Title:
Benchmarking and Optimization of Quantum Algorithms for Real-Time Dynamics Simulation
Abstract:
Real-time dynamics simulation is one of the most promising applications of quantum computing. With early fault-tolerant quantum devices expected soon, it is crucial to identify problems within reach of such hardware. In this work, we investigate the performance of quantum algorithms for simulating real-time dynamics through benchmarking and optimization across different scenarios.
We focus on quantum simulation of molecular Hamiltonians, implementing quantum circuits for Trotterization and Quantum Singular Value Transformation (QSVT), compiled using the Clifford + T universal gate set. Gate counts required for the time evolution of Fourier moments are empirically estimated using classical simulators. These observables are non-trivial to compute and provide insight into physical properties and energy distributions. To reduce QSVT's resource overhead, we apply classical preprocessing techniques that reduce the Hamiltonian 1-norm, including BLISS, orbital optimization, and anti-commuting regrouping. Additionally, we analyze how sparsification techniques impact the gate count in Trotterization.
Results for Trotterization show that the empirical gate requirements, particularly T gates and CNOT gates, are up to 4.791(9) orders of magnitude lower than theoretical predictions derived from analytical bounds at fixed simulation accuracy. In contrast, QSVT's theoretical bounds are significantly tighter. Applying BLISS and orbital optimization to the Hamiltonian leads to an average gate count reduction of 49.6(2)% for QSVT. Comparing the two algorithms, QSVT achieves an optimal scaling with respect to simulation accuracy, but its higher constant resource overhead makes Trotterization more favorable in low accuracy regimes. Finally, sparsification techniques applied to Trotterization reduce circuit complexity at low accuracy. Numerical analysis shows that the maximum error for which sparsification is preferred decreases inversely with the number of Hamiltonian terms.