Phase Estimation with Compressed Controlled Time Evolution

TL;DR

This paper presents a compression protocol for controlled time evolution in quantum simulations, significantly reducing circuit depth and control overhead, enabling more efficient quantum phase estimation on near-term hardware.

Contribution

It introduces a near-optimal compression method for controlled time evolution operators, improving efficiency and feasibility of quantum phase estimation algorithms.

Findings

Achieves circuit depth scaling of O(t polylog(t N/ε))

Enables quantum phase estimation with as few as 414 CNOT gates

Attains ground state energy errors below 1% on simulated hardware

Abstract

Many optimally scaling quantum simulation algorithms employ controlled time evolution of the Hamiltonian, which is typically the major bottleneck for their efficient implementation. This work establishes a compression protocol for encoding the controlled time evolution operator of translationally invariant, local Hamiltonians into a quantum circuit. It achieves a near-optimal in time $t$ scaling for circuit depth $\mathcal{O}(t \text{ polylog}(t N/\epsilon))$, while reducing the control overhead from a multiplicative to an additive factor. We report that this compression protocol enables the implementation of Iterative Quantum Phase Estimation with as few as 414 CNOT gates for a frustrated quantum spin system on a 6$\times$6 triangular lattice and delivers ground state energy errors below 1% (with $\pm$ 1.5% variation, calculated with a hardware noise aware pipeline) on a 4$\times$4 triangular lattice using the noisy emulator of the Quantinuum H2 trapped ion device.