Well-conditioned multi-product formulas for hardware-friendly Hamiltonian simulation

Abstract

Simulating the time-evolution of a Hamiltonian is one of the most promising applications of quantum computers. Multi-Product Formulas (MPFs) are well suited to replace standard product formulas since they scale better with respect to time and approximation errors. Hamiltonian simulation with MPFs was first proposed in a fully quantum setting using a linear combination of unitaries. Here, we analyze and demonstrate a hybrid quantum-classical approach to MPFs that classically combines expectation values evaluated with a quantum computer. This has the same approximation bounds as the fully quantum MPFs, but, in contrast, requires no additional qubits, no controlled operations, and is not probabilistic. We show how to design MPFs that do not amplify the hardware and sampling errors, and demonstrate their performance. In particular, we illustrate the potential of our work by theoretically analyzing the benefits when applied to a classically intractable spin-boson model, and by computing the dynamics of the transverse field Ising model using a classical simulator as well as quantum hardware. We observe an error reduction of up to an order of magnitude when compared to a product formula approach by suppressing hardware noise with Pauli Twirling, pulse efficient transpilation, and a novel zero-noise extrapolation based on scaled cross-resonance pulses. The MPF methodology reduces the circuit depth and may therefore represent an important step towards quantum advantage for Hamiltonian simulation on noisy hardware.

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• Mitigating crosstalk errors by randomized compiling: Simulation of the BCS model on a superconducting quantum computer
• Early Fault-Tolerant Quantum Algorithms in Practice: Application to Ground-State Energy Estimation
• Approximate Quantum Compiling for Quantum Simulation: A Tensor Network based approach
• Equivariant Variational Quantum Eigensolver to detect Phase Transitions through Energy Level Crossings
• Tensor Network enhanced Dynamic Multiproduct Formulas
• Semicoherent Symmetric Quantum Processes: Theory and Applications
• Phase estimation with partially randomized time evolution
• Trotter error time scaling separation via commutant decomposition
• Short-time simulation of quantum dynamics by Pauli measurements
• Realization of Two-dimensional Discrete Time Crystals with Anisotropic Heisenberg Coupling
• On the commutator scaling in Hamiltonian simulation with multi-product formulas
• Co-Designing Spectral Transformation Oracles with Hybrid Oscillator-Qubit Quantum Processors: From Algorithms to Compilation