SupercheQ: Quantum Advantage for Distributed Databases
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 $\mathrm{poly}(n^\ell)$ depth to enable verification for files with $O(n^\ell)$ bits for arbitrary constant $\ell$. The quantum advantage is achieved by random circuit sampling, thereby potentially 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 motivated by Infleqtion's Sqale neutral atom QPU gateset. The second variant, Supercheq-IE (Incremental Encoding), also achieves arbitrary-polynomial advantage in fingerprint size ($n$ qubits to verify files with size $O(n^{\ell})$ bits), while supporting incremental updates to the fingerprint using only a constant number of $(\ell-1)$-qubit gates. Moreover, Supercheq-IE at $\ell=2$ ($\geq 3$) only requires Clifford gates (gates in the $\ell-1$ level of the Clifford hierarchy), ensuring relatively modest overheads for error-corrected implementation. We experimentally demonstrate proof-of-concepts on quantum hardware from Diraq (spin qubit) and IBM (superconducting). We envision Supercheq could be deployed in distributed data settings, accompanying replicas of important databases.