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Fix minor problems in executors documentation (#292)
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* fix docstrings, add noise to CX, fix inverse of U

* change qc_vaccum to qc_zero

* add comment on eigen decomposition

* marge with master and fix doctest

* doctet: +SKIP added to qiskit circuits in docs
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@andreamari
andreamari authored Aug 12, 2020
1 parent 7151278 commit 5a1e346
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101 changes: 65 additions & 36 deletions docs/source/guide/guide_03-executors.rst
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Original file line number Diff line number Diff line change
Expand Up @@ -35,14 +35,14 @@ to be used in ``mitiq``.

def wvf_sim(circ: Circuit, obs: np.ndarray) -> float:
"""Simulates noiseless wavefunction evolution and returns the
expectation value of some observable.
expectation value of some observable.

Args:
circ: The quantum program as a cirq object.
obs: A numpy array representation of the observable.
circ: The input Cirq circuit.
obs: The observable to measure as a NumPy array.

Returns:
The observable's expectation value.
The expectation value of obs as a float.
"""
final_wvf = circ.final_wavefunction()
return np.real(final_wvf.conj().T @ obs @ final_wvf)
Expand Down Expand Up @@ -83,6 +83,18 @@ documentation `here <https://cirq.readthedocs.io/en/master/generated/cirq.PauliS
.. testcode::

def wvf_sampling_sim(circ: Circuit, obs: cirq.PauliString, shots: int) -> float:
"""Simulates noiseless wavefunction evolution and returns the
expectation value of a PauliString observable.

Args:
circ: The input Cirq circuit.
obs: The observable to measure as a cirq.PauliString.
shots: The number of measurements.

Returns:
The expectation value of obs as a float.
"""

# Do the sampling
psum = cirq.PauliSumCollector(circ, obs, samples_per_term=shots)
psum.collect(sampler=cirq.Simulator())
Expand Down Expand Up @@ -116,9 +128,9 @@ This executor can be used for noisy depolarizing simulation.
"""Simulates a circuit with depolarizing noise at level noise.

Args:
circ: The quantum program as a cirq circuit.
obs: The observable to measure as an np.ndarray
noise: The depolarizing noise as a float, i.e. 0.001 is 0.1% noise
circ: The input Cirq circuit.
obs: The observable to measure as a NumPy array.
noise: The depolarizing noise as a float, i.e. 0.001 is 0.1% noise.

Returns:
The expectation value of obs as a float.
Expand Down Expand Up @@ -160,9 +172,10 @@ You can also include both noise models and finite sampling in your executor.
"""Simulates a circuit with depolarizing noise at level noise.

Args:
circ: The quantum program as a cirq circuit.
obs: The observable to measure as an np.ndarray
noise: The depolarizing noise as a float, i.e. 0.001 is 0.1% noise
circ: The input Cirq circuit.
obs: The observable to measure as a NumPy array.
noise: The depolarizing noise strength as a float, i.e. 0.001 is 0.1%.
shots: The number of measurements.

Returns:
The expectation value of obs as a float.
Expand Down Expand Up @@ -215,14 +228,14 @@ to be used in ``mitiq``.

def qs_wvf_sim(circ: QuantumCircuit, obs: np.ndarray) -> float:
"""Simulates noiseless wavefunction evolution and returns the
expectation value of some observable.
expectation value of some observable.

Args:
circ: The quantum program as a qiskit circuit.
obs: A numpy array representation of the observable.
circ: The input Qiskit circuit.
obs: The observable to measure as a NumPy array.

Returns:
The observable's expectation value.
The expectation value of obs as a float.
"""
result = qiskit.execute(circ, wvf_simulator).result()
final_wvf = result.get_statevector()
Expand Down Expand Up @@ -256,24 +269,26 @@ behind how this example is available `here <https://quantumcomputing.stackexchan
QISKIT_SIMULATOR = qiskit.Aer.get_backend("qasm_simulator")

def qs_wvf_sampling_sim(circ: QuantumCircuit, obs: np.ndarray, shots: int) -> float:
"""Simulates the evolution of the circuit and measures the expectation value of the observable.
"""Simulates the evolution of the circuit and returns
the expectation value of the observable.

Args:
circuit (qiskit.QuantumCircuit): Ideal quantum circuit with no measurements.
shots (int): Number of shots to run the circuit.
obs (np.ndarray): A numpy array representation of the observable.
circ: The input Qiskit circuit.
obs: The observable to measure as a NumPy array.
shots: The number of measurements.

Returns:
The expectation value of obs as a float.

Returns:
expval: expected value of the observable obs.
"""
if len(circ.clbits) > 0:
raise ValueError("This executor only works on programs with no classical bits.")

circ = copy.deepcopy(circ)
# we need to modify the circuit to measure our observable
# we do this by appending a rotation U
eigvals, U = np.linalg.eigh(obs)
circ.unitary(U, qubits=range(circ.n_qubits))
# we need to modify the circuit to measure obs in its eigenbasis
# we do this by appending a unitary operation
eigvals, U = np.linalg.eigh(obs) # obtains a U s.t. obs = U diag(eigvals) U^dag
circ.unitary(np.linalg.inv(U), qubits=range(circ.n_qubits))

circ.measure_all()

Expand Down Expand Up @@ -307,6 +322,10 @@ behind how this example is available `here <https://quantumcomputing.stackexchan
out = qs_wvf_sampling_sim(qc, obs=np.diag([0, 0, 0, 1]), shots=int(1e5))
assert abs(out - 0.5) < 0.1

qc_zero = QuantumCircuit(1)
out = qs_wvf_sampling_sim(qc_zero, obs=np.diag([1, 0]), shots=50)
assert np.isclose(out, 1.0)


Qiskit: Density-matrix Simulation with Depolarizing Noise
-----------------------------------------------------------
Expand All @@ -330,33 +349,36 @@ This executor can be used for noisy depolarizing simulation.
QISKIT_SIMULATOR = qiskit.Aer.get_backend("qasm_simulator")

def qs_noisy_sampling_sim(circ: QuantumCircuit, obs: np.ndarray, noise: float, shots: int) -> float:
"""Simulates the evolution of the noisy circuit and returns the expectation value of the observable.
"""Simulates the evolution of the noisy circuit and returns
the expectation value of the observable.

Args:
circuit (qiskit.QuantumCircuit): Ideal quantum circuit with no measurements.
shots (int): Number of shots to run the circuit.
obs (np.ndarray): A numpy array representation of the observable.
circ: The input Cirq circuit.
obs: The observable to measure as a NumPy array.
noise: The depolarizing noise strength as a float, i.e. 0.001 is 0.1%.
shots: The number of measurements.

Returns:
expval: expected value of the observable obs.
Returns:
The expectation value of obs as a float.
"""
if len(circ.clbits) > 0:
raise ValueError("This executor only works on programs with no classical bits.")

circ = copy.deepcopy(circ)
# we need to modify the circuit to measure our observable
# we do this by appending a rotation U
eigvals, U = np.linalg.eigh(obs)
circ.unitary(U, qubits=range(circ.n_qubits))
# we need to modify the circuit to measure obs in its eigenbasis
# we do this by appending a unitary operation
eigvals, U = np.linalg.eigh(obs) # obtains a U s.t. obs = U diag(eigvals) U^dag
circ.unitary(np.linalg.inv(U), qubits=range(circ.n_qubits))

circ.measure_all()

# initialize a qiskit noise model
noise_model = NoiseModel()

# we assume a depolarizing error for each
# we assume the same depolarizing error for each
# gate of the standard IBM basis
noise_model.add_all_qubit_quantum_error(depolarizing_error(noise, 1), ["u1", "u2", "u3"])
noise_model.add_all_qubit_quantum_error(depolarizing_error(noise, 2), ["cx"])

# execution of the experiment
job = qiskit.execute(
Expand All @@ -366,8 +388,9 @@ This executor can be used for noisy depolarizing simulation.
noise_model=noise_model,
# we want all gates to be actually applied,
# so we skip any circuit optimization
basis_gates=noise_model.basis_gates,
optimization_level=0,
shots=shots
shots=shots,
)
results = job.result()
counts = results.get_counts()
Expand All @@ -386,6 +409,12 @@ This executor can be used for noisy depolarizing simulation.
qc.u1(0, 0)
assert 0.1 < qs_noisy_sampling_sim(qc, np.diag([1, 0]), 0.02, 1000) < 1.0

qc_zero = QuantumCircuit(2)
out = qs_noisy_sampling_sim(qc_zero, obs=np.diag([1, 0, 0, 0]), noise=0.0, shots=10)
assert np.isclose(out, 1.0)
out = qs_noisy_sampling_sim(qc_zero, obs=np.diag([1, 0, 0, 0]), noise=1.0, shots=10 ** 5)
assert np.isclose(out, 0.25, atol=0.1)

Other noise models can be defined using any functionality available in ``qiskit``.
More details can be found in the ``qiskit``
`simulator documentation <https://qiskit.org/documentation/tutorials/simulators/index.html>`_
Expand Down
25 changes: 12 additions & 13 deletions docs/source/guide/guide_04-folding.rst
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Original file line number Diff line number Diff line change
Expand Up @@ -118,14 +118,13 @@ following example, we fold a Qiskit circuit.
>>> circ = qiskit.QuantumCircuit(qreg)
>>> _ = circ.h(qreg[0])
>>> _ = circ.cnot(qreg[0], qreg[1])
>>> print("Original circuit:", circ, sep="\n") # doctest: +NORMALIZE_WHITESPACE
>>> print("Original circuit:", circ, sep="\n") # doctest: +SKIP +NORMALIZE_WHITESPACE
Original circuit:
┌───┐
q0_0: |0>┤ H ├──■──
└───┘┌─┴─┐
q0_1: |0>─────┤ X ├
└───┘

┌───┐
q31_0: ┤ H ├──■──
└───┘┌─┴─┐
q31_1: ─────┤ X ├
└───┘


This code (when the print statement is uncommented) should display something like:
Expand All @@ -136,13 +135,13 @@ We can now fold this circuit as follows.
.. doctest:: python

>>> folded = fold_gates_from_left(circ, scale_factor=2.)
>>> print("Folded circuit:", folded, sep="\n") # doctest: +NORMALIZE_WHITESPACE
>>> print("Folded circuit:", folded, sep="\n") # doctest: +SKIP +NORMALIZE_WHITESPACE
Folded circuit:
┌───┐┌───┐┌───┐
q_0: |0>┤ H ├┤ H ├┤ H ├──■──
└───┘└───┘└───┘┌─┴─┐
q_1: |0>───────────────┤ X ├
└───┘
┌───┐┌───┐┌───┐
q_0: ┤ H ├┤ H ├┤ H ├──■──
└───┘└───┘└───┘┌─┴─┐
q_1: ───────────────┤ X ├
└───┘

By default, the folded circuit has the same type as the input circuit. To return an internal ``mitiq`` representation
of the folded circuit (a Cirq circuit), one can use the keyword argument ``return_mitiq=True``.
Expand Down

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