[Paper Review] Interactive Protocols for Classically-Verifiable Quantum Advantage

Daiwei Zhu, Gregory D. Kahanamoku–Meyer+16 more|arXiv (Cornell University)|Dec 9, 2021

Quantum Computing Algorithms and Architecture60 references4 citations

TL;DR

This paper presents the first experimental implementation of interactive protocols for classically-verifiable quantum advantage using mid-circuit measurements in trapped-ion quantum computers. By spatially isolating qubits via shuttling, the protocol enables efficient classical verification of quantum computations through interaction, demonstrating scalable verification of quantumness with only hundreds to a few thousand qubits.

ABSTRACT

Achieving quantum computational advantage requires solving a classically intractable problem on a quantum device. Natural proposals rely upon the intrinsic hardness of classically simulating quantum mechanics; however, verifying the output is itself classically intractable. On the other hand, certain quantum algorithms (e.g. prime factorization via Shor's algorithm) are efficiently verifiable, but require more resources than what is available on near-term devices. One way to bridge the gap between verifiability and implementation is to use "interactions" between a prover and a verifier. By leveraging cryptographic functions, such protocols enable the classical verifier to enforce consistency in a quantum prover's responses across multiple rounds of interaction. In this work, we demonstrate the first implementation of an interactive quantum advantage protocol, using an ion trap quantum computer. We execute two complementary protocols -- one based upon the learning with errors problem and another where the cryptographic construction implements a computational Bell test. To perform multiple rounds of interaction, we implement mid-circuit measurements on a subset of trapped ion qubits, with subsequent coherent evolution. For both protocols, the performance exceeds the asymptotic bound for classical behavior; maintaining this fidelity at scale would conclusively demonstrate verifiable quantum advantage.

Motivation & Objective

• To demonstrate a scalable, classically-verifiable method for proving quantum advantage using interactive protocols.
• To overcome the limitations of non-interactive quantum verification, which scales exponentially with qubit count.
• To implement mid-circuit measurements in a trapped-ion quantum processor to enable coherent quantum computation after partial measurement.
• To validate the feasibility of interactive proofs for quantumness on near-term quantum hardware using practical parameters.
• To provide a framework for verifying untrusted quantum devices through interaction, with polynomial scaling in verification cost.

Proposed method

• Utilizes mid-circuit measurements by spatially isolating target qubits via shuttling in a trapped-ion quantum processor.
• Employs a trapdoor claw-free function (TCF) as the computational primitive for quantum advantage protocols.
• Applies interactive proof protocols where the classical verifier sends challenges and the quantum prover responds with quantum state preparations.
• Uses optimized quantum circuits that conserve qubits by computing output values element-by-element rather than storing full vectors.
• Employs both factoring-based and LWE-based TCFs, with parameter estimates for cryptographic security (e.g., 2048-bit RSA, n=256, q=4093 for LWE).
• Demonstrates that verification remains efficient (polynomial time) even as quantum advantage scales with qubit count.

Experimental results

Research questions

• RQ1 Can interactive protocols enable classically efficient verification of quantum advantage in a near-term quantum device?
• RQ2 How can mid-circuit measurements be implemented coherently in a trapped-ion system to support interactive verification?
• RQ3 What resource requirements (qubits, circuit depth) are needed to achieve a classically infeasible computational task with interactive verification?
• RQ4 Can the same protocol framework be applied to both factoring and LWE-based quantum advantage demonstrations?
• RQ5 What parameter choices ensure that classical supercomputers would require thousands of core-years to break the protocol, thus demonstrating quantum advantage?

Key findings

• The protocol achieves classically efficient verification of quantum advantage with polynomial scaling, unlike prior non-interactive approaches that scale exponentially.
• Mid-circuit measurements were successfully implemented via qubit shuttling, enabling coherent evolution after partial measurement in a trapped-ion system.
• For factoring-based quantum advantage, a 2048-bit RSA modulus requires approximately 4100 qubits with optimized circuits, while a 1600-qubit version suffices for a 795-bit semiprime.
• For LWE-based protocols, parameters with n=256 and q=4093 require roughly 6200 qubits to store input and output vectors, but can be reduced to ~3100 qubits using qubit reuse.
• The protocols are designed so that classical factoring or LWE breaking would require ~1000 core-years, exceeding current classical capabilities and demonstrating quantum advantage.
• The experimental implementation demonstrates that interactive verification is feasible on near-term devices, with full protocols expected to complete in hours on a scaled-up device.