Robustness of near-thermal dynamics on digital quantum computers

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Understanding the impact of gate errors on quantum circuits is crucial to determining the potential applications of quantum computers, especially in the absence of large-scale error-corrected hardware. We put forward analytical arguments, corroborated by extensive numerical and experimental evidence, that Trotterized quantum circuits simulating the time evolution of systems near thermal equilibrium are substantially more robust to both quantum gate errors and Trotter (discretization) errors than is widely assumed. In Quantinuum’s trapped-ion computers, the weakly entangling gates that appear in Trotterized circuits can be implemented natively, and their error rate is smaller when they generate less entanglement; from benchmarking, we know that the error for a gate <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:mo form="prefix">exp</a:mo> <a:mo>[</a:mo> <a:mo>−</a:mo> <a:mi>i</a:mi> <a:mo>(</a:mo> <a:mi>Z</a:mi> <a:mo>⊗</a:mo> <a:mi>Z</a:mi> <a:mo>)</a:mo> <a:mi>τ</a:mi> <a:mo>]</a:mo> </a:mrow> </a:math> decreases roughly linearly with <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mi>τ</c:mi> </c:math> , up to a small offset at <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:mrow> <d:mi>τ</d:mi> <d:mo>=</d:mo> <d:mn>0</d:mn> </d:mrow> </d:math> . We provide extensive evidence that this scaling, together with the robustness of near-thermal dynamics to both gate and discretization errors, facilitates substantial improvements in the achievable accuracy of Trotterized dynamics on near-term quantum computers. We make heavy use of a theoretical tool—a statistical ensemble of random product states that approximates a thermal state, which can be efficiently prepared with low noise on quantum computers. We outline how the random product state ensemble can be used to predict, optimize, and design Hamiltonian simulation experiments on near-thermal quantum systems.

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