Simulations of Shor’s algorithm using matrix product states

Simulations of Shor’s algorithm using matrix product states We show that under the matrix product state formalism the states produced in Shor’s algorithm can be represented using $$O(\max (4lr^2, 2^{2l}))$$ O ( max ( 4 l r 2 , 2 2 l ) ) space, where l is the number of bits in the number to factorise and r is the order and the solution to the related order-finding problem. The reduction in space compared to an amplitude formalism approach is significant, allowing simulations as large as 42 qubits to be run on a single processor with 32 GB RAM. This approach is readily adapted to a distributed memory environment, and we have simulated a 45-qubit case using 8 cores with 16 GB RAM in approximately 1 h. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

Simulations of Shor’s algorithm using matrix product states

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Publisher
Springer Journals
Copyright
Copyright © 2017 by Springer Science+Business Media New York
Subject
Physics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-017-1587-x
Publisher site
See Article on Publisher Site

Abstract

We show that under the matrix product state formalism the states produced in Shor’s algorithm can be represented using $$O(\max (4lr^2, 2^{2l}))$$ O ( max ( 4 l r 2 , 2 2 l ) ) space, where l is the number of bits in the number to factorise and r is the order and the solution to the related order-finding problem. The reduction in space compared to an amplitude formalism approach is significant, allowing simulations as large as 42 qubits to be run on a single processor with 32 GB RAM. This approach is readily adapted to a distributed memory environment, and we have simulated a 45-qubit case using 8 cores with 16 GB RAM in approximately 1 h.

Journal

Quantum Information ProcessingSpringer Journals

Published: Jun 3, 2017

References

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