SupercheQ: Quantum Advantage for Distributed Databases

TL;DR

SupercheQ introduces quantum protocols that achieve exponential communication complexity advantages for file verification tasks, with scalable and incremental variants validated through simulations and quantum hardware experiments.

Contribution

The paper presents novel quantum fingerprinting protocols with exponential and quadratic advantages, scalable implementations, and practical validation on quantum hardware.

Findings

SupercheQ-EE achieves exponential communication advantage over classical protocols.

SupercheQ-IE supports incremental updates with modest quantum gate overhead.

Experimental demonstrations validate the protocols on IBM quantum hardware.

Abstract

We introduce SupercheQ, a family of quantum protocols that achieves asymptotic advantage over classical protocols for checking the equivalence of files, a task also known as fingerprinting. The first variant, SupercheQ-EE (Efficient Encoding), uses n qubits to verify files with 2^O(n) bits -- an exponential advantage in communication complexity (i.e. bandwidth, often the limiting factor in networked applications) over the best possible classical protocol in the simultaneous message passing setting. Moreover, SupercheQ-EE can be gracefully scaled down for implementation on circuits with poly(n^l) depth to enable verification for files with O(n^l) bits for arbitrary constant l. The quantum advantage is achieved by random circuit sampling, thereby endowing circuits from recent quantum supremacy and quantum volume experiments with a practical application. We validate SupercheQ-EE's performance at scale through GPU simulation. The second variant, SupercheQ-IE (Incremental Encoding), uses n qubits to verify files with O(n^2) bits while supporting constant-time incremental updates to the fingerprint. Moreover, SupercheQ-IE only requires Clifford gates, ensuring relatively modest overheads for error-corrected implementation. We experimentally demonstrate proof-of-concepts through Qiskit Runtime on IBM quantum hardware. We envision SupercheQ could be deployed in distributed data settings, accompanying replicas of important databases.