Composite Quantum Simulations

Abstract

In this paper we provide a framework for combining multiple quantum simulation methods, such as Trotter-Suzuki formulas and QDrift into a single Composite channel that builds upon older coalescing ideas for reducing gate counts. The central idea behind our approach is to use a partitioning scheme that allocates a Hamiltonian term to the Trotter or QDrift part of a channel within the simulation. This allows us to simulate small but numerous terms using QDrift while simulating the larger terms using a high-order Trotter-Suzuki formula. We prove rigorous bounds on the diamond distance between the Composite channel and the ideal simulation channel and show under what conditions the cost of implementing the Composite channel is asymptotically upper bounded by the methods that comprise it for both probabilistic partitioning of terms and deterministic partitioning. Finally, we discuss strategies for determining partitioning schemes as well as methods for incorporating different simulation methods within the same framework.

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• Early Fault-Tolerant Quantum Algorithms in Practice: Application to Ground-State Energy Estimation
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• Chemically Motivated Simulation Problems are Efficiently Solvable by a Quantum Computer
• Faster Algorithmic Quantum and Classical Simulations by Corrected Product Formulas
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• Quantum Computing Beyond Ground State Electronic Structure: A Review of Progress Toward Quantum Chemistry Out of the Ground State
• Quantum Simulation via Stochastic Combination of Unitaries
• Does Quantum Mechanics Breed Larger, More Intricate Quantum Theories? The Case for Experience-Centric Quantum Theory and the Interactome of Quantum Theories
• Optimising Trotter-Suzuki Simulations of Markovian Open Quantum Systems via Classical Search