MarQSim: Reconciling Determinism and Randomness in Compiler Optimization for Quantum Simulation

TL;DR

MarQSim is a novel quantum compiler framework that combines deterministic and randomized compilation techniques using a Markov chain approach, improving efficiency and correctness in quantum Hamiltonian simulation.

Contribution

It introduces MarQSim, a new compilation framework that employs a Markov chain model and flow optimization to reconcile deterministic and randomized compilation benefits.

Findings

Produces more efficient quantum circuits for Hamiltonian simulation

Maintains high precision and correctness in generated circuits

Outperforms existing compilation methods in experiments

Abstract

Quantum simulation, fundamental in quantum algorithm design, extends far beyond its foundational roots, powering diverse quantum computing applications. However, optimizing the compilation of quantum Hamiltonian simulation poses significant challenges. Existing approaches fall short in reconciling deterministic and randomized compilation, lack appropriate intermediate representations, and struggle to guarantee correctness. Addressing these challenges, we present MarQSim, a novel compilation framework. MarQSim leverages a Markov chain-based approach, encapsulated in the Hamiltonian Term Transition Graph, adeptly reconciling deterministic and randomized compilation benefits. We rigorously prove its algorithmic efficiency and correctness criteria. Furthermore, we formulate a Min-Cost Flow model that can tune transition matrices to enforce correctness while accommodating various optimization objectives. Experimental results demonstrate MarQSim's superiority in generating more efficient quantum circuits for simulating various quantum Hamiltonians while maintaining precision.