# AN ALGEBRAIC QUANTUM CIRCUIT COMPRESSION ALGORITHM FOR HAMILTONIAN SIMULATION

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS（2022）

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) com-puters 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 sim-ulation 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 nu-merical circuit compression algorithm behaves backward stable and scales cubically in the number of spins enabling circuit synthesis beyond 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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Key words

quantum computing, quantum circuit synthesis, algebraic circuit compression, Hamiltonian simulation, free fermions, NISQ

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