phayes

phayes is a python package for easy and efficient quantum phase estimation.

Extensive details on Bayesian quantum phase estimation can be found in the accompanying paper, Yamamoto et al, 2023.

Quantum phase estimation Wiebe et al, 2015, O'Brien et al, 2018, van den Berg, 2021 (and quantum amplitude estimation Suzuki et al, 2019) can be implemented as an instance of Bayesian inference. Shots are generated from a quantum circuit with likelihood $$p(m \mid \phi, k, \beta) = \frac12\left(1 + (1 - q)\cos(k\phi + \beta - m \pi)\right),$$ where $m \in {0,1}$ is the binary shot produced by the quantum device, $\phi$ is the unknown underlying phase, $q$ is a noise parameter or error rate. $k$ and $\beta$ are circuit parameters that are chosen by the user (or phayes).

Starting with a uniform prior over $\phi$, phayes uses Bayesian inference to hone in on the true value (with uncertainty quantification) through repeated measurements.

Install

pip install phayes

Bayesian updates

The core functions are phayes.get_k_and_beta and phayes.update, which determine the experiment parameters and then update the posterior distribution in light of a new measurement (or series of measurements)

from jax import numpy as jnp
import phayes

num_shots = 100

posterior_state = phayes.init()
for _ in range(num_shots):
    k, beta = phayes.get_k_and_beta(posterior_state)
    m = get_shot(k, beta)
    posterior_state = phayes.update(posterior_state, m, k, beta)

Here the function get_shot executes the quantum circuit above and returns a binary shot (or multiple shots) according the likelihood $p(m\mid \phi, k, \beta)$.

There's more

The probability density function can be visualised easily

prior_state = phayes.init()
m = jnp.array([0, 1, 1, 0, 0, 1])
k = jnp.array([1, 4, 3, 8, 5, 10])
beta = jnp.array([1.4, 0.6, 1.2, 1.1, 1.9, 0.3])

posterior_state = phayes.update(prior_state, m, k, beta)

import matplotlib.pyplot as plt
linsp = jnp.linspace(-jnp.pi, jnp.pi, 1000)
pdf = phayes.pdf(linsp, posterior_state)
plt.plot(linsp, pdf)

phayes also has a host of other useful functions

posterior_mean = phayes.circular_mean(posterior_state)
posterior_circular_variance = phayes.circular_variance(posterior_state)
posterior_holevo_variance = phayes.holevo_variance(posterior_state)

Example notebooks can be found in the examples folder.

Precision

By default JAX uses 32-bit precision, for phase estimation experiments you may well want to enable 64-bit precision by adding the following to the top of your script

from jax.config import config
config.update(“jax_enable_x64”, True)

Citation

@software{phayes,
author={Duffield, Samuel},
title={phayes: A python package for easy and efficient Bayesian quantum phase estimation},
year={2023},
url={https://github.com/CQCL/phayes}
}