-1] = 1 / np.sqrt(2) psi = Statevector(vec, dims=(2, 10)) print(psi.to_dict()) """ return self._vector_to_dict(self.data, self._dims, decimals=decimals, string_labels=True)
@property def _shape(self): """Return the tensor shape of the matrix operator""" return tuple(reversed(self.dims())) @staticmethod def _evolve_operator(statevec, oper, qargs=None): """Evolve a qudit statevector""" is_qubit = bool(statevec.num_qubits and oper.num_qubits) if qargs is None: # Full system evolution statevec._data = np.dot(oper._data, statevec._data) if not is_qubit: statevec._set_dims(oper._output_dims) return statevec # Calculate contraction dimensions if is_qubit: # Qubit contraction new_dim = statevec._dim num_qargs = statevec.num_qubits else: # Qudit contraction new_dims = list(statevec._dims) for i, qubit in enumerate(qargs): new_dims[qubit] = oper._output_dims[i] new_dim = np.product(new_dims) num_qargs = len(new_dims) # Get transpose axes indices = [num_qargs - 1 - i for i in reversed(qargs)] axes = indices + [i for i in range(num_qargs) if i not in indices] axes_inv = np.argsort(axes).tolist() # Calculate contraction dimensions if is_qubit: pre_tensor_shape = num_qargs * (2,) post_tensor_shape = pre_tensor_shape contract_shape = (1 << oper.num_qubits, 1 << (num_qargs - oper.num_qubits)) else: contract_dim = np.product(oper._input_dims) pre_tensor_shape = statevec._shape contract_shape = (contract_dim, statevec._dim // contract_dim) post_tensor_shape = list(reversed(oper._output_dims)) + [ pre_tensor_shape[i] for i in range(num_qargs) if i not in indices] # reshape input for contraction statevec._data = np.reshape(np.transpose( np.reshape(statevec.data, pre_tensor_shape), axes), contract_shape) statevec._data = np.reshape(np.dot(oper.data, statevec._data), post_tensor_shape) statevec._data = np.reshape(np.transpose(statevec._data, axes_inv), new_dim) # Update dimension if not is_qubit: statevec._set_dims(new_dims) return statevec @staticmethod def _evolve_instruction(statevec, obj, qargs=None): """Update the current Statevector by applying an instruction.""" from qiskit.circuit.reset import Reset from qiskit.circuit.barrier import Barrier mat = Operator._instruction_to_matrix(obj) if mat is not None: # Perform the composition and inplace update the current state # of the operator return Statevector._evolve_operator(statevec, Operator(mat), qargs=qargs) # Special instruction types if isinstance(obj, Reset): statevec._data = statevec.reset(qargs)._data return statevec if isinstance(obj, Barrier): return statevec # If the instruction doesn't have a matrix defined we use its # circuit decomposition definition if it exists, otherwise we # cannot compose this gate and raise an error. if obj.definition is None: raise QiskitError('Cannot apply Instruction: {}'.format(obj.name)) if not isinstance(obj.definition, QuantumCircuit): raise QiskitError('{} instruction definition is {}; expected QuantumCircuit'.format( obj.name, type(obj.definition))) if obj.definition.global_phase: statevec._data *= np.exp(1j * float(obj.definition.global_phase)) qubits = {qubit: i for i, qubit in enumerate(obj.definition.qubits)} for instr, qregs, cregs in obj.definition: if cregs: raise QiskitError( 'Cannot apply instruction with classical registers: {}'.format( instr.name)) # Get the integer position of the flat register if qargs is None: new_qargs = [qubits[tup] for tup in qregs] else: new_qargs = [qargs[qubits[tup]] for tup in qregs] Statevector._evolve_instruction(statevec, instr, qargs=new_qargs) return statevec

© Copyright 2020, Qiskit Development Team. Last updated on 2021/02/18.

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