Algebraic Compression of Quantum Circuits for Hamiltonian Evolution

Abstract

Unitary evolution under a time dependent Hamiltonian is a key component of simulation on quantum hardware. Synthesizing the corresponding quantum circuit is typically done by breaking the evolution into small time steps, also known as Trotterization, which leads to circuits whose depth scales with the number of steps. When the circuit elements are limited to a subset of SU(4) -- or equivalently, when the Hamiltonian may be mapped onto free fermionic models -- several identities exist that combine and simplify the circuit. Based on this, we present an algorithm that compresses the Trotter steps into a single block of quantum gates. This results in a fixed depth time evolution for certain classes of Hamiltonians. We explicitly show how this algorithm works for several spin models, and demonstrate its use for adiabatic state preparation of the transverse field Ising model.

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Cited by in corpus (24)

• Fixed Depth Hamiltonian Simulation via Cartan Decomposition
• Quantum dynamics simulations beyond the coherence time on NISQ hardware by variational Trotter compression
• Algebraic Bethe Circuits
• An entanglement perspective on the quantum approximate optimization algorithm
• On the complexity of implementing Trotter steps
• Quantum time dynamics of 1D-Heisenberg models employing the Yang-Baxter equation for circuit compression
• Classification of dynamical Lie algebras for translation-invariant 2-local spin systems in one dimension
• An Algebraic Quantum Circuit Compression Algorithm for Hamiltonian Simulation
• Quantum criticality using a superconducting quantum processor
• Generalization of Quantum Machine Learning Models Using Quantum Fisher Information Metric
• Computing exact moments of local random quantum circuits via tensor networks
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