Add Task and Simulation utilities for Discrete Time Crystal Experiments

recirq/time_crystals/__init__.py

@@ -18,3 +18,9 @@
     EXPERIMENT_NAME,
     DEFAULT_BASE_DIR,
 )
+
+from recirq.time_crystals.dtc_simulation import (
+    run_comparison_experiment,
+    signal_ratio,
+    symbolic_dtc_circuit_list,
+)

recirq/time_crystals/dtc_simulation.py

@@ -0,0 +1,357 @@
+# Copyright 2022 Google
+#
+# 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
+#
+#     https://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.
+
+from typing import Sequence, Tuple, List, Iterator
+
+import functools
+import numpy as np
+import sympy as sp
+
+import cirq
+from recirq.time_crystals.dtcexperiment import DTCExperiment, comparison_experiments
+
+
+def symbolic_dtc_circuit_list(
+    qubits: Sequence[cirq.Qid], cycles: int
+) -> List[cirq.Circuit]:
+    """Create a list of symbolically parameterized dtc circuits, with increasing cycles
+
+    Args:
+        qubits: ordered sequence of available qubits, which are connected in a chain
+        cycles: maximum number of cycles to generate up to
+
+    Returns:
+        list of circuits with `0, 1, 2, ... cycles` many cycles
+
+    """
+    num_qubits = len(qubits)
+
+    # Symbol for g
+    g_value = sp.Symbol("g")
+
+    # Symbols for random variance (h) and initial state, one per qubit
+    local_fields = sp.symbols(f"local_field_:{num_qubits}")
+    initial_state = sp.symbols(f"initial_state_:{num_qubits}")
+
+    # Symbols used for PhasedFsimGate, one for every qubit pair in the chain
+    thetas = sp.symbols(f"theta_:{num_qubits - 1}")
+    zetas = sp.symbols(f"zeta_:{num_qubits - 1}")
+    chis = sp.symbols(f"chi_:{num_qubits - 1}")
+    gammas = sp.symbols(f"gamma_:{num_qubits - 1}")
+    phis = sp.symbols(f"phi_:{num_qubits - 1}")
+
+    # Initial moment of Y gates, conditioned on initial state
+    initial_operations = cirq.Moment(
+        [cirq.Y(qubit) ** initial_state[index] for index, qubit in enumerate(qubits)]
+    )
+
+    # First component of U cycle, a moment of XZ gates.
+    sequence_operations = []
+    for index, qubit in enumerate(qubits):
+        sequence_operations.append(
+            cirq.PhasedXZGate(
+                x_exponent=g_value,
+                axis_phase_exponent=0.0,
+                z_exponent=local_fields[index],
+            )(qubit)
+        )
+
+    # Initialize U cycle
+    u_cycle = [cirq.Moment(sequence_operations)]
+
+    # Second and third components of U cycle, a chain of 2-qubit PhasedFSim gates
+    #   The first component is all the 2-qubit PhasedFSim gates starting on even qubits
+    #   The second component is the 2-qubit gates starting on odd qubits
+    even_qubit_moment = []
+    odd_qubit_moment = []
+    for index, (qubit, next_qubit) in enumerate(zip(qubits, qubits[1:])):
+        # Add an fsim gate
+        coupling_gate = cirq.ops.PhasedFSimGate(
+            theta=thetas[index],
+            zeta=zetas[index],
+            chi=chis[index],
+            gamma=gammas[index],
+            phi=phis[index],
+        )
+
+        if index % 2:
+            even_qubit_moment.append(coupling_gate.on(qubit, next_qubit))
+        else:
+            odd_qubit_moment.append(coupling_gate.on(qubit, next_qubit))
+
+    # Add the two components into the U cycle
+    u_cycle.append(cirq.Moment(even_qubit_moment))
+    u_cycle.append(cirq.Moment(odd_qubit_moment))
+
+    # Prepare a list of circuits, with n=0,1,2,3 ... cycles many cycles
+    circuit_list = []
+    total_circuit = cirq.Circuit(initial_operations)
+    circuit_list.append(total_circuit.copy())
+    for _ in range(cycles):
+        for moment in u_cycle:
+            total_circuit.append(moment)
+        circuit_list.append(total_circuit.copy())
+
+    return circuit_list
+
+
+def simulate_dtc_circuit_list(
+    circuit_list: Sequence[cirq.Circuit],
+    param_resolver: cirq.ParamResolver,
+    qubit_order: Sequence[cirq.Qid],
+    simulator: "cirq.SimulatesIntermediateState" = None,
+) -> np.ndarray:
+    """Simulate a dtc circuit list for a particular param_resolver
+
+        Utilizes the fact that simulating the last circuit in the list also
+            simulates each previous circuit along the way
+
+    Args:
+        circuit_list: DTC circuit list; each element is a circuit with
+            increasingly many cycles
+        param_resolver: `cirq.ParamResolver` to resolve symbolic parameters
+        qubit_order: ordered sequence of qubits connected in a chain
+        simulator: Optional simulator object which must
+            support the `simulate_moment_steps` function
+
+    Returns:
+        `np.ndarray` of shape (len(circuit_list), 2**number of qubits) representing
+            the probability of measuring each bit string, for each circuit in the list
+
+    """
+    # prepare simulator
+    if simulator is None:
+        simulator = cirq.Simulator()
+
+    # record lengths of circuits in list
+    if not all(len(x) < len(y) for x, y in zip(circuit_list, circuit_list[1:])):
+        raise ValueError("circuits in circuit_list are not in increasing order of size")
+    circuit_positions = {len(c) - 1 for c in circuit_list}
+
+    # only simulate one circuit, the last one
+    circuit = circuit_list[-1]
+
+    # use simulate_moment_steps to recover all of the state vectors necessary,
+    #   while only simulating the circuit list once
+    probabilities = []
+    for k, step in enumerate(
+        simulator.simulate_moment_steps(
+            circuit=circuit, param_resolver=param_resolver, qubit_order=qubit_order
+        )
+    ):
+        # add the state vector if the number of moments simulated so far is equal
+        #   to the length of a circuit in the circuit_list
+        if k in circuit_positions:
+            probabilities.append(np.abs(step.state_vector()) ** 2)
+
+    return np.asarray(probabilities)
+
+
+def simulate_dtc_circuit_list_sweep(
+    circuit_list: Sequence[cirq.Circuit],
+    param_resolvers: Sequence[cirq.ParamResolver],
+    qubit_order: Sequence[cirq.Qid],
+) -> Iterator[np.ndarray]:
+    """Simulate a dtc circuit list over a sweep of param_resolvers
+
+    Args:
+        circuit_list: DTC circuit list; each element is a circuit with
+            increasingly many cycles
+        param_resolvers: list of `cirq.ParamResolver`s to sweep over
+        qubit_order: ordered sequence of qubits connected in a chain
+
+    Yields:
+        for each param_resolver, `np.ndarray`s of shape
+            (len(circuit_list), 2**number of qubits) representing the probability
+            of measuring each bit string, for each circuit in the list
+
+    """
+    # iterate over param resolvers and simulate for each
+    for param_resolver in param_resolvers:
+        yield simulate_dtc_circuit_list(circuit_list, param_resolver, qubit_order)
+
+
+def get_polarizations(
+    probabilities: np.ndarray,
+    num_qubits: int,
+    initial_states: np.ndarray = None,
+) -> np.ndarray:
+    """Get polarizations from matrix of probabilities, possibly autocorrelated on
+        the initial state.
+
+    A polarization is the marginal probability for a qubit to measure zero or one,
+        over all possible basis states, scaled to the range [-1. 1].
+
+    Args:
+        probabilities: `np.ndarray` of shape (:, cycles, 2**qubits)
+            representing probability to measure each bit string
+        num_qubits: the number of qubits in the circuit the probabilities
+            were generated from
+        initial_states: `np.ndarray` of shape (:, qubits) representing the initial
+            state for each dtc circuit list
+
+    Returns:
+        `np.ndarray` of shape (:, cycles, qubits) that represents each
+            qubit's polarization
+
+    """
+    # prepare list of polarizations for each qubit
+    polarizations = []
+    for qubit_index in range(num_qubits):
+        # select all indices in range(2**num_qubits) for which the
+        #   associated element of the statevector has qubit_index as zero
+        shift_by = num_qubits - qubit_index - 1
+        state_vector_indices = [
+            i for i in range(2**num_qubits) if not (i >> shift_by) % 2
+        ]
+
+        # sum over all probabilities for qubit states for which qubit_index is zero,
+        #   and rescale them to [-1,1]
+        polarization = (
+            2.0
+            * np.sum(
+                probabilities.take(indices=state_vector_indices, axis=-1),
+                axis=-1,
+            )
+            - 1.0
+        )
+        polarizations.append(polarization)
+
+    # turn polarizations list into an array,
+    #   and move the new, leftmost axis for qubits to the end
+    polarizations = np.moveaxis(np.asarray(polarizations), 0, -1)
+
+    # flip polarizations according to the associated initial_state, if provided
+    #   this means that the polarization of a qubit is relative to it's initial state
+    if initial_states is not None:
+        initial_states = 1 - 2.0 * initial_states
+        polarizations = initial_states * polarizations
+
+    return polarizations
+
+
+def signal_ratio(zeta_1: np.ndarray, zeta_2: np.ndarray) -> np.ndarray:
+    """Calculate signal ratio between two signals
+
+    Signal ratio measures how different two signals are,
+        proportional to how large they are.
+
+    Args:
+        zeta_1: signal (`np.ndarray` to represent polarization over time)
+        zeta 2: signal (`np.ndarray` to represent polarization over time)
+
+    Returns:
+        computed ratio of the signals zeta_1 and zeta_2 (`np.ndarray`)
+            to represent polarization over time)
+
+    """
+    return np.abs(zeta_1 - zeta_2) / (np.abs(zeta_1) + np.abs(zeta_2))
+
+
+def simulate_for_polarizations(
+    dtcexperiment: DTCExperiment,
+    circuit_list: Sequence[cirq.Circuit],
+    autocorrelate: bool = True,
+    take_abs: bool = False,
+) -> np.ndarray:
+    """Simulate and get polarizations for a single DTCExperiment and circuit list
+
+    Args:
+        dtcexperiment: DTCExperiment noting the parameters to simulate over some
+            number of disorder instances
+        circuit_list: symbolic dtc circuit list
+        autocorrelate: whether or not to autocorrelate the polarizations with their
+            respective initial states
+        take_abs: whether or not to take the absolute value of the polarizations
+
+    Returns:
+        simulated polarizations (np.ndarray of shape (num_cycles, num_qubits)) from
+            the experiment, averaged over disorder instances
+
+    """
+    # create param resolver sweep
+    param_resolvers = dtcexperiment.param_resolvers()
+
+    # prepare simulation generator
+    probabilities_generator = simulate_dtc_circuit_list_sweep(
+        circuit_list, param_resolvers, dtcexperiment.qubits
+    )
+
+    # map get_polarizations over probabilities_generator
+    polarizations_generator = map(
+        lambda probabilities, initial_state: get_polarizations(
+            probabilities,
+            num_qubits=len(dtcexperiment.qubits),
+            initial_states=(initial_state if autocorrelate else None),
+        ),
+        probabilities_generator,
+        dtcexperiment.initial_states,
+    )
+
+    # take sum of (absolute value of) polarizations over different disorder instances
+    polarization_sum = functools.reduce(
+        lambda x, y: x + (np.abs(y) if take_abs else y),
+        polarizations_generator,
+        np.zeros((len(circuit_list), len(dtcexperiment.qubits))),
+    )
+
+    # get average over disorder instances
+    disorder_averaged_polarizations = (
+        polarization_sum / dtcexperiment.disorder_instances
+    )
+
+    return disorder_averaged_polarizations
+
+
+def run_comparison_experiment(
+    qubits: Sequence[cirq.Qid],
+    cycles: int,
+    disorder_instances: int,
+    autocorrelate: bool = True,
+    take_abs: bool = False,
+    **kwargs,
+) -> Iterator[np.ndarray]:
+    """Run multiple DTC experiments for qubit polarizations over different parameters.
+
+    This uses the default parameter options noted in
+        `dtcexperiment.comparison_experiments` for any parameter not supplied in
+        kwargs. A DTC experiment is then created and simulated for each possible
+        parameter combination before qubit polarizations by DTC cycle are
+        computed and yielded. Each yield is an `np.ndarray` of shape (qubits, cycles)
+        for a specific combination of parameters.
+
+    Args:
+        qubits: ordered sequence of available qubits, which are connected in a chain
+        cycles: maximum number of cycles to generate up to
+        autocorrelate: whether or not to autocorrelate the polarizations with their
+            respective initial states
+        take_abs: whether or not to take the absolute value of the polarizations
+        kwargs: lists of non-default argument configurations to pass through
+            to `dtcexperiment.comparison_experiments`
+
+    Yields:
+        disorder averaged polarizations, ordered by
+            `dtcexperiment.comparison_experiments`, with all other parameters default
+
+    """
+    circuit_list = symbolic_dtc_circuit_list(qubits, cycles)
+    for dtcexperiment in comparison_experiments(
+        qubits=qubits, disorder_instances=disorder_instances, **kwargs
+    ):
+        yield simulate_for_polarizations(
+            dtcexperiment=dtcexperiment,
+            circuit_list=circuit_list,
+            autocorrelate=autocorrelate,
+            take_abs=take_abs,
+        )