Abstract
We detail techniques to optimise high-level classical simulations of Shor's quantum factoring algorithm. Chief among these is to examine the entangling properties of the circuit and to effectively map it across the one-dimensional structure of a matrix product state. Compared to previous approaches whose space requirements depend on r, the solution to the underlying order-finding problem of Shor's algorithm, our approach depends on its factors. We performed a matrix product state simulation of a 60-qubit instance of Shor's algorithm that would otherwise be infeasible to complete without an optimised entanglement mapping.
Highlights
With the potential for quantum computers to outperform the best classical computing resources available, achieving this quantum supremacy promises to be a major milestone in computing
The ability to demonstrate quantum supremacy [1,2,3] depends on several factors, including the computational task under consideration, as well as properties of the physical quantum computer
We examine how the entanglement structure of Shor’s algorithm for integer factorisation lends itself to a particular matrix product state representation that quantifiably reduces the computational requirements for classical simulation
Summary
With the potential for quantum computers to outperform the best classical computing resources available, achieving this quantum supremacy promises to be a major milestone in computing. We examine how the entanglement structure of Shor’s algorithm for integer factorisation lends itself to a particular matrix product state representation that quantifiably reduces the computational requirements for classical simulation. Existing physical implementations of Shor’s algorithm [10,11,12,13] have been produced to factor small semiprimes no longer than five bits in length This is significantly less than even the 15-bit instances first simulated in [14], requiring 45 qubits. By examining the entanglement introduced by a high-level circuit of Shor’s algorithm, we were able to improve space requirements over previous simulations [14] by sensibly mapping this entanglement across the one-dimensional structure of a matrix product state.
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