Two-level Quantum Walkers on Directed Graphs I: Universal Quantum Computing

TL;DR

This paper introduces a model of universal quantum computation using multi-particle continuous-time quantum walks on directed graphs, employing a novel roundabout gate and dual-rail encoding without the need for time-dependent control.

Contribution

It presents a new quantum computing model based on quantum walks with internal states, utilizing a single type of gate and encoding, eliminating the need for ancilla qubits and dynamic control.

Findings

Developed a roundabout gate using directed weighted graphs.

Constructed universal quantum gates from combined roundabout and internal state gates.

Achieved universal quantum computation with no time-dependent control.

Abstract

In the present paper, the first in a series of two, we propose a model of universal quantum computation using a fermionic/bosonic multi-particle continuous-time quantum walk with two internal states (e.g., the spin-up and down states of an electron). A dual-rail encoding is adopted to convert information: a single-qubit is represented by the presence of a single quantum walker in either of the two parallel paths. We develop a roundabout gate that moves a walker from one path to the next, either clockwise or counterclockwise, depending on its internal state. It can be realized by a single-particle scattering on a directed weighted graph with the edge weights $1$ and $\pm i$. The roundabout gate also allows the spatial information of the quantum walker to be temporarily encoded in its internal states. The universal gates are constructed by appropriately combining several roundabout gates, some unitary gates that act on the internal states and two-particle scatterings on straight paths. Any ancilla qubit is not required in our model. The computation is done by just passing quantum walkers through properly designed paths. Namely, there is no need for any time-dependent control. A physical implementation of quantum random access memory compatible with the present model will be considered in the second paper (arXiv:2204.08709).