Quantum gates via continuous time quantum walks in multiqubit systems with non-local auxiliary states

TL;DR

This paper introduces a novel method using continuous time quantum walks to perform multiqubit gates in systems with non-local auxiliary states, enabling concurrent operations and efficient gate compression.

Contribution

It proposes a new approach leveraging quantum walks over non-local states for multiqubit gate implementation, addressing spectral crowding and resource limitations.

Findings

Quantum walks can perform single-, two-, and three-qubit gates.

The method is scalable for quantum registers with nearest-neighbor interactions.

Configurations suitable for quantum dots, diamond defects, and superconducting qubits are discussed.

Abstract

Non-local higher-energy auxiliary states have been successfully used to entangle pairs of qubits in different quantum computing systems. Typically a longer-span non-local state or sequential application of few-qubit entangling gates are needed to produce a non-trivial multiqubit gate. In many cases a single non-local state that span over the entire system is difficult to use due to spectral crowding or impossible to have. At the same time, many multiqubit systems can naturally develop a network of multiple non-local higher-energy states that span over few qubits each. We show that continuous time quantum walks can be used to address this problem by involving multiple such states to perform local and entangling operations concurrently on many qubits. This introduces an alternative approach to multiqubit gate compression based on available physical resources. We formulate general requirements for such walks and discuss configurations of non-local auxiliary states that can emerge in quantum computing architectures based on self-assembled quantum dots, defects in diamond, and superconducting qubits, as examples. Specifically, we discuss a scalable multiqubit quantum register constructed as a single chain with nearest-neighbor interactions. We illustrate how quantum walks can be configured to perform single-, two- and three-qubit gates, including Hadamard, Control-NOT, and Toffoli gates. Continuous time quantum walks on graphs involved in these gates are investigated.