Demonstration of algorithmic quantum speedup

TL;DR

This paper demonstrates a clear algorithmic quantum speedup on NISQ devices by implementing the Bernstein-Vazirani algorithm, showing quantum advantage in problem-solving times without relying on conjectures or additional assumptions.

Contribution

First experimental demonstration of a provable algorithmic quantum speedup on NISQ hardware using the Bernstein-Vazirani algorithm with dynamical decoupling.

Findings

Speedup observed on one of two IBM Quantum processors.

Dynamical decoupling enhances quantum computation performance.

No reliance on complexity-theoretic conjectures or assumptions.

Abstract

Quantum algorithms theoretically outperform classical algorithms in solving problems of increasing size, but computational errors must be kept to a minimum to realize this potential. Despite the development of increasingly capable quantum computers (QCs), an experimental demonstration of a provable algorithmic quantum speedup employing today's non-fault-tolerant, noisy intermediate-scale quantum (NISQ) devices has remained elusive. Here, we unequivocally demonstrate such a speedup, quantified in terms of the scaling with the problem size of the time-to-solution metric. We implement the single-shot Bernstein-Vazirani algorithm, which solves the problem of identifying a hidden bitstring that changes after every oracle query, utilizing two different 27-qubit IBM Quantum (IBMQ) superconducting processors. The speedup is observed on only one of the two QCs (ibmq_montreal) when the quantum computation is protected by dynamical decoupling (DD) -- a carefully designed sequence of pulses applied to the QC that suppresses its interaction with the environment, but not without DD. In contrast to recent quantum supremacy demonstrations, the quantum speedup reported here does not rely on any additional assumptions or complexity-theoretic conjectures and solves a bona fide computational problem, in the setting of a game with an oracle and a verifier.