Exclusive-or encoded algebraic structure for efficient quantum dynamics

• URL: http://arxiv.org/abs/2404.09312v2
• Date: Wed, 29 May 2024 14:02:09 GMT
• Title: Exclusive-or encoded algebraic structure for efficient quantum dynamics
• Authors: Lukas Broers, Ludwig Mathey,
• Abstract summary: We propose a formalism that captures the structure of many-body two-level quantum systems. We show how this formalism applies to real-time evolution, dissipative Lindblad action, imaginary-time evolution, and projective measurement processes.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We propose a formalism that captures the algebraic structure of many-body two-level quantum systems, and directly motivates an efficient numerical method. This formalism is based on the binary representation of the enumeration-indices of the elements of the corresponding Lie algebra. The action of arbitrarily large elements of that algebra reduces to a few bit-wise exclusive-or operations. This formalism naturally produces sparse representations of many-body density operators, the size of which we control through a dynamic truncation method. We demonstrate how this formalism applies to real-time evolution, dissipative Lindblad action, imaginary-time evolution, and projective measurement processes. We find that this approach to calculating quantum dynamics scales close to linearly with the number of non-zero components in the density operator. We refer to this exclusive-or represented quantum algebra as ORQA. As a proof of concept, we provide a numerical demonstration of this formalism by simulating quantum annealing processes for the maximum independent set problem for up to 22 two-level systems.

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