Qiskit addon: sample-based quantum diagonalization (SQD)

Table of contents

• About
• Documentation
• Installation
• Computational requirements
• Deprecation Policy
• Contributing
• License
• References

About

Qiskit addons are a collection of modular tools for building utility-scale workloads powered by Qiskit.

This package contains the Qiskit addon for sample-based quantum diagonalization (SQD) -- a technique for finding eigenvalues and eigenvectors of quantum operators, such as a quantum system Hamiltonian, using quantum and distributed classical computing together.

Classical distributed computing is used to process samples obtained from a quantum processor and to project and diagonalize a target Hamiltonian in a subspace spanned by them. This allows SQD to be robust to samples corrupted by quantum noise and deal with large Hamiltonians, such as chemistry Hamiltonians with millions of interaction terms, beyond the reach of any exact diagonalization methods.

The SQD tool can target Hamiltonians expressed as linear combination of Pauli operators, or second-quantized fermionic operators. The input samples are obtained by quantum circuits defined by the user, which are believed to be good representations of eigenstates (e.g. the ground state) of a target operator. The convergence rate of SQD as a function of the number of samples improves with the sparseness of the target eigenstate.

The projection and diagonalization steps are performed by a classical solver. We provide here two generic solvers, one for fermionic systems and another for qubit systems. Other solvers that might be more efficient for specific systems can be interfaced by the users.

Documentation

All documentation is available at https://qiskit.github.io/qiskit-addon-sqd/.

Installation

We encourage installing this package via pip, when possible:

pip install 'qiskit-addon-sqd'

For more installation information refer to these installation instructions.

Computational requirements

The computational cost of SQD is dominated by the eigenstate solver calls. At each step of the self-consistent configuration recovery iteration, n_batches of eigenstate solver calls are performed. The different calls are embarrassingly parallel. In this tutorial, those calls are inside a for loop. It is highly recommended to perform these calls in parallel.

The qiskit_addon_sqd.fermion.solve_fermion() function is multithreaded and capable of handling systems with ~25 spacial orbitals and ~10 electrons with subspace dimensions of ~$10^7$, using ~10-30 cores.

Choosing subspace dimensions

The choice of the subspace dimension affects the accuracy and runtime of the eigenstate solver. The larger the subspace the more accurate the calculation, at the cost of increasing the runtime and memory requirements. The optimal subspace size for a given system is not known, thus a convergence study with the subspace dimension may be performed as described in this example.

The subspace dimension is set indirectly

In this package, the user controls the number of bitstrings (see the samples_per_batch argument in qiskit_addon_sqd.subsampling.postselect_and_subsample()) contained in each subspace. The value of this argument sets an upper bound to the subspace dimension in the case of quantum chemistry applications. See this example for more details.

Deprecation Policy

We follow semantic versioning and are guided by the principles in Qiskit's deprecation policy. We may occasionally make breaking changes in order to improve the user experience. When possible, we will keep old interfaces and mark them as deprecated, as long as they can co-exist with the new ones. Each substantial improvement, breaking change, or deprecation will be documented in the release notes.

Contributing

The source code is available on GitHub.

The developer guide is located at CONTRIBUTING.md in the root of this project's repository. By participating, you are expected to uphold Qiskit's code of conduct.

We use GitHub issues for tracking requests and bugs.

License

Apache License 2.0

References

[1] Javier Robledo-Moreno, et al., Chemistry Beyond Exact Solutions on a Quantum-Centric Supercomputer, arXiv:2405.05068 [quant-ph].

[2] Keita Kanno, et al., Quantum-Selected Configuration Interaction: classical diagonalization of Hamiltonians in subspaces selected by quantum computers, arXiv:2302.11320 [quant-ph].