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Title: Versatile Formal Methods Applied to Quantum Information.

Abstract

Using a novel formal methods approach, we have generated computer-veri ed proofs of major theorems pertinent to the quantum phase estimation algorithm. This was accomplished using our Prove-It software package in Python. While many formal methods tools are available, their practical utility is limited. Translating a problem of interest into these systems and working through the steps of a proof is an art form that requires much expertise. One must surrender to the preferences and restrictions of the tool regarding how mathematical notions are expressed and what deductions are allowed. Automation is a major driver that forces restrictions. Our focus, on the other hand, is to produce a tool that allows users the ability to con rm proofs that are essentially known already. This goal is valuable in itself. We demonstrate the viability of our approach that allows the user great exibility in expressing state- ments and composing derivations. There were no major obstacles in following a textbook proof of the quantum phase estimation algorithm. There were tedious details of algebraic manipulations that we needed to implement (and a few that we did not have time to enter into our system) and some basic components that we needed to rethink,more » but there were no serious roadblocks. In the process, we made a number of convenient additions to our Prove-It package that will make certain algebraic manipulations easier to perform in the future. In fact, our intent is for our system to build upon itself in this manner.« less

Authors:
 [1];  [1];  [1]
  1. Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)
Publication Date:
Research Org.:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1331534
Report Number(s):
SAND-2015-9617R
607608
DOE Contract Number:  
AC04-94AL85000
Resource Type:
Technical Report
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING

Citation Formats

Witzel, Wayne, Rudinger, Kenneth Michael, and Sarovar, Mohan. Versatile Formal Methods Applied to Quantum Information.. United States: N. p., 2015. Web. doi:10.2172/1331534.
Witzel, Wayne, Rudinger, Kenneth Michael, & Sarovar, Mohan. Versatile Formal Methods Applied to Quantum Information.. United States. https://doi.org/10.2172/1331534
Witzel, Wayne, Rudinger, Kenneth Michael, and Sarovar, Mohan. 2015. "Versatile Formal Methods Applied to Quantum Information.". United States. https://doi.org/10.2172/1331534. https://www.osti.gov/servlets/purl/1331534.
@article{osti_1331534,
title = {Versatile Formal Methods Applied to Quantum Information.},
author = {Witzel, Wayne and Rudinger, Kenneth Michael and Sarovar, Mohan},
abstractNote = {Using a novel formal methods approach, we have generated computer-veri ed proofs of major theorems pertinent to the quantum phase estimation algorithm. This was accomplished using our Prove-It software package in Python. While many formal methods tools are available, their practical utility is limited. Translating a problem of interest into these systems and working through the steps of a proof is an art form that requires much expertise. One must surrender to the preferences and restrictions of the tool regarding how mathematical notions are expressed and what deductions are allowed. Automation is a major driver that forces restrictions. Our focus, on the other hand, is to produce a tool that allows users the ability to con rm proofs that are essentially known already. This goal is valuable in itself. We demonstrate the viability of our approach that allows the user great exibility in expressing state- ments and composing derivations. There were no major obstacles in following a textbook proof of the quantum phase estimation algorithm. There were tedious details of algebraic manipulations that we needed to implement (and a few that we did not have time to enter into our system) and some basic components that we needed to rethink, but there were no serious roadblocks. In the process, we made a number of convenient additions to our Prove-It package that will make certain algebraic manipulations easier to perform in the future. In fact, our intent is for our system to build upon itself in this manner.},
doi = {10.2172/1331534},
url = {https://www.osti.gov/biblio/1331534}, journal = {},
number = ,
volume = ,
place = {United States},
year = {Sun Nov 01 00:00:00 EDT 2015},
month = {Sun Nov 01 00:00:00 EDT 2015}
}