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"""Implements expectation_value, estimating expectation values via repeated quantum kernel sampling."""
import jax
import jax.numpy as jnp
from qrisp.jasp.tracing_logic import quantum_kernel
@jax.jit
def _backend_shots_marker(val):
"""Identity marker for the shot count.
Allows ``backend_sampler`` to reliably locate the shot count inside a traced
expectation_value Jaxpr.
"""
return val
# The following function implements the expectation_value feature.
# The basic functionality would be relatively straightforward to implement,
# however there are some complications. The reason for that is that the resulting
# jaxpr should be "readable" by the terminal sampling interpreter.
# Terminal sampling means that instead of performing the simulations "shots"-times
# it is performed once and the shots are then sampled from that distribution.
# Naturally this implies a massive performance increase, which is why a lot
# of effort is spent to realize a smooth implementation.
# The underlying idea to make the feature easily "readable" by the terminal
# sampling interpreter is to structure one iteration of sampling into three
# steps.
# 1. Evaluating the user function, which generates the distribution.
# 2. Sampling from that distribution via the "measure" function.
# 3. Decoding and postprocessing the measurement results.
# For the final two steps we deploy some custom logic to realize the terminal
# sampling behavior. To simplify the automatic processing of these steps,
# we capture each into individual pjit calls.
# The terminal sampling interpreter then identifies each steps via the
# eqn.params["name"] attribute and executes the custom logic.
[docs]
def expectation_value(state_prep, shots, return_dict=False, post_processor=None):
r"""Estimates the expectation value from a sampling kernel.
The ``expectation_value`` function allows to estimate the expectation value
from a *sampling kernel* — a Python function that receives only classical
arguments and returns arbitrary values. Any
:ref:`QuantumVariables <QuantumVariable>` in the return are automatically
measured and decoded; classical values are interleaved in-place.
.. note::
When used inside :func:`~qrisp.jasp.jaspify` with
``terminal_sampling=True``, the same restrictions apply as for
:func:`~qrisp.jasp.sample`: kernels that return classical values are
rejected, and kernels whose quantum state depends on mid-circuit
measurement outcomes may produce invalid results. Use
``terminal_sampling=False`` (the default) for those cases. See
:func:`~qrisp.jasp.terminal_sampling` for details.
Parameters
----------
sampling_kernel : callable
A sampling kernel — a function receiving only classical arguments and
returning one or more :ref:`QuantumVariables <QuantumVariable>`,
classical measurement results, or a mixture of both.
The function must **not** receive quantum arguments because a quantum
value would need to be copied for each sampling iteration, which is
prohibited by the no-cloning theorem.
shots : int or jax.core.Tracer
The amount of samples to take to compute the expectation value.
post_processor : callable, optional
A classical Jax traceable function to apply to the results
directly after measuring. By default no post processing is applied.
Raises
------
Exception
Tried to sample from sampling kernel taking a quantum value
Returns
-------
callable
A function returning a Jax array containing the expectation value.
Examples
--------
We prepare the state
.. math::
\ket{\psi_k} = \frac{1}{\sqrt{2}} \left(\ket{0}\ket{0}\ket{\text{False}} + \ket{k}\ket{k}\ket{\text{True}}\right)
::
from qrisp import *
from qrisp.jasp import *
def sampling_kernel(k):
a = QuantumFloat(4)
b = QuantumFloat(4)
qbl = QuantumBool()
h(qbl)
with control(qbl[0]):
a[:] = k
cx(a, b)
return a, b
And compute the expectation value of the QuantumFloats
::
@jaspify
def main(k):
ev_function = expectation_value(sampling_kernel, shots = 50)
return ev_function(k)
print(main(3))
# Yields e.g.
# [1.44 1.44]
The true value 1.5 is not reached exactly because of `shot noise <https://en.wikipedia.org/wiki/Shot_noise>`_ —
the printed value fluctuates around 1.5 from run to run. To improve the
approximation, feel free to increase the shots!
To demonstrate the ``post_processor`` keyword we define a simple post processing
function
::
def post_processor(x, y):
return x*y
@jaspify
def main(k):
ev_function = expectation_value(state_prep, shots = 50,
post_processor = post_processor)
return ev_function(k)
print(main(3))
# Yields e.g.
# 4.86
This result is expected because the inputs of ``post_processor`` are
either (0,0) or (3,3) with 50% probability, so the expectation value is
.. math::
4.5 = \frac{3\cdot 3 + 0\cdot 0}{2}
As with the previous example, the printed value fluctuates around this
expectation from run to run because of shot noise.
"""
from qrisp.core import QuantumVariable, measure
from qrisp.jasp import make_tracer, qache
if isinstance(shots, int):
shots = make_tracer(shots)
if post_processor is None:
def identity(*args):
return args
post_processor = identity
# Qache the user function
@qache
def user_func(*args):
return state_prep(*args)
# This function performs the logic to evaluate the expectation value
def expectation_value_eval_function(*args, shots=0):
for arg in args:
if isinstance(arg, QuantumVariable):
raise Exception("Tried to sample from state preparation function taking a quantum value")
# Marker: allows backend_sampler to locate the shot count in the
# traced Jaxpr without fragile position-based extraction.
_backend_shots_marker(shots)
# We now construct a loop to evaluate the expectation value via adding
# the decoded and postprocessed measurement result into an accumulator.
# The following function is the loop body, which is kernelized.
@quantum_kernel
def sampling_body_func(i, args):
# Evaluate the user function
acc = args[0]
result_tuple = user_func(*args[1:])
if not isinstance(result_tuple, tuple):
result_tuple = (result_tuple,)
# Build a per-position mask: QuantumVariable -> True, classical -> False.
is_quantum = [isinstance(x, QuantumVariable) for x in result_tuple]
# Separate quantum and classical returns.
qv_tuple = tuple(x for x, is_q in zip(result_tuple, is_quantum) if is_q)
classical_tuple = tuple(x for x, is_q in zip(result_tuple, is_quantum) if not is_q)
if qv_tuple:
# Measure quantum registers only.
@qache
def sampling_helper_1(*args):
res_list = [measure(reg) for reg in args]
return tuple(res_list)
measurement_ints = sampling_helper_1(*[qv.reg for qv in qv_tuple])
# Decode quantum, interleave with classical values, apply
# post-processing. Classical values are passed as explicit
# arguments (before measurement ints). When present the
# helper is named sampling_helper_2_mixed for detection.
if classical_tuple:
def sampling_helper_2_mixed(*args):
n_classical = len(classical_tuple)
classical_vals = args[:n_classical]
meas_ints = args[n_classical:]
decoded_q = [qv.jdecoder(meas_int) for qv, meas_int in zip(qv_tuple, meas_ints)]
q_iter = iter(decoded_q)
c_iter = iter(classical_vals)
full = [next(q_iter) if is_q else next(c_iter) for is_q in is_quantum]
return post_processor(*full)
sampling_helper_2 = jax.jit(sampling_helper_2_mixed)
else:
def sampling_helper_2(*meas_ints):
res_list = [qv.jdecoder(meas) for qv, meas in zip(qv_tuple, meas_ints)]
return post_processor(*res_list)
sampling_helper_2 = jax.jit(sampling_helper_2)
decoded_values = sampling_helper_2(*classical_tuple, *measurement_ints)
else:
# Pure classical — just apply post-processing directly.
decoded_values = post_processor(*classical_tuple)
if isinstance(decoded_values, tuple) and len(decoded_values) != 1:
# Save the return amount (for more details check the comment of the)
# initialization command of return_amount
return_amount.append(len(decoded_values))
if acc.shape[0] == 1:
raise _MultiReturnDetected()
# Turn into jax array and add to the accumulator
meas_res = jnp.array(decoded_values)
acc += meas_res
# Return the updated accumulator for the next loop iteration.
return (acc, *args[1:])
# This list captures the amount of return values. The strategy here is
# to initially assume only one QuantumVariable is returned, which is then
# added to the expectation value accumulator. If more than one is returned,
# the amount is saved in this list and an exception is raised, which
# subsequently causes another call but this time with the correct accumulator
# dimension.
return_amount = []
try:
# loop_res = jax.lax.fori_loop(0, shots, sampling_body_func, (jax.lax.broadcast(0., (1,)), *args))
loop_res = jax.lax.fori_loop(0, shots, sampling_body_func, (jnp.zeros(1), *args))
return loop_res[0][0] / shots
except _MultiReturnDetected:
loop_res = jax.lax.fori_loop(0, shots, sampling_body_func, (jnp.zeros(return_amount), *args))
return loop_res[0] / shots
if return_dict:
expectation_value_eval_function.__name__ = "dict_sampling_eval_function"
def return_function(*args):
return jax.jit(expectation_value_eval_function)(*args, shots=shots)
return return_function
class _MultiReturnDetected(Exception):
"""Internal signal raised when the post-processor returns multiple values (a tuple) instead of a single scalar.
This triggers a retry of the sampling loop with a multi-dimensional accumulator of the correct shape.
"""
