Proof of efficient, parallelized, universal adiabatic quantum computation

TL;DR

This paper proves that a parallelized form of adiabatic quantum computation can efficiently simulate universal gate-based quantum computation, using explicit Hamiltonians for different qubit configurations.

Contribution

It provides a detailed proof demonstrating the efficiency of parallelized adiabatic quantum computation for universal quantum simulation.

Findings

Parallelized adiabatic quantum computation can simulate universal gate models efficiently.

Explicit Hamiltonians are constructed for different qubit configurations.

The approach applies to both 1D nearest neighbor and all-to-all qubit interactions.

Abstract

We give a careful proof that a parallelized version of adiabatic quantum computation can efficiently simulate universal gate model quantum computation. The proof specifies an explicit parameter-dependent Hamiltonian $H({\lambda})$ that is based on ground state quantum computation [1]. We treat both a 1-dimensional configuration in which qubits on a line undergo nearest neighbor 2-qubit gates and an all-to-all configuration in which every qubit undergoes 2-qubit gates with every other qubit in the system.