Algebraic compression of quantum circuits for Hamiltonian evolution

Here 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 the depth of which s...

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Bibliographic Details
Published in:Physical review. A 2022-03, Vol.105 (3), Article 032420
Main Authors: Kökcü, Efekan, Camps, Daan, Bassman Oftelie, Lindsay, Freericks, J. K., de Jong, Wibe A., Van Beeumen, Roel, Kemper, Alexander F.
Format: Article
Language:English
Subjects:
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
quantum algorithms
quantum computation
quantum gates
Quantum simulation
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Summary:Here 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 the depth of which 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 using algebraic relations between adjacent circuit elements. 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.
ISSN:2469-9926
2469-9934
DOI:10.1103/PhysRevA.105.032420