dynamiqs 0.2.2

High-performance quantum systems simulation with JAX (GPU-accelerated & differentiable solvers).

P. Guilmin, R. Gautier, A. Bocquet, E. Genois

High-performance quantum systems simulation with JAX.

Dynamiqs is a Python library for GPU-accelerated and differentiable quantum simulations. Solvers are available for the Schrödinger equation, the Lindblad master equation, and the stochastic master equation. The library is built with JAX and the main solvers are based on Diffrax.

Documentation is available on our website, https://www.dynamiqs.org; see the Python API for a list of all implemented functions.

The main features of Dynamiqs are:

• Running simulations on CPUs and GPUs with high-performance.
• Executing many simulations concurrently by batching over Hamiltonians, initial states or jump operators.
• Computing gradients of arbitrary functions with respect to arbitrary parameters of the system.
• Full compatibility with the JAX ecosystem with a QuTiP-like API.

We hope that this library will prove useful to the community for e.g. simulation of large quantum systems, gradient-based parameter estimation or quantum optimal control. The library is designed for large-scale problems, but also runs efficiently on CPUs for smaller problems.

⚠️ This library is under active development and while the APIs and solvers are still finding their footing, we're working hard to make it worth the wait. Check back soon for the grand opening!

Installation

You can install Dynamiqs with pip:

pip install dynamiqs

ℹ️ If you're using a GPU, please refer to the JAX installation documentation page for detailed instructions on how to install JAX for your device.

Examples

Simulate a lossy quantum harmonic oscillator

This first example shows simulation of a lossy harmonic oscillator with Hamiltonian $H=\omega a^\dagger a$ and a single jump operator $L=\sqrt{\kappa} a$ from time $0$ to time $T$, starting from the initial coherent state $\ket{\alpha_0}$.

import dynamiqs as dq
import jax.numpy as jnp

# parameters
n = 16          # Hilbert space dimension
omega = 1.0     # frequency
kappa = 0.1     # decay rate
alpha0 = 1.0    # initial coherent state amplitude
T = 2 * jnp.pi  # total evolution time (one full revolution)

# initialize operators, initial state and saving times
a = dq.destroy(n)
H = omega * dq.dag(a) @ a
jump_ops = [jnp.sqrt(kappa) * a]
psi0 = dq.coherent(n, alpha0)
tsave = jnp.linspace(0, T, 101)

# run simulation
result = dq.mesolve(H, jump_ops, psi0, tsave)
print(result)

|██████████| 100.0% ◆ elapsed 6.30ms ◆ remaining 0.00ms
==== MESolveResult ====
Solver : Tsit5
Infos  : 40 steps (40 accepted, 0 rejected)
States : Array complex64 (101, 16, 16) | 202.0 Kb

Compute gradients with respect to some parameters

Suppose that in the above example, we want to compute the gradient of the number of photons in the final state at time $T$, $\bar{n} = \mathrm{Tr}[a^\dagger a \rho(T)]$, with respect to the frequency $\omega$, the decay rate $\kappa$ and the initial coherent state amplitude $\alpha_0$.

import dynamiqs as dq
import jax.numpy as jnp
import jax

# parameters
n = 16          # Hilbert space dimension
omega = 1.0     # frequency
kappa = 0.1     # decay rate
alpha0 = 1.0    # initial coherent state amplitude
T = 2 * jnp.pi  # total evolution time (one full revolution)

def population(omega, kappa, alpha0):
    """Return the oscillator population after time evolution."""
    # initialize operators, initial state and saving times
    a = dq.destroy(n)
    H = omega * dq.dag(a) @ a
    jump_ops = [jnp.sqrt(kappa) * a]
    psi0 = dq.coherent(n, alpha0)
    tsave = jnp.linspace(0, T, 101)

    # run simulation
    result = dq.mesolve(H, jump_ops, psi0, tsave)

    return dq.expect(dq.number(n), result.states[-1]).real

# compute gradient with respect to omega, kappa and alpha
grad_population = jax.grad(population, argnums=(0, 1, 2))
grads = grad_population(omega, kappa, alpha0)
print(f'Gradient w.r.t. omega : {grads[0]:.4f}')
print(f'Gradient w.r.t. kappa : {grads[1]:.4f}')
print(f'Gradient w.r.t. alpha0: {grads[2]:.4f}')

|██████████| 100.0% ◆ elapsed 5.94ms ◆ remaining 0.00ms
Gradient w.r.t. omega : 0.0000
Gradient w.r.t. kappa : -3.3520
Gradient w.r.t. alpha0: 1.0670

ℹ️ On this specific example, we can verify the result analytically. The state remains a coherent state at all time with complex amplitude $\alpha(t) = \alpha_0 e^{-\kappa t/2} e^{i\omega t}$, and the final photon number is thus $\bar{n} = |\alpha(T)|^2 = \alpha_0^2 e^{-\kappa T}$. We can then compute the gradient with respect to the three parameters $\theta = (\omega, \kappa, \alpha_0)$:

$$ \nabla_\theta\ \bar{n} = \begin{pmatrix} \partial\bar{n} / \partial\omega \ \partial\bar{n} / \partial\kappa \ \partial\bar{n} / \partial\alpha_0 \end{pmatrix} = \begin{pmatrix} 0\ -\alpha_0^2 T e^{-\kappa T} \ 2 \alpha_0 e^{-\kappa T} \end{pmatrix} \approx \begin{pmatrix} 0.0 \ -3.3520 \ 1.0670 \end{pmatrix} $$

More features!

Below are some cool features of Dynamiqs that are either already available or planned for the near future.

Solvers

• Choose between a variety of solvers, from modern explicit and implicit ODE solvers (e.g. Tsit5 and PID controllers for adaptive step-sizing) to quantum-tailored solvers that preserve the physicality of the evolution (the state trace and positivity are preserved).
• Simulate time-varying problems (both Hamiltonian and jump operators) with support for various formats (piecewise constant operator, constant operator modulated by a time-dependent factor, etc.).
• Define a custom save function during the evolution (e.g. to register only the state purity, to track a subsystem by taking the partial trace of the full system, or to compute the population in the last Fock states to regularise your QOC problem).
• Easily implement your own solvers by subclassing our base solver class and focusing directly on the solver logic.
• Simulate SME trajectories orders of magnitude faster by batching the simulation over the stochastic trajectories.
• Use adaptive step-size solvers to solve the SME (based on Brownian bridges to generate the correct statistics).
• Parallelise large simulations across multiple CPUs/GPUs.

Gradients

• Choose between various methods to compute the gradient, to tradeoff speed and memory (e.g. use the optimal online checkpointing scheme of Diffrax to compute gradients for large systems).
• Compute gradients with machine-precision accuracy.
• Evaluate derivatives with respect to evolution time (e.g. for time-optimal quantum control).
• Compute higher order derivatives (e.g. the Hessian).

Utilities

• Balance accuracy and speed by choosing between single precision (float32 and complex64) or double precision (float64 and complex128).
• Plot beautiful figures by using our handcrafted plotting function.
• Apply any functions to batched arrays (e.g. dq.wigner(states) to compute the wigners of many states at once).
• Use QuTiP objects as arguments to any functions (e.g. if you have existing code to define your Hamiltonian in QuTiP, or if you want to use our nice plotting functions on a list of QuTiP states).

Library development

• Enjoy modern software development practices and tools.
• Build confidence from the analytical tests that verify state correctness and gradient accuracy for every solver, at each commit.

Coming soon

• Discover a custom sparse format, with substantial speedups for large systems.
• Simulate using propagators solvers based on Krylov subspace methods.
• Benchmark code to compare solvers and performance for different systems.

The Dynamiqs project

Philosophy

There is a noticeable gap in the availability of an open-source library that simplifies gradient-based parameter estimation and quantum optimal control. In addition, faster simulations of large systems are essential to accelerate the development of quantum technologies. The Dynamiqs library addresses both of these needs. It aims to be a fast and reliable building block for GPU-accelerated and differentiable solvers. We also work to make the library compatible with the existing Python ecosystem (i.e. JAX and QuTiP) to allow easy interfacing with other libraries.

Team and sponsoring

The library is being developed by a team of physicists and developers. We are working with theorists, experimentalists, machine learning practitioners, optimisation and numerical methods experts to make the library as useful and as powerful as possible. The library is sponsored by the startup Alice & Bob, where it is being used to simulate, calibrate and control chips made of superconducting-based dissipative cat qubits.

History

Development started in early 2023, the library was originally based on PyTorch with homemade solvers and gradient methods. It was completely rewritten in JAX in early 2024 for performance.

Let's talk!

If you're curious, have questions or suggestions, wish to contribute or simply want to say hello, please don't hesitate to engage with us, we're always happy to chat! You can join the community on Slack via this invite link, open an issue on GitHub, or contact the lead developer via email at [e-mail].

Contributing

We warmly welcome all contributions. If you're a junior developer or physicist, you can start with a small utility function, and move on to bigger problems as you discover the library's internals. If you're more experienced and want to implement more advanced features, don't hesitate to get in touch to discuss what would suit you. Please refer to CONTRIBUTING.md for detailed instructions.

Citing Dynamiqs

If you have found this library useful in your academic research, you can cite:

@unpublished{guilmin2024dynamiqs,
  title  = {Dynamiqs: an open-source Python library for GPU-accelerated and differentiable simulation of quantum systems},
  author = {Pierre Guilmin and Ronan Gautier and Adrien Bocquet and {\'{E}}lie Genois},
  year   = {2024},
  url    = {https://github.com/dynamiqs/dynamiqs}
}

P. Guilmin, R. Gautier, A. Bocquet, E. Genois. Dynamiqs: an open-source Python library for GPU-accelerated and differentiable simulation of quantum systems (2024), in preparation.