Experimental Superposition of Orders of Quantum Gates

TL;DR

This paper experimentally demonstrates that superposing the order of quantum gates can enhance computational efficiency, allowing certain problems to be solved with fewer gate uses than fixed-order quantum circuits, indicating a potential exponential advantage.

Contribution

The first experimental realization of superposing quantum gate orders, showing improved efficiency in determining gate commutation with fewer queries.

Findings

Single-query determination of gate commutation achieved.

Superposition of gate orders offers exponential scaling advantage.

Demonstrates practical implementation of superposed causal orders.

Abstract

In a quantum computer, creating superpositions of quantum bits (qubits) in different states can lead to a speed-up over classical computers [1], but quantum mechanics also allows for the superposition of quantum circuits [2]. In fact, it has recently been theoretically predicted that superimposing quantum circuits, each with a different gate order, could provide quantum computers with an even further computational advantage [3-5]. Here, we experimentally demonstrate this enhancement by applying two quantum gates in a superposition of both possible orders to determine whether the two gates commute or anti-commute. We are able to make this determination with only a single use (or query) of each gate, while all quantum circuits with a fixed order of gates would require at least two uses of one of the gates [3]. Remarkably, when the problem is scaled to N gates, creating a superposition of quantum circuits is likely to provide an exponential advantage over classical algorithms, and a linear advantage over quantum algorithms with fixed gate order [4]. The new resource that we exploit in our experiment can be interpreted as a "superposition of causal orders". We demonstrate such a superposition could allow some quantum algorithms to be implemented with an efficiency that is unlikely to be achieved on a quantum computer with a fixed gate order.