[Paper Review] Experimental Cryptographic Verification for Near-Term Quantum Cloud Computing

Xi Chen, Bin Cheng+5 more|arXiv (Cornell University)|Aug 22, 2018

Quantum Computing Algorithms and Architecture4 citations

TL;DR

This paper proposes a cryptographic verification scheme for near-term quantum cloud computing that allows a classical client to verify the quantumness of a remote quantum server without requiring quantum capabilities. By encoding a secret string in a scrambled instantaneous quantum polynomial (IQP) circuit and measuring output probability biases, the scheme enables detection of classical simulations; experimental validation on a 5-qubit NMR processor achieved ~2.5% error after noise compensation, while IBM's 5- and 16-qubit cloud processors failed due to high noise levels (~42% error).

ABSTRACT

Recently, there are more and more organizations offering quantum-cloud services, where any client can access a quantum computer remotely through the internet. In the near future, these cloud servers may claim to offer quantum computing power out of reach of classical devices. An important task is to make sure that there is a real quantum computer running, instead of a simulation by a classical device. Here we explore the applicability of a cryptographic verification scheme that avoids the need of implementing a full quantum algorithm or requiring the clients to communicate with quantum resources. In this scheme, the client encodes a secret string in a scrambled IQP (instantaneous quantum polynomial) circuit sent to the quantum cloud in the form of classical message, and verify the computation by checking the probability bias of a class of output strings generated by the server. We provided a theoretical extension and implemented the scheme on a 5-qubit NMR quantum processor in the laboratory and a 5-qubit and 16-qubit processors of the IBM quantum cloud. We found that the experimental results of the NMR processor can be verified by the scheme with about $2.5\%$ error, after noise compensation by standard techniques. However, the fidelity of the IBM quantum cloud is currently too low to pass the test (about $42\%$ error). This verification scheme shall become practical when servers claim to offer quantum-computing resources that can achieve quantum supremacy.

Motivation & Objective

• To address the critical challenge of verifying whether a quantum cloud server is genuinely performing quantum computation or merely simulating it with classical resources.
• To develop a verification protocol that requires no quantum capabilities from the client, making it practical for classical users accessing remote quantum services.
• To test the feasibility of the scheme on real-world quantum hardware, including NMR and IBM quantum processors, under near-term noisy conditions.
• To evaluate the robustness of the verification method against noise and assess its viability when quantum supremacy is claimed.
• To establish a practical benchmark for quantum cloud service providers to demonstrate genuine quantum advantage.

Proposed method

• The client prepares a secret classical string and encodes it into a scrambled instantaneous quantum polynomial (IQP) circuit, which is sent to the quantum server as a classical message.
• The quantum server executes the circuit and returns the output probability distribution for a specific set of measurement outcomes.
• The client computes the probability bias of a designated output string (e.g., the secret vector) and compares it to the expected quantum value under ideal conditions.
• The scheme relies on the cryptographic hardness of distinguishing the true quantum output distribution from a uniform (classical) one, based on the bias in the output string probabilities.
• Noise compensation techniques are applied to experimental data to improve fidelity estimates, particularly in the NMR implementation.
• The protocol is implemented on a 5-qubit nuclear magnetic resonance (NMR) quantum processor and on IBM’s 5- and 16-qubit cloud processors for comparative evaluation.

Experimental results

Research questions

• RQ1 Can a purely classical client verify the quantumness of a remote quantum server without requiring quantum resources or full quantum algorithm execution?
• RQ2 How robust is the IQP-based verification scheme against noise in near-term quantum processors?
• RQ3 To what extent can noise-compensated experimental data from NMR processors pass the verification test compared to noisy cloud-based implementations?
• RQ4 What is the fidelity threshold required for the verification scheme to successfully distinguish genuine quantum computation from classical simulation?
• RQ5 Can the scheme be practically applied when quantum cloud providers claim to achieve quantum supremacy?

Key findings

• The experimental implementation on a 5-qubit NMR quantum processor achieved a verification error of approximately 2.5% after applying standard noise compensation techniques.
• The fidelity of the IBM quantum cloud processors (both 5-qubit and 16-qubit) was too low to pass the verification test, with an error rate of about 42%.
• The output probability bias for the IBM devices was found to be close to that of a completely mixed state, indicating strong noise-induced decoherence and failure to preserve quantum coherence.
• The verification scheme successfully detected the quantum nature of the NMR processor, demonstrating that it can distinguish genuine quantum behavior from classical simulation under controlled noise.
• The results indicate that current cloud-based quantum processors, despite their scalability, are not yet sufficiently coherent to pass cryptographic verification under this scheme.
• The study establishes that the proposed scheme is viable for near-term verification when hardware fidelity is sufficiently high, highlighting the need for improved error mitigation in cloud quantum systems.