Prime factorization using quantum variational imaginary time evolution

Journal Article · 21 October 2021 · Scientific Reports

DOI: https://doi.org/10.1038/s41598-021-00339-x · OSTI ID:1826814

Selvarajan, Raja; Dixit, Vivek; Cui, Xingshan; Humble, Travis S.; Kais, Sabre

Abstract The road to computing on quantum devices has been accelerated by the promises that come from using Shor’s algorithm to reduce the complexity of prime factorization. However, this promise hast not yet been realized due to noisy qubits and lack of robust error correction schemes. Here we explore a promising, alternative method for prime factorization that uses well-established techniques from variational imaginary time evolution. We create a Hamiltonian whose ground state encodes the solution to the problem and use variational techniques to evolve a state iteratively towards these prime factors. We show that the number of circuits evaluated in each iteration scales as $$$$O(n^{5}d)$$$$ $O\left(n^{5}d\right)$ , where n is the bit-length of the number to be factorized and d is the depth of the circuit. We use a single layer of entangling gates to factorize 36 numbers represented using 7, 8, and 9-qubit Hamiltonians. We also verify the method’s performance by implementing it on the IBMQ Lima hardware to factorize 55, 65, 77 and 91 which are greater than the largest number (21) to have been factorized on IBMQ hardware.

• Research Organization: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)
• Sponsoring Organization: National Science Foundation (NSF); USDOE; USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
• Grant/Contract Number: AC05-00OR22725
• OSTI ID: 1826814
• Journal Information: Scientific Reports, Journal Name: Scientific Reports Journal Issue: 1 Vol. 11; ISSN 2045-2322
• Publisher: Nature Publishing GroupCopyright Statement
• Country of Publication: United Kingdom
• Language: English