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arXiv:1010.4926

QOperAv, a Code Generator for Generating Quantum Circuits for Evaluating Certain Quantum Operator Averages

Robert R. Tucci

Published Oct 24, 2010• 0 citations
arXivHTMLPDF

Abstract

This paper introduces QOperAv v1.5, a Java application available for free. (Source code included in the distribution.) QOperAv is a "code generator" for generating quantum circuits. The quantum circuits generated by QOperAv can be used to evaluate with polynomial efficiency the average of $f(A)$ for some simple (that is, computable with polynomial efficiency) function $f$ and a Hermitian operator $A$, provided that we know how to compile $\exp(iA)$ with polynomial efficiency. QOperAv implements an algorithm described in earlier papers, that combines various standard techniques such as quantum phase estimation and quantum multiplexors.

DOI
10.48550/arxiv.1010.4926

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This paper introduces QOperAv v1.5, a Java application available for free. (Source code included in the distribution.) QOperAv is a "code generator" for generating quantum circuits. The quantum circuits generated by QOperAv can be used to evaluate with polynomial efficiency the average of f(A)f(A)f(A) for some simple (that is, computable with polynomial efficiency) function fff and a Hermitian operator AAA, provided that we know how to compile exp⁡(iA)\exp(iA)exp(iA) with polynomial efficiency. QOperAv implements an algorithm described in earlier papers, that combines various standard techniques such as quantum phase estimation and quantum multiplexors.
This paper introduces QuSAnn v1.2 and Multiplexor Expander v1.2, two Java applications available for free. (Source code included in the distribution.) QuSAnn is a "code generator" for quantum simulated annealing: after the user inputs some parameters, it outputs a quantum circuit for performing simulated annealing on a quantum computer. The quantum circuit implements the algorithm of Wocjan et al. (arXiv:0804.4259), which improves on the original algorithm of Somma et al. (arXiv:0712.1008). The quantum circuit generated by QuSAnn includes some quantum multiplexors. The application Multiplexor Expander allows the user to replace each of those multiplexors by a sequence of more elementary gates such as multiply controlled NOTs and qubit rotations.
This paper introduces Quibbs v1.3, a Java application available for free. (Source code included in the distribution.) Quibbs is a "code generator" for quantum Gibbs sampling: after the user inputs some files that specify a classical Bayesian network, Quibbs outputs a quantum circuit for performing Gibbs sampling of that Bayesian network on a quantum computer. Quibbs implements an algorithm described in earlier papers, that combines various apple pie techniques such as: an adaptive fixed-point version of Grover's algorithm, Szegedy operators, quantum phase estimation and quantum multiplexors.
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Understanding the capacity of quantum circuits through the lens of approximation theory is essential for evaluating the complexity of quantum circuits required to solve various problems in scientific computation. We design quantum circuits capable of approximating d-dimensional functions within the Korobov function space. This is achieved by leveraging the quantum signal processing (QSP) and the linear combination of unitaries (LCU) algorithms to build quantum circuits that output Chebyshev polynomials. We also present a quantitative analysis of the approximation error rates and evaluates the computational complexity of implementing the proposed circuits. Since the Korobov function space is a subspace of the certain Sobolev spaces, our work develops a theoretical foundation for implementing a large class of functions suitable for applications on a quantum computer.