Universal 2-local Hamiltonian Quantum Computing

TL;DR

This paper introduces a universal 2-local Hamiltonian quantum computing scheme that operates efficiently without perturbation gadgets or slow adiabatic processes, using a fixed, simple Hamiltonian structure.

Contribution

It presents a new universal quantum computation model with a fixed, constant-norm 2-local Hamiltonian that is efficient and does not rely on perturbation gadgets or slow evolution.

Findings

Runs in time proportional to the square of the number of gates

Uses a polynomial number of fixed, 2-local interaction terms

Avoids the need for large energy penalties or slow adiabatic evolution

Abstract

We present a Hamiltonian quantum computation scheme universal for quantum computation (BQP). Our Hamiltonian is a sum of a polynomial number (in the number of gates L in the quantum circuit) of time-independent, constant-norm, 2-local qubit-qubit interaction terms. Furthermore, each qubit in the system interacts only with a constant number of other qubits. The computer runs in three steps - starts in a simple initial product-state, evolves it for time of order L^2 (up to logarithmic factors) and wraps up with a two-qubit measurement. Our model differs from the previous universal 2-local Hamiltonian constructions in that it does not use perturbation gadgets, does not need large energy penalties in the Hamiltonian and does not need to run slowly to ensure adiabatic evolution.