Adiabatic Quantum Simulators

TL;DR

This paper proposes an adiabatic quantum simulation method for approximating ground state properties of sparse Hamiltonians, potentially offering a more feasible alternative to gate-based quantum computing for complex quantum problems.

Contribution

It introduces a novel adiabatic quantum simulation scheme that uses sparse Hamiltonians with at most three-local interactions, enabling ground state energy estimation and verification of QMA-complete problems.

Findings

Efficient approximation of ground state properties using adiabatic evolution.

Ability to verify QMA-complete problems like LOCAL HAMILTONIAN.

Potential for more feasible quantum simulation implementations.

Abstract

In his famous 1981 talk, Feynman proposed that unlike classical computers, which would presumably experience an exponential slowdown when simulating quantum phenomena, a universal quantum simulator would not. An ideal quantum simulator would be controllable, and built using existing technology. In some cases, moving away from gate-model-based implementations of quantum computing may offer a more feasible solution for particular experimental implementations. Here we consider an adiabatic quantum simulator which simulates the ground state properties of sparse Hamiltonians consisting of one- and two-local interaction terms, using sparse Hamiltonians with at most three-local interactions. Properties of such Hamiltonians can be well approximated with Hamiltonians containing only two-local terms. The register holding the simulated ground state is brought adiabatically into interaction with a probe qubit, followed by a single diabatic gate operation on the probe which then undergoes free evolution until measured. This allows one to recover e.g. the ground state energy of the Hamiltonian being simulated. Given a ground state, this scheme can be used to verify the QMA-complete problem LOCAL HAMILTONIAN, and is therefore likely more powerful than classical computing.