Entanglement Scaling in Quantum Advantage Benchmarks

TL;DR

This paper establishes an entanglement scaling bound for quantum advantage benchmarks, linking the depth of random circuits to the amount of bipartite entanglement needed for quantum advantage demonstrations.

Contribution

It derives a lattice geometry-dependent upper bound on circuit depth for generating maximal bipartite entanglement, connecting entanglement properties to quantum advantage validation.

Findings

Supports super-logarithmic entanglement across qubit partitions

Provides a testable entanglement criterion for quantum advantage claims

Highlights the importance of volumetric entanglement scaling

Abstract

A contemporary technological milestone is to build a quantum device performing a computational task beyond the capability of any classical computer, an achievement known as quantum adversarial advantage. In what ways can the entanglement realized in such a demonstration be quantified? Inspired by the area law of tensor networks, we derive an upper bound for the minimum random circuit depth needed to generate the maximal bipartite entanglement correlations between all problem variables (qubits). This bound is (i) lattice geometry dependent and (ii) makes explicit a nuance implicit in other proposals with physical consequence. The hardware itself should be able to support super-logarithmic ebits of entanglement across some poly($n$) number of qubit-bipartitions, otherwise the quantum state itself will not possess volumetric entanglement scaling and full-lattice-range correlations. Hence, as we present a connection between quantum advantage protocols and quantum entanglement, the entanglement implicitly generated by such protocols can be tested separately to further ascertain the validity of any quantum advantage claim.