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Stabilizer Rank Strong Simulation v.0.1

Lucas Kocia

Published Jan 1, 2021• 0 citations
Publisher

Abstract

This software improves upon the Clifford gate+T gate magic state strong simulation algorithm by Brayvi and Gosset. It provides a better stabilizer state decomposition that scales as 2^{0.463t}, an improvement over 2^{0.468t}, for t T gate magic states. This code enables simulations of universal quantum computing with that asymptotic scaling cost. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525 SAND2020-14293 O

DOI
10.11578/dc.20210818.1

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This software improves upon the Clifford gate+T gate magic state strong simulation algorithm by Brayvi and Gosset. It provides a better stabilizer state decomposition that scales as 2^{0.463t}, an improvement over 2^{0.468t}, for t T gate magic states. This code enables simulations of universal quantum computing with that asymptotic scaling cost. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525 SAND2020-14293 O
SAND2022-3281 O Weak Simulation sparsifies the stabilizer decomposition of a qubit t-tensored T gate magic state to some additive error. It can accomplish this either by independent L1 sampling like in the popular SPARSIFY algorithm or with correlated L1 sampling, which offers a more efficient decomposition. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.
Universal quantum circuits can be formulated in the Pauli measurement-based formalism as input T gate magic states, Clifford gates, and then multi-Pauli measurements. This code simulates single-Pauli measurements to show some theoretical bounds on the cost of full multi-Pauli measurements. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525. SAND2020-14080 O
The SPARSIFY algorithm implemented by the code allows for classical simulation of universal quantum computer sample outcomes. The code sparsifies the stabilizer decomposition of a qubit t-tensored T gate magic state to some additive error. This is accomplished by either independent L1 sampling or with correlated L1 sampling to supplement an independent subset, which offers a more efficient decomposition: for a given t, a sparser decomposition is sufficient with correlated L1 sampling to satisfy a given additive error. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525. SAND2021-8296 O
This is software in Python that simulates the quantum approximate optimization algorithm (QAOA) as described in https://arxiv.org/abs/1411.4028. The software has customization that speeds up simulation and provides interface to the Rapid Optimization Library (ROL) developed at Sandia. SAND2019-8935 M Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.
SAND2021-1511 O. The code takes a description of a system comprised of two leads that are sources and sinks of electrons, a set of abstract sites that those electrons can occupy, and their connectivity. It then predicts the current passing between the two leads through the set of abstract sites. There are numerical parameters that define the rate at which electrons tunnel between sites and another parameter that determines the energy of having two electrons on the same site. When the ratio of these energies and biases are set just right, they can be used to predict the existence of Coulomb blockade in which no current flows because the energetic penalty would be too high. That is, the code predicts a current and the absence of a current which is predictive of Coulomb blockade. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.