Verifier-on-a-Leash: New Schemes for Verifiable Delegated Quantum Computation, with Quasilinear Resources

Abstract

The problem of reliably certifying the outcome of a computation performed by a quantum device is rapidly gaining relevance. We present two protocols for a classical verifier to verifiably delegate a quantum computation to two non-communicating but entangled quantum provers. Our protocols have near-optimal complexity in terms of the total resources employed by the verifier and the honest provers, with the total number of operations of each party, including the number of entangled pairs of qubits required of the honest provers, scaling as O(g log g) for delegating a circuit of size g. This is in contrast to previous protocols, whose overhead in terms of resources employed, while polynomial, is far beyond what is feasible in practice. Our first protocol requires a number of rounds that is linear in the depth of the circuit being delegated, and is blind, meaning neither prover can learn the circuit or its input. The second protocol is not blind, but requires only a constant number of rounds of interaction.Our main technical innovation is an efficient rigidity theorem that allows a verifier to test that two entangled provers perform measurements specified by an arbitrary m-qubit tensor product of singlequbit Clifford observables on their respective halves of m shared EPR pairs, with a robustness that is independent of m. Our two-prover classical-verifier delegation protocols are obtained by combining this rigidity theorem with a single-prover quantum-verifier protocol for the verifiable delegation of a quantum computation, introduced by Broadbent (Theory of Computing, 2018).

Resource-efficient verification of quantum computing using Serfling’s bound

“…Eqs. (38) and (39) means that when the state ρ of the remaining N total − nN test (≡ N rest ) registers is expanded by these basis states:…”

“…In their protocols, a client is required to prepare single-qubit states whereas single-qubit measurements are required in our setup. In order to make the client classical, several multi-server protocols have been proposed [35][36][37][38][39].…”

“…Particularly, Coladangelo et al have recently constructed two resource-efficient protocols for a classical client to verifiably delegate quantum computing to two non-communicating but entangled quantum servers [38]. Other multi-server protocols have also been proposed to make verification protocols device independent [40,41].…”

QFactory: Classically-Instructed Remote Secret Qubits Preparation

“…In Appendix D we list three simpler scenarios (of increasing complication) that lead to the most general case given here, following similar steps with the extension of simple i.i.d. self-testing to fully robust and rigid self-testing in existing literature [MMMO06,MHYS12,HYN12,RUV13,CGJV17].…”

Parallel Self-Testing of the GHZ State with a Proof by Diagrams

“…Such games are a resource not only for cryptography, but also for quantum computation: these games can be manipulated to force untrusted devices to perform measurements on copies of the Bell state which carry out complex circuits. This idea originated in [32] and has seen variants and improvements since then [21,26,11]. For such applications, it is important that the result include an error term which is (at most) bounded by some polynomial function of the number of copies of the state.…”