Quantum Signatures Bypass Tricky Quantum Memory with Classical Computing Power

Researchers are developing new methods for digital signatures that leverage the potential of quantum computation without demanding fully fault-tolerant hardware. Pradeep Niroula, Minzhao Liu, and Sivaprasad Omanakuttan, all from Global Technology Applied Research at JPMorganChase, alongside David Amaro from Quantinuum and Soumik Ghosh from the University of Chicago et al., present a digital signature scheme utilising classical shadows of states generated by random quantum circuits as public keys. This approach circumvents the need for long-lived quantum memory, a significant obstacle in current quantum cryptography, and offers a pathway towards practical quantum digital signatures on near-term quantum computers. Their work introduces an improved state-certification primitive, achieving enhanced noise tolerance and reduced sample complexity, and demonstrates a proof-of-principle signature using 32-qubit states, representing a crucial step towards realising quantum-enhanced security in the coming years.

Classical shadows enable secure quantum-inspired digital signatures via classical channels, offering a practical alternative to fully quantum cryptography

Researchers have developed a novel digital signature scheme leveraging quantum mechanics yet relying solely on classical communication channels. This breakthrough circumvents the need for transmitting fragile quantum states, a major obstacle in practical quantum cryptography. The work introduces a method using “classical shadows” of quantum states, essentially, the statistical fingerprints obtained from numerous measurements, as public keys for a digital signature.

Theoretical and numerical evidence supports the conjecture that discerning the original quantum circuit (the private key) from these shadows is computationally intractable, forming the basis of the scheme’s security. A key innovation lies in an enhanced state-certification primitive, improving tolerance to noise and reducing the number of samples required compared to previous methods.

This certification is achieved through a specifically designed, high-rate error-detecting code tailored for random quantum circuits. Experimentally, the team generated classical shadows for 32-qubit states using circuits containing at least 80 logical (and 582 physical) two-qubit gates, attaining a fidelity of 0.90 ±0.01.

This level of fidelity demonstrates a significant advancement in the reliable preparation and characterization of multi-qubit states. The hardware demonstration extends beyond state preparation to a proof-of-principle digital signature, showcasing the near-term feasibility of the proposed scheme. Increasing the number of measurement samples further validates the approach, suggesting a pathway towards practical implementation.

This research offers a new cryptographic paradigm grounded in the principles of quantum mechanics, independent of traditional computational hardness assumptions like integer factorization or learning-with-errors. The study’s security rests on the “computational no-learning” conjecture, positing that learning a quantum circuit from its classical shadows is fundamentally difficult.

Analyses demonstrate that existing algorithms for learning shallow circuits, as well as a specialized algorithm tailored to the circuits used in this work, fail to effectively reconstruct the private key. Furthermore, the team proves that successfully forging a signature is exponentially more difficult than verifying one, bolstering the scheme’s robustness against potential attacks. The implementation of a multi-block Iceberg encoding achieved beyond-break-even performance on circuits with 40 logical qubits and 680 logical gates, representing a notable result in quantum error mitigation.

Experimental validation of shadow-based digital signatures on a superconducting processor demonstrates promising results

A 72-qubit superconducting processor underpinned the experimental validation of a novel digital signature scheme. This research introduced a method utilising classical shadows of states produced by random circuits as public keys, circumventing the need for quantum communication. The study focused on establishing the conjectured hardness of deducing the private key, the circuit itself, from its classical shadow representation.

A key innovation was an improved state-certification primitive designed to enhance noise tolerance and reduce the number of samples required compared to previous approaches. Researchers designed a high-rate error-detecting code specifically tailored to the random-circuit ensemble employed in the study.

This code facilitated the experimental generation of classical shadows for 32-qubit states using circuits containing at least 80 logical, and 582 physical, two-qubit gates. The generated shadows achieved a fidelity of 0.90 ±0.01, demonstrating the precision of the state preparation and measurement process.

This high fidelity was crucial for validating the security assumptions underlying the digital signature scheme. The work then demonstrated a proof-of-principle quantum digital signature by increasing the number of measurement samples used in the primitive. This hardware demonstration highlighted the near-term feasibility of the proposed scheme, offering a potential pathway towards quantum-resistant cryptography.

The team’s methodology deliberately avoided reliance on one-way functions, instead grounding security in the conjectured hardness of learning quantum states from classical shadows, an approach independent of traditional cryptographic assumptions. This computational no-learning conjecture was supported by analysis showing that existing algorithms for learning shallow circuits are ineffective in this setting.

High-fidelity quantum digital signatures via classical shadow certification offer practical security guarantees

Researchers developed a digital signature scheme utilising only classical computing resources and achieved a fidelity of 0.90 with a standard deviation of 0.01 when generating shadows for 32-qubit states. This fidelity was attained using circuits containing logical two-qubit gates with 2 physical gates.

The work introduces a state-certification primitive demonstrating improved noise tolerance and reduced sample complexity compared to previous methods. This enhanced certification relies on a high-rate error-detecting code specifically designed for the random-circuit ensemble employed in the study. The core of this research lies in the creation of a digital signature protocol based on shadow overlap, a technique for verifying the similarity between a generated quantum state and a hypothesised state.

The protocol’s success hinges on the difficulty of learning the circuit used to generate the quantum state from its classical shadow. A key component is the ability to certify that a given classical shadow corresponds to a specific quantum circuit, establishing a link between the observed data and the underlying quantum process.

Implementation of the protocol involved defining a (T, δ, ε, τ(·)) protocol, where T represents the number of measurement samples, δ and ε define the acceptable error rates, and τ(·) is a function dependent on the hypothesis state. Each shadow consists of a uniformly random subset of qubits, a random Clifford operation applied to those qubits, and the resulting computational basis measurement outcome.

The study demonstrates a proof-of-principle digital signature, indicating the near-term feasibility of this approach for secure communication. Furthermore, the researchers explored multi-bit signatures using an [M, k, d] error detection code, encoding k-bit logical messages into M-bit codespaces with a minimum Hamming distance of at least d.

This allows for certification to occur on only a subset of the bits, substantially reducing the computational burden and improving efficiency. The work establishes a general compiler converting any shadow overlap protocol into a digital signature protocol, offering a flexible framework for future development.

Classical shadow cryptography via certified random quantum circuits offers provable security against semi-honest adversaries

Researchers have developed a digital signature scheme reliant on classical computing, utilizing classical shadows of quantum states as public keys to establish cryptographic security independent of traditional cryptographic assumptions. This approach circumvents the need for low-noise and long-lived quantum memory, which currently pose significant practical challenges.

The scheme’s security rests on the conjectured difficulty of learning the circuit that generates the public key from its classical shadow, and is supported by both theoretical analysis and numerical evidence. A crucial component of this work is an enhanced state-certification primitive, designed to tolerate higher levels of noise and require fewer samples than previous methods.

This certification is achieved through a high-rate error-detecting code specifically tailored to the random-circuit ensemble used, and experimentally validated by generating shadows for 32-qubit states with circuits containing a substantial number of two-qubit gates, achieving a fidelity of 0.90 with a standard deviation of 0.01. Demonstrations with an increasing number of measurement samples have successfully realized a proof-of-principle digital signature, indicating the potential for near-term implementation.

The authors acknowledge a gap between the amount of information available in polynomially many copies of a quantum state and the ability to efficiently learn its properties, even when sufficient statistical information exists. This information-computation gap is explored through the lens of low-degree algorithms, which are limited in their ability to learn certain quantum circuits. Future research may focus on further investigating the hardness of learning with low-degree polynomials and exploring the connections between learning and hypothesis testing to refine the security bounds of the proposed digital signature scheme.