Source code for pennylane._qubit_device

# Copyright 2018-2021 Xanadu Quantum Technologies Inc.

# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at

#     http://www.apache.org/licenses/LICENSE-2.0

# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
"""
This module contains the :class:`QubitDevice` abstract base class.
"""

# For now, arguments may be different from the signatures provided in Device
# e.g. instead of expval(self, observable, wires, par) have expval(self, observable)
# pylint: disable=arguments-differ, abstract-method, no-value-for-parameter,too-many-instance-attributes,too-many-branches, no-member, bad-option-value, arguments-renamed
import abc
import itertools
import warnings

import numpy as np

import pennylane as qml
from pennylane import DeviceError
from pennylane.operation import operation_derivative
from pennylane.measurements import (
    Sample,
    Counts,
    Variance,
    Expectation,
    Probability,
    State,
    VnEntropy,
    MutualInfo,
)

from pennylane import Device
from pennylane.math import sum as qmlsum
from pennylane.math import multiply as qmlmul
from pennylane.wires import Wires

from pennylane.measurements import MeasurementProcess


[docs]class QubitDevice(Device): """Abstract base class for PennyLane qubit devices. The following abstract method **must** be defined: * :meth:`~.apply`: append circuit operations, compile the circuit (if applicable), and perform the quantum computation. Devices that generate their own samples (such as hardware) may optionally overwrite :meth:`~.probabilty`. This method otherwise automatically computes the probabilities from the generated samples, and **must** overwrite the following method: * :meth:`~.generate_samples`: Generate samples from the device from the exact or approximate probability distribution. Analytic devices **must** overwrite the following method: * :meth:`~.analytic_probability`: returns the probability or marginal probability from the device after circuit execution. :meth:`~.marginal_prob` may be used here. This device contains common utility methods for qubit-based devices. These do not need to be overwritten. Utility methods include: * :meth:`~.expval`, :meth:`~.var`, :meth:`~.sample`: return expectation values, variances, and samples of observables after the circuit has been rotated into the observable eigenbasis. Args: wires (int, Iterable[Number, str]]): Number of subsystems represented by the device, or iterable that contains unique labels for the subsystems as numbers (i.e., ``[-1, 0, 2]``) or strings (``['ancilla', 'q1', 'q2']``). Default 1 if not specified. shots (None, int, list[int]): Number of circuit evaluations/random samples used to estimate expectation values of observables. If ``None``, the device calculates probability, expectation values, and variances analytically. If an integer, it specifies the number of samples to estimate these quantities. If a list of integers is passed, the circuit evaluations are batched over the list of shots. r_dtype: Real floating point precision type. c_dtype: Complex floating point precision type. """ # pylint: disable=too-many-public-methods _asarray = staticmethod(np.asarray) _dot = staticmethod(np.dot) _abs = staticmethod(np.abs) _reduce_sum = staticmethod(lambda array, axes: np.sum(array, axis=tuple(axes))) _reshape = staticmethod(np.reshape) _flatten = staticmethod(lambda array: array.flatten()) _gather = staticmethod(lambda array, indices: array[indices]) _einsum = staticmethod(np.einsum) _cast = staticmethod(np.asarray) _transpose = staticmethod(np.transpose) _tensordot = staticmethod(np.tensordot) _conj = staticmethod(np.conj) _imag = staticmethod(np.imag) _roll = staticmethod(np.roll) _stack = staticmethod(np.stack) _outer = staticmethod(np.outer) _diag = staticmethod(np.diag) _real = staticmethod(np.real) @staticmethod def _scatter(indices, array, new_dimensions): new_array = np.zeros(new_dimensions, dtype=array.dtype.type) new_array[indices] = array return new_array @staticmethod def _const_mul(constant, array): """Data type preserving multiply operation""" return qmlmul(constant, array, dtype=array.dtype) def _permute_wires(self, observable): r"""Given an observable which acts on multiple wires, permute the wires to be consistent with the device wire order. Suppose we are given an observable :math:`\hat{O} = \Identity \otimes \Identity \otimes \hat{Z}`. This observable can be represented in many ways: .. code-block:: python O_1 = qml.Identity(wires=0) @ qml.Identity(wires=1) @ qml.PauliZ(wires=2) O_2 = qml.PauliZ(wires=2) @ qml.Identity(wires=0) @ qml.Identity(wires=1) Notice that while the explicit tensor product matrix representation of :code:`O_1` and :code:`O_2` is different, the underlying operator is identical due to the wire labelling (assuming the labels in ascending order are {0,1,2}). If we wish to compute the expectation value of such an observable, we must ensure it is identical in both cases. To facilitate this, we permute the wires in our state vector such that they are consistent with this swapping of order in the tensor observable. .. code-block:: python >>> print(0_1.wires) <Wires = [0, 1, 2]> >>> print(O_2.wires) <Wires = [2, 0, 1]> We might naively think that we must permute our state vector to match the wire order of our tensor observable. We must be careful and realize that the wire order of the terms in the tensor observable DOES NOT match the permutation of the terms themselves. As an example we directly compare :code:`O_1` and :code:`O_2`: The first term in :code:`O_1` (:code:`qml.Identity(wires=0)`) became the second term in :code:`O_2`. By similar comparison we see that each term in the tensor product was shifted one position forward (i.e 0 --> 1, 1 --> 2, 2 --> 0). The wires in our permuted quantum state should follow their respective terms in the tensor product observable. Thus, the correct wire ordering should be :code:`permuted_wires = <Wires = [1, 2, 0]>`. But if we had taken the naive approach we would have permuted our state according to :code:`permuted_wires = <Wires = [2, 0, 1]>` which is NOT correct. This function uses the observable wires and the global device wire ordering in order to determine the permutation of the wires in the observable required such that if our quantum state vector is permuted accordingly then the amplitudes of the state will match the matrix representation of the observable. Args: observable (Observable): the observable whose wires are to be permuted. Returns: permuted_wires (Wires): permuted wires object """ ordered_obs_wire_lst = self.order_wires( observable.wires ).tolist() # order according to device wire order mapped_wires = self.map_wires(observable.wires) if isinstance(mapped_wires, Wires): # by default this should be a Wires obj, but it is overwritten to list object in default.qubit mapped_wires = mapped_wires.tolist() permutation = np.argsort(mapped_wires) # extract permutation via argsort permuted_wires = Wires([ordered_obs_wire_lst[index] for index in permutation]) return permuted_wires observables = { "PauliX", "PauliY", "PauliZ", "Hadamard", "Hermitian", "Identity", "Projector", } def __init__( self, wires=1, shots=None, *, r_dtype=np.float64, c_dtype=np.complex128, analytic=None ): super().__init__(wires=wires, shots=shots, analytic=analytic) if "float" not in str(r_dtype): raise DeviceError("Real datatype must be a floating point type.") if "complex" not in str(c_dtype): raise DeviceError("Complex datatype must be a complex floating point type.") self.C_DTYPE = c_dtype self.R_DTYPE = r_dtype self._samples = None """None or array[int]: stores the samples generated by the device *after* rotation to diagonalize the observables."""
[docs] @classmethod def capabilities(cls): capabilities = super().capabilities().copy() capabilities.update( model="qubit", supports_finite_shots=True, supports_tensor_observables=True, returns_probs=True, ) return capabilities
[docs] def reset(self): """Reset the backend state. After the reset, the backend should be as if it was just constructed. Most importantly the quantum state is reset to its initial value. """ self._samples = None
[docs] def execute(self, circuit, **kwargs): """Execute a queue of quantum operations on the device and then measure the given observables. For plugin developers: instead of overwriting this, consider implementing a suitable subset of * :meth:`apply` * :meth:`~.generate_samples` * :meth:`~.probability` Additional keyword arguments may be passed to the this method that can be utilised by :meth:`apply`. An example would be passing the ``QNode`` hash that can be used later for parametric compilation. Args: circuit (~.CircuitGraph): circuit to execute on the device Raises: QuantumFunctionError: if the value of :attr:`~.Observable.return_type` is not supported Returns: array[float]: measured value(s) """ self.check_validity(circuit.operations, circuit.observables) # apply all circuit operations self.apply(circuit.operations, rotations=circuit.diagonalizing_gates, **kwargs) # generate computational basis samples if self.shots is not None or circuit.is_sampled: self._samples = self.generate_samples() multiple_sampled_jobs = circuit.is_sampled and self._has_partitioned_shots() # compute the required statistics if not self.analytic and self._shot_vector is not None: results = [] s1 = 0 for shot_tuple in self._shot_vector: s2 = s1 + np.prod(shot_tuple) r = self.statistics( circuit.observables, shot_range=[s1, s2], bin_size=shot_tuple.shots ) if qml.math._multi_dispatch(r) == "jax": # pylint: disable=protected-access r = r[0] elif not isinstance(r[0], dict): # Measurement types except for Counts r = qml.math.squeeze(r) if isinstance(r, (np.ndarray, list)) and r.shape and isinstance(r[0], dict): # This happens when measurement type is Counts results.append(r) elif shot_tuple.copies > 1: results.extend(r.T) else: results.append(r.T) s1 = s2 if not multiple_sampled_jobs: # Can only stack single element outputs results = qml.math.stack(results) else: results = self.statistics(circuit.observables) if not circuit.is_sampled: ret_types = [m.return_type for m in circuit.measurements] if len(circuit.measurements) == 1: if circuit.measurements[0].return_type is qml.measurements.State: # State: assumed to only be allowed if it's the only measurement results = self._asarray(results, dtype=self.C_DTYPE) elif circuit.measurements[0].return_type is not qml.measurements.Counts: # Measurements with expval, var or probs results = self._asarray(results, dtype=self.R_DTYPE) elif all( ret in (qml.measurements.Expectation, qml.measurements.Variance) for ret in ret_types ): # Measurements with expval or var results = self._asarray(results, dtype=self.R_DTYPE) elif any(ret is not qml.measurements.Counts for ret in ret_types): # all the other cases except all counts results = self._asarray(results) elif circuit.all_sampled and not self._has_partitioned_shots(): results = self._asarray(results) else: results = tuple(self._asarray(r) for r in results) # increment counter for number of executions of qubit device self._num_executions += 1 if self.tracker.active: self.tracker.update(executions=1, shots=self._shots) self.tracker.record() return results
[docs] def batch_execute(self, circuits): """Execute a batch of quantum circuits on the device. The circuits are represented by tapes, and they are executed one-by-one using the device's ``execute`` method. The results are collected in a list. For plugin developers: This function should be overwritten if the device can efficiently run multiple circuits on a backend, for example using parallel and/or asynchronous executions. Args: circuits (list[.tapes.QuantumTape]): circuits to execute on the device Returns: list[array[float]]: list of measured value(s) """ # TODO: This method and the tests can be globally implemented by Device # once it has the same signature in the execute() method results = [] for circuit in circuits: # we need to reset the device here, else it will # not start the next computation in the zero state self.reset() res = self.execute(circuit) results.append(res) if self.tracker.active: self.tracker.update(batches=1, batch_len=len(circuits)) self.tracker.record() return results
[docs] @abc.abstractmethod def apply(self, operations, **kwargs): """Apply quantum operations, rotate the circuit into the measurement basis, and compile and execute the quantum circuit. This method receives a list of quantum operations queued by the QNode, and should be responsible for: * Constructing the quantum program * (Optional) Rotating the quantum circuit using the rotation operations provided. This diagonalizes the circuit so that arbitrary observables can be measured in the computational basis. * Compile the circuit * Execute the quantum circuit Both arguments are provided as lists of PennyLane :class:`~.Operation` instances. Useful properties include :attr:`~.Operation.name`, :attr:`~.Operation.wires`, and :attr:`~.Operation.parameters`, and :attr:`~.Operation.inverse`: >>> op = qml.RX(0.2, wires=[0]) >>> op.name # returns the operation name "RX" >>> op.wires # returns a Wires object representing the wires that the operation acts on <Wires = [0]> >>> op.parameters # returns a list of parameters [0.2] >>> op.inverse # check if the operation should be inverted False >>> op = qml.RX(0.2, wires=[0]).inv >>> op.inverse True Args: operations (list[~.Operation]): operations to apply to the device Keyword args: rotations (list[~.Operation]): operations that rotate the circuit pre-measurement into the eigenbasis of the observables. hash (int): the hash value of the circuit constructed by `CircuitGraph.hash` """
[docs] @staticmethod def active_wires(operators): """Returns the wires acted on by a set of operators. Args: operators (list[~.Operation]): operators for which we are gathering the active wires Returns: Wires: wires activated by the specified operators """ list_of_wires = [op.wires for op in operators] return Wires.all_wires(list_of_wires)
[docs] def statistics(self, observables, shot_range=None, bin_size=None): """Process measurement results from circuit execution and return statistics. This includes returning expectation values, variance, samples, probabilities, states, and density matrices. Args: observables (List[.Observable]): the observables to be measured shot_range (tuple[int]): 2-tuple of integers specifying the range of samples to use. If not specified, all samples are used. bin_size (int): Divides the shot range into bins of size ``bin_size``, and returns the measurement statistic separately over each bin. If not provided, the entire shot range is treated as a single bin. Raises: QuantumFunctionError: if the value of :attr:`~.Observable.return_type` is not supported Returns: Union[float, List[float]]: the corresponding statistics .. details:: :title: Usage Details The ``shot_range`` and ``bin_size`` arguments allow for the statistics to be performed on only a subset of device samples. This finer level of control is accessible from the main UI by instantiating a device with a batch of shots. For example, consider the following device: >>> dev = qml.device("my_device", shots=[5, (10, 3), 100]) This device will execute QNodes using 135 shots, however measurement statistics will be **course grained** across these 135 shots: * All measurement statistics will first be computed using the first 5 shots --- that is, ``shots_range=[0, 5]``, ``bin_size=5``. * Next, the tuple ``(10, 3)`` indicates 10 shots, repeated 3 times. We will want to use ``shot_range=[5, 35]``, performing the expectation value in bins of size 10 (``bin_size=10``). * Finally, we repeat the measurement statistics for the final 100 shots, ``shot_range=[35, 135]``, ``bin_size=100``. """ results = [] for obs in observables: # Pass instances directly if obs.return_type is Expectation: results.append(self.expval(obs, shot_range=shot_range, bin_size=bin_size)) elif obs.return_type is Variance: results.append(self.var(obs, shot_range=shot_range, bin_size=bin_size)) elif obs.return_type is Sample: results.append( self.sample(obs, shot_range=shot_range, bin_size=bin_size, counts=False) ) elif obs.return_type is Counts: results.append( self.sample(obs, shot_range=shot_range, bin_size=bin_size, counts=True) ) elif obs.return_type is Probability: results.append( self.probability(wires=obs.wires, shot_range=shot_range, bin_size=bin_size) ) elif obs.return_type is State: if len(observables) > 1: raise qml.QuantumFunctionError( "The state or density matrix cannot be returned in combination" " with other return types" ) # Check if the state is accessible and decide to return the state or the density # matrix. results.append(self.access_state(wires=obs.wires)) elif obs.return_type is VnEntropy: if self.wires.labels != tuple(range(self.num_wires)): raise qml.QuantumFunctionError( "Returning the Von Neumann entropy is not supported when using custom wire labels" ) results.append(self.vn_entropy(wires=obs.wires, log_base=obs.log_base)) elif obs.return_type is MutualInfo: if self.wires.labels != tuple(range(self.num_wires)): raise qml.QuantumFunctionError( "Returning the mutual information is not supported when using custom wire labels" ) wires0, wires1 = obs.raw_wires results.append( self.mutual_info(wires0=wires0, wires1=wires1, log_base=obs.log_base) ) elif obs.return_type is not None: raise qml.QuantumFunctionError( f"Unsupported return type specified for observable {obs.name}" ) return results
[docs] def access_state(self, wires=None): """Check that the device has access to an internal state and return it if available. Args: wires (Wires): wires of the reduced system Raises: QuantumFunctionError: if the device is not capable of returning the state Returns: array or tensor: the state or the density matrix of the device """ if not self.capabilities().get("returns_state"): raise qml.QuantumFunctionError( "The current device is not capable of returning the state" ) state = getattr(self, "state", None) if state is None: raise qml.QuantumFunctionError("The state is not available in the current device") if wires: density_matrix = self.density_matrix(wires) return density_matrix return state
[docs] def generate_samples(self): r"""Returns the computational basis samples generated for all wires. Note that PennyLane uses the convention :math:`|q_0,q_1,\dots,q_{N-1}\rangle` where :math:`q_0` is the most significant bit. .. warning:: This method should be overwritten on devices that generate their own computational basis samples, with the resulting computational basis samples stored as ``self._samples``. Returns: array[complex]: array of samples in the shape ``(dev.shots, dev.num_wires)`` """ number_of_states = 2**self.num_wires rotated_prob = self.analytic_probability() samples = self.sample_basis_states(number_of_states, rotated_prob) return QubitDevice.states_to_binary(samples, self.num_wires)
[docs] def sample_basis_states(self, number_of_states, state_probability): """Sample from the computational basis states based on the state probability. This is an auxiliary method to the generate_samples method. Args: number_of_states (int): the number of basis states to sample from state_probability (array[float]): the computational basis probability vector Returns: array[int]: the sampled basis states """ if self.shots is None: raise qml.QuantumFunctionError( "The number of shots has to be explicitly set on the device " "when using sample-based measurements." ) shots = self.shots basis_states = np.arange(number_of_states) return np.random.choice(basis_states, shots, p=state_probability)
[docs] @staticmethod def generate_basis_states(num_wires, dtype=np.uint32): """ Generates basis states in binary representation according to the number of wires specified. The states_to_binary method creates basis states faster (for larger systems at times over x25 times faster) than the approach using ``itertools.product``, at the expense of using slightly more memory. Due to the large size of the integer arrays for more than 32 bits, memory allocation errors may arise in the states_to_binary method. Hence we constraint the dtype of the array to represent unsigned integers on 32 bits. Due to this constraint, an overflow occurs for 32 or more wires, therefore this approach is used only for fewer wires. For smaller number of wires speed is comparable to the next approach (using ``itertools.product``), hence we resort to that one for testing purposes. Args: num_wires (int): the number wires dtype=np.uint32 (type): the data type of the arrays to use Returns: array[int]: the sampled basis states """ if 2 < num_wires < 32: states_base_ten = np.arange(2**num_wires, dtype=dtype) return QubitDevice.states_to_binary(states_base_ten, num_wires, dtype=dtype) # A slower, but less memory intensive method basis_states_generator = itertools.product((0, 1), repeat=num_wires) return np.fromiter(itertools.chain(*basis_states_generator), dtype=int).reshape( -1, num_wires )
[docs] @staticmethod def states_to_binary(samples, num_wires, dtype=np.int64): """Convert basis states from base 10 to binary representation. This is an auxiliary method to the generate_samples method. Args: samples (array[int]): samples of basis states in base 10 representation num_wires (int): the number of qubits dtype (type): Type of the internal integer array to be used. Can be important to specify for large systems for memory allocation purposes. Returns: array[int]: basis states in binary representation """ powers_of_two = 1 << np.arange(num_wires, dtype=dtype) states_sampled_base_ten = samples[:, None] & powers_of_two return (states_sampled_base_ten > 0).astype(dtype)[:, ::-1]
@property def circuit_hash(self): """The hash of the circuit upon the last execution. This can be used by devices in :meth:`~.apply` for parametric compilation. """ raise NotImplementedError @property def state(self): """Returns the state vector of the circuit prior to measurement. .. note:: Only state vector simulators support this property. Please see the plugin documentation for more details. """ raise NotImplementedError
[docs] def density_matrix(self, wires): """Returns the reduced density matrix over the given wires. Args: wires (Wires): wires of the reduced system Returns: array[complex]: complex array of shape ``(2 ** len(wires), 2 ** len(wires))`` representing the reduced density matrix of the state prior to measurement. """ state = getattr(self, "state", None) wires = self.map_wires(wires) return qml.math.reduced_dm(state, indices=wires, c_dtype=self.C_DTYPE)
[docs] def vn_entropy(self, wires, log_base): r"""Returns the Von Neumann entropy prior to measurement. .. math:: S( \rho ) = -\text{Tr}( \rho \log ( \rho )) Args: wires (Wires): Wires of the considered subsystem. log_base (float): Base for the logarithm, default is None the natural logarithm is used in this case. Returns: float: returns the Von Neumann entropy """ try: state = self.access_state() except qml.QuantumFunctionError as e: # pragma: no cover raise NotImplementedError( f"Cannot compute the Von Neumman entropy with device {self.name} that is not capable of returning the " f"state. " ) from e wires = wires.tolist() return qml.math.vn_entropy(state, indices=wires, c_dtype=self.C_DTYPE, base=log_base)
[docs] def mutual_info(self, wires0, wires1, log_base): r"""Returns the mutual information prior to measurement: .. math:: I(A, B) = S(\rho^A) + S(\rho^B) - S(\rho^{AB}) where :math:`S` is the von Neumann entropy. Args: wires0 (Wires): wires of the first subsystem wires1 (Wires): wires of the second subsystem log_base (float): base to use in the logarithm Returns: float: the mutual information """ try: state = self.access_state() except qml.QuantumFunctionError as e: # pragma: no cover raise NotImplementedError( f"Cannot compute the mutual information with device {self.name} that is not capable of returning the " f"state. " ) from e wires0 = wires0.tolist() wires1 = wires1.tolist() return qml.math.mutual_info( state, indices0=wires0, indices1=wires1, c_dtype=self.C_DTYPE, base=log_base )
[docs] def analytic_probability(self, wires=None): r"""Return the (marginal) probability of each computational basis state from the last run of the device. PennyLane uses the convention :math:`|q_0,q_1,\dots,q_{N-1}\rangle` where :math:`q_0` is the most significant bit. If no wires are specified, then all the basis states representable by the device are considered and no marginalization takes place. .. note:: :meth:`marginal_prob` may be used as a utility method to calculate the marginal probability distribution. Args: wires (Iterable[Number, str], Number, str, Wires): wires to return marginal probabilities for. Wires not provided are traced out of the system. Returns: array[float]: list of the probabilities """ raise NotImplementedError
[docs] def estimate_probability(self, wires=None, shot_range=None, bin_size=None): """Return the estimated probability of each computational basis state using the generated samples. Args: wires (Iterable[Number, str], Number, str, Wires): wires to calculate marginal probabilities for. Wires not provided are traced out of the system. shot_range (tuple[int]): 2-tuple of integers specifying the range of samples to use. If not specified, all samples are used. bin_size (int): Divides the shot range into bins of size ``bin_size``, and returns the measurement statistic separately over each bin. If not provided, the entire shot range is treated as a single bin. Returns: array[float]: list of the probabilities """ wires = wires or self.wires # convert to a wires object wires = Wires(wires) # translate to wire labels used by device device_wires = self.map_wires(wires) sample_slice = Ellipsis if shot_range is None else slice(*shot_range) samples = self._samples[sample_slice, device_wires] # convert samples from a list of 0, 1 integers, to base 10 representation powers_of_two = 2 ** np.arange(len(device_wires))[::-1] indices = samples @ powers_of_two # count the basis state occurrences, and construct the probability vector if bin_size is not None: bins = len(samples) // bin_size indices = indices.reshape((bins, -1)) prob = np.zeros([2 ** len(device_wires), bins], dtype=np.float64) # count the basis state occurrences, and construct the probability vector for b, idx in enumerate(indices): basis_states, counts = np.unique(idx, return_counts=True) prob[basis_states, b] = counts / bin_size else: basis_states, counts = np.unique(indices, return_counts=True) prob = np.zeros([2 ** len(device_wires)], dtype=np.float64) prob[basis_states] = counts / len(samples) return self._asarray(prob, dtype=self.R_DTYPE)
[docs] def probability(self, wires=None, shot_range=None, bin_size=None): """Return either the analytic probability or estimated probability of each computational basis state. Devices that require a finite number of shots always return the estimated probability. Args: wires (Iterable[Number, str], Number, str, Wires): wires to return marginal probabilities for. Wires not provided are traced out of the system. Returns: array[float]: list of the probabilities """ if self.shots is None: return self.analytic_probability(wires=wires) return self.estimate_probability(wires=wires, shot_range=shot_range, bin_size=bin_size)
[docs] def marginal_prob(self, prob, wires=None): r"""Return the marginal probability of the computational basis states by summing the probabiliites on the non-specified wires. If no wires are specified, then all the basis states representable by the device are considered and no marginalization takes place. .. note:: If the provided wires are not in the order as they appear on the device, the returned marginal probabilities take this permutation into account. For example, if the addressable wires on this device are ``Wires([0, 1, 2])`` and this function gets passed ``wires=[2, 0]``, then the returned marginal probability vector will take this 'reversal' of the two wires into account: .. math:: \mathbb{P}^{(2, 0)} = \left[ |00\rangle, |10\rangle, |01\rangle, |11\rangle \right] Args: prob: The probabilities to return the marginal probabilities for wires (Iterable[Number, str], Number, str, Wires): wires to return marginal probabilities for. Wires not provided are traced out of the system. Returns: array[float]: array of the resulting marginal probabilities. """ if wires is None: # no need to marginalize return prob wires = Wires(wires) # determine which subsystems are to be summed over inactive_wires = Wires.unique_wires([self.wires, wires]) # translate to wire labels used by device device_wires = self.map_wires(wires) inactive_device_wires = self.map_wires(inactive_wires) # reshape the probability so that each axis corresponds to a wire prob = self._reshape(prob, [2] * self.num_wires) # sum over all inactive wires # hotfix to catch when default.qubit uses this method # since then device_wires is a list if isinstance(inactive_device_wires, Wires): prob = self._flatten(self._reduce_sum(prob, inactive_device_wires.labels)) else: prob = self._flatten(self._reduce_sum(prob, inactive_device_wires)) # The wires provided might not be in consecutive order (i.e., wires might be [2, 0]). # If this is the case, we must permute the marginalized probability so that # it corresponds to the orders of the wires passed. num_wires = len(device_wires) basis_states = self.generate_basis_states(num_wires) basis_states = basis_states[:, np.argsort(np.argsort(device_wires))] powers_of_two = 2 ** np.arange(len(device_wires))[::-1] perm = basis_states @ powers_of_two return self._gather(prob, perm)
[docs] def expval(self, observable, shot_range=None, bin_size=None): if observable.name == "Projector": # branch specifically to handle the projector observable idx = int("".join(str(i) for i in observable.parameters[0]), 2) probs = self.probability( wires=observable.wires, shot_range=shot_range, bin_size=bin_size ) return probs[idx] # exact expectation value if self.shots is None: try: eigvals = self._asarray(observable.eigvals(), dtype=self.R_DTYPE) except qml.operation.EigvalsUndefinedError as e: raise qml.operation.EigvalsUndefinedError( f"Cannot compute analytic expectations of {observable.name}." ) from e # the probability vector must be permuted to account for the permuted wire order of the observable permuted_wires = self._permute_wires(observable) prob = self.probability(wires=permuted_wires) return self._dot(eigvals, prob) # estimate the ev samples = self.sample(observable, shot_range=shot_range, bin_size=bin_size) return np.squeeze(np.mean(samples, axis=0))
[docs] def var(self, observable, shot_range=None, bin_size=None): if observable.name == "Projector": # branch specifically to handle the projector observable idx = int("".join(str(i) for i in observable.parameters[0]), 2) probs = self.probability( wires=observable.wires, shot_range=shot_range, bin_size=bin_size ) return probs[idx] - probs[idx] ** 2 # exact variance value if self.shots is None: try: eigvals = self._asarray(observable.eigvals(), dtype=self.R_DTYPE) except qml.operation.EigvalsUndefinedError as e: # if observable has no info on eigenvalues, we cannot return this measurement raise qml.operation.EigvalsUndefinedError( f"Cannot compute analytic variance of {observable.name}." ) from e # the probability vector must be permuted to account for the permuted wire order of the observable permuted_wires = self._permute_wires(observable) prob = self.probability(wires=permuted_wires) return self._dot((eigvals**2), prob) - self._dot(eigvals, prob) ** 2 # estimate the variance samples = self.sample(observable, shot_range=shot_range, bin_size=bin_size) return np.squeeze(np.var(samples, axis=0))
[docs] def sample(self, observable, shot_range=None, bin_size=None, counts=False): def _samples_to_counts(samples, no_observable_provided): """Group the obtained samples into a dictionary. **Example** >>> samples tensor([[0, 0, 1], [0, 0, 1], [1, 1, 1]], requires_grad=True) >>> self._samples_to_counts(samples) {'111':1, '001':2} """ if no_observable_provided: # If we describe a state vector, we need to convert its list representation # into string (it's hashable and good-looking). # Before converting to str, we need to extract elements from arrays # to satisfy the case of jax interface, as jax arrays do not support str. samples = ["".join([str(s.item()) for s in sample]) for sample in samples] states, counts = np.unique(samples, return_counts=True) return dict(zip(states, counts)) # translate to wire labels used by device device_wires = self.map_wires(observable.wires) name = observable.name sample_slice = Ellipsis if shot_range is None else slice(*shot_range) no_observable_provided = isinstance(observable, MeasurementProcess) if isinstance(name, str) and name in {"PauliX", "PauliY", "PauliZ", "Hadamard"}: # Process samples for observables with eigenvalues {1, -1} samples = 1 - 2 * self._samples[sample_slice, device_wires[0]] elif no_observable_provided: # if no observable was provided then return the raw samples if ( len(observable.wires) != 0 ): # if wires are provided, then we only return samples from those wires samples = self._samples[sample_slice, np.array(device_wires)] else: samples = self._samples[sample_slice] else: # Replace the basis state in the computational basis with the correct eigenvalue. # Extract only the columns of the basis samples required based on ``wires``. samples = self._samples[ sample_slice, np.array(device_wires) ] # Add np.array here for Jax support. powers_of_two = 2 ** np.arange(samples.shape[-1])[::-1] indices = samples @ powers_of_two indices = np.array(indices) # Add np.array here for Jax support. try: samples = observable.eigvals()[indices] except qml.operation.EigvalsUndefinedError as e: # if observable has no info on eigenvalues, we cannot return this measurement raise qml.operation.EigvalsUndefinedError( f"Cannot compute samples of {observable.name}." ) from e if bin_size is None: if counts: return _samples_to_counts(samples, no_observable_provided) return samples if counts: shape = (-1, bin_size, 3) if no_observable_provided else (-1, bin_size) return [ _samples_to_counts(bin_sample, no_observable_provided) for bin_sample in samples.reshape(shape) ] return ( samples.reshape((3, bin_size, -1)) if no_observable_provided else samples.reshape((bin_size, -1)) )
[docs] def adjoint_jacobian(self, tape, starting_state=None, use_device_state=False): """Implements the adjoint method outlined in `Jones and Gacon <https://arxiv.org/abs/2009.02823>`__ to differentiate an input tape. After a forward pass, the circuit is reversed by iteratively applying inverse (adjoint) gates to scan backwards through the circuit. .. note:: The adjoint differentiation method has the following restrictions: * As it requires knowledge of the statevector, only statevector simulator devices can be used. * Only expectation values are supported as measurements. * Does not work for parametrized observables like :class:`~.Hamiltonian` or :class:`~.Hermitian`. Args: tape (.QuantumTape): circuit that the function takes the gradient of Keyword Args: starting_state (tensor_like): post-forward pass state to start execution with. It should be complex-valued. Takes precedence over ``use_device_state``. use_device_state (bool): use current device state to initialize. A forward pass of the same circuit should be the last thing the device has executed. If a ``starting_state`` is provided, that takes precedence. Returns: array: the derivative of the tape with respect to trainable parameters. Dimensions are ``(len(observables), len(trainable_params))``. Raises: QuantumFunctionError: if the input tape has measurements that are not expectation values or contains a multi-parameter operation aside from :class:`~.Rot` """ # broadcasted inner product not summing over first dimension of b sum_axes = tuple(range(1, self.num_wires + 1)) # pylint: disable=unnecessary-lambda-assignment) dot_product_real = lambda b, k: self._real(qmlsum(self._conj(b) * k, axis=sum_axes)) for m in tape.measurements: if m.return_type is not Expectation: raise qml.QuantumFunctionError( "Adjoint differentiation method does not support" f" measurement {m.return_type.value}" ) if m.obs.name == "Hamiltonian": raise qml.QuantumFunctionError( "Adjoint differentiation method does not support Hamiltonian observables." ) if not hasattr(m.obs, "base_name"): m.obs.base_name = None # This is needed for when the observable is a tensor product if self.shots is not None: warnings.warn( "Requested adjoint differentiation to be computed with finite shots." " The derivative is always exact when using the adjoint differentiation method.", UserWarning, ) # Initialization of state if starting_state is not None: ket = self._reshape(starting_state, [2] * self.num_wires) else: if not use_device_state: self.reset() self.execute(tape) ket = self._pre_rotated_state n_obs = len(tape.observables) bras = np.empty([n_obs] + [2] * self.num_wires, dtype=np.complex128) for kk in range(n_obs): bras[kk, ...] = self._apply_operation(ket, tape.observables[kk]) expanded_ops = [] for op in reversed(tape.operations): if op.num_params > 1: if isinstance(op, qml.Rot) and not op.inverse: ops = op.decomposition() expanded_ops.extend(reversed(ops)) else: raise qml.QuantumFunctionError( f"The {op.name} operation is not supported using " 'the "adjoint" differentiation method' ) else: if op.name not in ("QubitStateVector", "BasisState", "Snapshot"): expanded_ops.append(op) trainable_params = [] for k in tape.trainable_params: # pylint: disable=protected-access if hasattr(tape._par_info[k]["op"], "return_type"): warnings.warn( "Differentiating with respect to the input parameters of " f"{tape._par_info[k]['op'].name} is not supported with the " "adjoint differentiation method. Gradients are computed " "only with regards to the trainable parameters of the circuit.\n\n Mark " "the parameters of the measured observables as non-trainable " "to silence this warning.", UserWarning, ) else: trainable_params.append(k) jac = np.zeros((len(tape.observables), len(trainable_params))) param_number = len(tape.get_parameters(trainable_only=False, operations_only=True)) - 1 trainable_param_number = len(trainable_params) - 1 for op in expanded_ops: if (op.grad_method is not None) and (param_number in trainable_params): d_op_matrix = operation_derivative(op) op.inv() # Ideally use use op.adjoint() here # then we don't have to re-invert the operation at the end ket = self._apply_operation(ket, op) if op.grad_method is not None: if param_number in trainable_params: ket_temp = self._apply_unitary(ket, d_op_matrix, op.wires) jac[:, trainable_param_number] = 2 * dot_product_real(bras, ket_temp) trainable_param_number -= 1 param_number -= 1 for kk in range(n_obs): bras[kk, ...] = self._apply_operation(bras[kk, ...], op) op.inv() return jac