Adiabatic and Hamiltonian computing on a 2D lattice with simple 2-qubit interactions

TL;DR

This paper demonstrates how to perform universal quantum computation on a 2D lattice using simple 2-qubit interactions and a time-independent Hamiltonian, enabling potentially practical implementations.

Contribution

It introduces a novel 2D lattice model for universal quantum computing with simple interactions and avoids complex perturbation gadgets, simplifying physical realization.

Findings

Uses a single first-order perturbation to derive the effective Hamiltonian.

Models universal quantum computation with only ZZ and XX+YY interactions.

Potentially realizable with superconducting or solid-state qubits.

Abstract

We show how to perform universal Hamiltonian and adiabatic computing using a time-independent Hamiltonian on a 2D grid describing a system of hopping particles which string together and interact to perform the computation. In this construction, the movement of one particle is controlled by the presence or absence of other particles, an effective quantum field effect transistor that allows the construction of controlled-NOT and controlled-rotation gates. The construction translates into a model for universal quantum computation with time-independent 2-qubit ZZ and XX+YY interactions on an (almost) planar grid. The effective Hamiltonian is arrived at by a single use of first-order perturbation theory avoiding the use of perturbation gadgets. The dynamics and spectral properties of the effective Hamiltonian can be fully determined as it corresponds to a particular realization of a mapping between a quantum circuit and a Hamiltonian called the space-time circuit-to-Hamiltonian construction. Because of the simple interactions required, and because no higher-order perturbation gadgets are employed, our construction is potentially realizable using superconducting or other solid-state qubits.