Abstract

Author’s note: Changed topic to incorporate Cartan decomposition.

Unitary synthesis, e.g. in constructing unitary coupled cluster factors or for evolution under a time dependent Hamiltonian is a key component of quantum simulation on quantum computers. Synthesizing the corresponding quantum circuit is typically done by breaking the operator into small circuit elements, which leads to circuits whose depth often scales unfavorably. 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 circuit elements into a single block of quantum gates. This results, for example, 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. Based on these ideas, we will also present an extension to controlled gates and imaginary time evolution.