Fast Universal Quantum Computation with Railroad-switch Local Hamiltonians

TL;DR

This paper introduces two models of universal quantum computation using time-independent, frustration-free Hamiltonians with local projectors, leveraging a railroad-switch clock register to efficiently simulate quantum circuits.

Contribution

It presents novel 2- and 3-local Hamiltonian models for universal quantum computation with efficient resources and simplified proofs of universality.

Findings

Achieves universal quantum computation with O(L) local systems

Runs in O(L log^2 L) time, scalable with circuit size

Provides simplified proof of 3-local Adiabatic Quantum Computation universality

Abstract

We present two universal models of quantum computation with a time-independent, frustration-free Hamiltonian. The first construction uses 3-local (qubit) projectors, and the second one requires only 2-local qubit-qutrit projectors. We build on Feynman's Hamiltonian computer idea and use a railroad-switch type clock register. The resources required to simulate a quantum circuit with L gates in this model are O(L) small-dimensional quantum systems (qubits or qutrits), a time-independent Hamiltonian composed of O(L) local, constant norm, projector terms, the possibility to prepare computational basis product states, a running time O(L log^2 L), and the possibility to measure a few qubits in the computational basis. Our models also give a simplified proof of the universality of 3-local Adiabatic Quantum Computation.