An Algebraic Quantum Circuit Compression Algorithm for Hamiltonian Simulation

Abstract

Quantum computing is a promising technology that harnesses the peculiarities of quantum mechanics to deliver computational speedups for some problems that are intractable to solve on a classical computer. Current generation noisy intermediate-scale quantum (NISQ) computers are severely limited in terms of chip size and error rates. Shallow quantum circuits with uncomplicated topologies are essential for successful applications in the NISQ era. Based on matrix analysis, we derive localized circuit transformations to efficiently compress quantum circuits for simulation of certain spin Hamiltonians known as free fermions. The depth of the compressed circuits is independent of simulation time and grows linearly with the number of spins. The proposed numerical circuit compression algorithm behaves backward stable and scales cubically in the number of spins enabling circuit synthesis beyond $\mathcal{O}(10^3)$ spins. The resulting quantum circuits have a simple nearest-neighbor topology, which makes them ideally suited for NISQ devices.

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Cited by in corpus (13)

• Fixed Depth Hamiltonian Simulation via Cartan Decomposition
• Classification of dynamical Lie algebras for translation-invariant 2-local spin systems in one dimension
• Efficient Hamiltonian Simulation for Solving Option Price Dynamics
• Time Evolution of Uniform Sequential Circuits
• Qutrit Circuits and Algebraic Relations: A Pathway to Efficient Spin-1 Hamiltonian Simulation
• Riemannian quantum circuit optimization for Hamiltonian simulation
• Two-dimensional coherent spectrum of high-spin models via a quantum computing approach
• Navigating the noise-depth tradeoff in adiabatic quantum circuits
• QuYBE -- An Algebraic Compiler for Quantum Circuit Compression
• Parallel-in-time quantum simulation via Page and Wootters quantum time
• Reinforcement learning with learned gadgets to tackle hard quantum problems on real hardware
• Cost of Emulating a Small Quantum Annealing Problem in the Circuit-Model
• Quantum Algorithms for State Preparation and Data Classification based on Stabilizer Codes