Matrix Product Operator Simulations of Quantum Algorithms
University of Melbourne School of Physics Melbourne Australia
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We develop simulation methods for matrix product operators, and perform simulations of the Quantum Fourier Transform, Shors algorithm and Grovers algorithm using matrix product states and matrix product operators. By doing so, we provide numerical evidence that a constant number of QFTs can be efficiently classically simulated on any state whose Schmidt rank grows only polynomially with the number of qubits, and quantify the amount of entanglement present in Shors algorithm. The efficiency of the matrix product state and operator representation allows us to perform moderately large simulations of both Shors algorithm with Z errors and Grovers algorithm with up to 15 X, Y and Z errors. While larger simulations have been performed, our results have been computed with little computational power and provide new methods to perform large-scale quantum algorithm simulations.
- Quantum Theory and Relativity
- Operations Research