https://github.com/cqcl/phayes
Easy and efficient Bayesian quantum phase estimation
https://github.com/cqcl/phayes
Last synced: about 1 year ago
JSON representation
Easy and efficient Bayesian quantum phase estimation
- Host: GitHub
- URL: https://github.com/cqcl/phayes
- Owner: CQCL
- License: apache-2.0
- Created: 2023-05-22T11:17:16.000Z (about 3 years ago)
- Default Branch: main
- Last Pushed: 2023-07-11T13:28:35.000Z (almost 3 years ago)
- Last Synced: 2025-02-06T21:46:27.882Z (over 1 year ago)
- Language: Python
- Homepage:
- Size: 998 KB
- Stars: 2
- Watchers: 2
- Forks: 1
- Open Issues: 4
-
Metadata Files:
- Readme: README.md
- License: LICENSE
Awesome Lists containing this project
README
# 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](https://arxiv.org/abs/2306.16608).
Quantum phase estimation
[Wiebe et al, 2015](https://arxiv.org/abs/1508.00869),
[O'Brien et al, 2018](https://iopscience.iop.org/article/10.1088/1367-2630/aafb8e/pdf),
[van den Berg, 2021](https://quantum-journal.org/papers/q-2021-06-07-469/pdf/) (and
quantum amplitude estimation [Suzuki et al, 2019](https://arxiv.org/abs/1904.10246)) 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)
```python
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
```python
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
```python
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](examples) folder.
## Precision
By default [JAX uses 32-bit precision](https://jax.readthedocs.io/en/latest/notebooks/Common_Gotchas_in_JAX.html#double-64bit-precision),
for phase estimation experiments you may well want to enable 64-bit precision by
adding the following to the top of your script
```python
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}
}
```