Double-bracket quantum algorithms for diagonalization

Marek Gluza

School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, 637371 Singapore, Republic of Singapore

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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.

A method for preparing on a quantum computer states of complicated materials.

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Cited by

[1] Jeongrak Son, Marek Gluza, Ryuji Takagi, and Nelly H. Y. Ng, "Quantum Dynamic Programming", arXiv:2403.09187, (2024).

[2] Michael Kreshchuk, James P. Vary, and Peter J. Love, "Simulating Scattering of Composite Particles", arXiv:2310.13742, (2023).

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