Compilation of Trotter-Based Time Evolution for Partially Fault-Tolerant Quantum Computing Architecture

Achieving practical quantum speedup with limited resources is a crucial challenge in both academic and industrial communities. To address this, a partially fault-tolerant quantum computing architecture called “space-time efficient analog rotation quantum computing architecture” (STAR architecture) been recently been proposed. This architecture focuses on minimizing resource requirements while maximizing the precision of non-Clifford gates, essential for universal quantum computation. However, nondeterministic processes such as the repeat-until-success (RUS) protocol and state injection can introduce significant computational overhead. Therefore, optimizing the logical circuit to minimize this overhead by using efficient fault-tolerant operations is essential. This paper presents an efficient method for simulating the time evolution of the two-dimensional (2D) Hubbard-model Hamiltonian, a promising application of the STAR architecture. We present two techniques, the parallel-injection protocol and adaptive injection-region updating, to reduce unnecessary time overhead specific to our architecture. By integrating these with the existing fermionic (f) technique, we develop an efficient Trotter-based time-evolution operation for the 2D Hubbard model. Our analysis reveals an acceleration of over 10 times compared to naive serial compilation. Based on this optimized compilation, we estimate the computational resources required for the quantum phase estimation of the 2D Hubbard model. For devices with a physical error rate of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msub> <a:mi>p</a:mi> <a:mi>phys</a:mi> </a:msub> <a:mo>=</a:mo> <a:msup> <a:mn>10</a:mn> <a:mrow> <a:mo>−</a:mo> <a:mn>4</a:mn> </a:mrow> </a:msup> </a:math> , we estimate that approximately <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mn>6.2</c:mn> <c:mo>×</c:mo> <c:msup> <c:mn>10</c:mn> <c:mn>4</c:mn> </c:msup> </c:math> physical qubits are required to achieve faster ground-state energy estimation of the <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mn>8</e:mn> <e:mo>×</e:mo> <e:mn>8</e:mn> </e:math> Hubbard model compared to classical computation.