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arXiv · 2303.06161

Simulating non-unitary dynamics using quantum signal processing with unitary block encoding

Hans Hon Sang Chan·David Muñoz Ramo·Nathan Fitzpatrick
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Abstract

We adapt a recent advance in resource-frugal quantum signal processing - the Quantum Eigenvalue Transform with Unitary matrices (QET-U) - to explore non-unitary imaginary time evolution on early fault-tolerant quantum computers using exactly emulated quantum circuits. We test strategies for optimising the circuit depth and the probability of successfully preparing the desired imaginary-time evolved states. For the task of ground state preparation, we confirm that the probability of successful post-selection is quadratic in the initial reference state overlap $\gamma$ as $O(\gamma^2)$. When applied instead to thermal state preparation, we show QET-U can directly estimate partition functions at exponential cost. Finally, we combine QET-U with Trotter product formula to perform non-normal Hamiltonian simulation in the propagation of Lindbladian open quantum system dynamics. We find that QET-U for non-unitary dynamics is flexible, intuitive and straightforward to use, and suggest ways for delivering quantum advantage in simulation tasks.

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Hans Hon Sang Chan, David Muñoz Ramo, Nathan Fitzpatrick. 2023-03-10. Simulating non-unitary dynamics using quantum signal processing with unitary block encoding. https://arxiv.org/abs/2303.06161

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