Abstract
We decompose two implementations of Shor’s algorithm for prime factorization into universal gate units at the logical level and predict the number of physical qubits and execution time when surface codes are used. Logical qubit encoding using a rotated surface code and logical qubits with all-to-all connectivity are assumed. We express the number of physical qubits and execution time in terms of the bit length of the number to be factorized and error rate of the physical quantum gate. We confirm the relationship between the number of qubits and the execution time by analyzing two algorithms using various bit lengths and physical gate error rates .
Highlights
Since Peter Shor introduced a polynomial-time quantum algorithm for factoring integers and computing discrete logarithms in 1994, interest in quantum computing has increased significantly [1]
We formulated closed-form equations for the number of physical qubits and execution time required by two quantum factoring algorithms, the Beauregard and Pavlidis algorithms, assuming all-to-all connectivity
The AQ F T was used instead of the Q F T, and an arbitrary rotation gate was decomposed into a universal gate set using the Gridsynth algorithm
Summary
Since Peter Shor introduced a polynomial-time quantum algorithm for factoring integers and computing discrete logarithms in 1994, interest in quantum computing has increased significantly [1]. Several companies such as Google and IBM are leading efforts toward the practical use of quantum computers [2,3]. Technological advances are still needed to perform large scale operations such as Shor’s algorithm. Noisy-intermediate-scale-quantum operations can be performed, and even quantum error correcting (QEC) codes cannot be used properly [4]
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