Yann Beaujeault - Quantum generator coordinate method: a multi-reference algorithm for eigendecomposition

Quantum generator coordinate method: a multi-reference algorithm for eigendecomposition

This seminar, given by Yann Beaujeault, will happend on 12 October 2023, at 14:0. It will take place in Room 509 Corridor 24-25.

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Abstract

In the current stage of noisy intermediate-scale quantum devices (NISQ), the leading eigenvalue algorithms typically rely on variational techniques familiar to many-body practitioners. These methods often involve evolving or optimising one state at a time, falling under the single-reference category.

We propose a novel algorithm, also inspired from many-body physics, that projects the matrix to be diagonalised into a low-energy subspace, resulting in a generalised eigenvalue problem of small dimension. Our approach stands out as a multi-reference technique due to the simultaneous use of multiple trial states. A key advantage of our method is that it does not require the preparation of high-quality initial states. Instead, it efficiently estimates eigenvalues using simple parametric ansatzes. This flexibility sets our algorithm apart from single-reference methods, since the preparation of good trial states is optional rather than mandatory.

During this talk, I will outline the benefits of multi-reference formulations and present an implementation of our algorithm based on coherent states of SU(2). These states form an overcomplete basis of the full Hilbert space, ensuring exactness of the method if a sufficient number of trial states is employed. Additionally, their straightforward algebraic structure allows us to factorise the expectation values of the matrices to be diagonalised, making it possible to retrieve the necessary matrix elements using only sequences of one-qubit expectation values. To demonstrate the power and limitations of the method, I will showcase its application to a toy example involving interacting fermions.