Double-bracket quantum algorithms for quantum imaginary-time evolution

• URL: http://arxiv.org/abs/2412.04554v1
• Date: Thu, 05 Dec 2024 19:00:09 GMT
• Title: Double-bracket quantum algorithms for quantum imaginary-time evolution
• Authors: Marek Gluza, Jeongrak Son, Bi Hong Tiang, Yudai Suzuki, Zoë Holmes, Nelly H. Y. Ng,
• Abstract summary: We prove that our Double-Bracket Quantum Imaginary-Time Evolution (DB-QITE) algorithm inherits the cooling guarantees of imaginary-time evolution.<n>DB-QITE provides a means to systematically improve the approximation of a ground-state using shallow circuits.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Efficiently preparing approximate ground-states of large, strongly correlated systems on quantum hardware is challenging and yet nature is innately adept at this. This has motivated the study of thermodynamically inspired approaches to ground-state preparation that aim to replicate cooling processes via imaginary-time evolution. However, synthesizing quantum circuits that efficiently implement imaginary-time evolution is itself difficult, with prior proposals generally adopting heuristic variational approaches or using deep block encodings. Here, we use the insight that quantum imaginary-time evolution is a solution of Brockett's double-bracket flow and synthesize circuits that implement double-bracket flows coherently on the quantum computer. We prove that our Double-Bracket Quantum Imaginary-Time Evolution (DB-QITE) algorithm inherits the cooling guarantees of imaginary-time evolution. Concretely, each step is guaranteed to i) decrease the energy of an initial approximate ground-state by an amount proportion to the energy fluctuations of the initial state and ii) increase the fidelity with the ground-state. Thus DB-QITE provides a means to systematically improve the approximation of a ground-state using shallow circuits.

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