Double-bracket quantum algorithms for diagonalization

TL;DR

This paper introduces double-bracket quantum algorithms for diagonalization that are efficient for near-term quantum computers, avoiding qubit overheads and offering a new framework for practical quantum physics computations.

Contribution

It proposes a recursive double-bracket iteration framework for diagonalization that is more trainable and resource-efficient than traditional methods, suitable for near-term quantum devices.

Findings

Numerical examples show effective approximation of eigenstates with few recursion steps.

The method avoids trainability issues of unstructured circuit optimization.

Implementation cost is lower than quantum phase estimation, suitable for near-term experiments.

Abstract

This work proposes double-bracket iterations as a framework for obtaining diagonalizing quantum circuits. Their implementation on a quantum computer consists of interlacing evolutions generated by the input Hamiltonian with diagonal evolutions which can be chosen variationally. No qubit overheads or controlled-unitary operations are needed but the method is recursive which makes the circuit depth grow exponentially with the number of recursion steps. To make near-term implementations viable, the proposal includes optimization of diagonal evolution generators and of recursion step durations. Indeed, thanks to this numerical examples show that the expressive power of double-bracket iterations suffices to approximate eigenstates of relevant quantum models with few recursion steps. Compared to brute-force optimization of unstructured circuits double-bracket iterations do not suffer from the same trainability limitations. Moreover, with an implementation cost lower than required for quantum phase estimation they are more suitable for near-term quantum computing experiments. More broadly, this work opens a pathway for constructing purposeful quantum algorithms based on so-called double-bracket flows also for tasks different from diagonalization and thus enlarges the quantum computing toolkit geared towards practical physics problems.