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    Review of 'Factoring integers with sublinear resources on a superconducting quantum processor'

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    Factoring integers with sublinear resources on a superconducting quantum processor
    Promising quantum algorithm for integer factorization w/ sublinear resources on a superconducting QP
    Average rating:
        Rated 3 of 5.
    Level of importance:
        Rated 3 of 5.
    Level of validity:
        Rated 4 of 5.
    Level of completeness:
        Rated 3 of 5.
    Level of comprehensibility:
        Rated 2 of 5.
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    Factoring integers with sublinear resources on a superconducting quantum processor

    Shor's algorithm has seriously challenged information security based on public key cryptosystems. However, to break the widely used RSA-2048 scheme, one needs millions of physical qubits, which is far beyond current technical capabilities. Here, we report a universal quantum algorithm for integer factorization by combining the classical lattice reduction with a quantum approximate optimization algorithm (QAOA). The number of qubits required is O(logN/loglog N), which is sublinear in the bit length of the integer \(N\), making it the most qubit-saving factorization algorithm to date. We demonstrate the algorithm experimentally by factoring integers up to 48 bits with 10 superconducting qubits, the largest integer factored on a quantum device. We estimate that a quantum circuit with 372 physical qubits and a depth of thousands is necessary to challenge RSA-2048 using our algorithm. Our study shows great promise in expediting the application of current noisy quantum computers, and paves the way to factor large integers of realistic cryptographic significance.
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      Review information

      10.14293/S2199-1006.1.SOR-PHYS.A2212.12372.v1.RWOACQ
      This work has been published open access under Creative Commons Attribution License CC BY 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Conditions, terms of use and publishing policy can be found at www.scienceopen.com.

      Quantum physics & Field theory

      Review text

      This article presents a quantum algorithm for integer factorization using sublinear resources, achieved by combining the classical Schnorr’s algorithm with a quantum approximate optimization algorithm (QAOA). The algorithm is demonstrated experimentally by factoring integers up to 48 bits with 10 superconducting qubits, and the authors estimate that a quantum circuit with 372 physical qubits and a depth of thousands is necessary to challenge RSA-2048 using this algorithm. The article is well-written and provides detailed information about the algorithm and experimental setup.

      Some revisions that could improve the article include adding more information about the classical Schnorr’s algorithm and explaining the optimization process in more detail. The article could also benefit from more thorough explanations of the experimental setup, such as how the virtual-z gates are implemented and how the single-qubit rotations and CZ gates are achieved.

      One potential weakness of the article is that it may be difficult for readers without a background in quantum computing to fully understand the technical details. Additionally, the article does not provide much discussion of the implications of this research for cryptography and information security.

      The strength of the article is the clear presentation of the algorithm and experimental results, with detailed information about the number of qubits required and the largest integer that has been factored using this method. The experimental results are impressive, demonstrating the successful factorization of integers up to 48 bits using only 10 qubits.

      Overall, this article presents an important advancement in quantum computing and integer factorization algorithms, with potential implications for cryptography and information security.

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