scholarly journals Fast equivalence -- checking for quantum circuits

2010 ◽  
Vol 10 (9&10) ◽  
pp. 721-734
Author(s):  
Shigeru Yamashita ◽  
Igor L. Markov
Keyword(s):  
Formal Verification ◽  
Quantum Algorithms ◽  
Quantum Circuits ◽  
Equivalence Checking ◽  
Sat Solvers ◽  
Reversible Circuits ◽  
Verification Tools ◽  
Verification Methodology ◽  
Verification Techniques ◽  
Factoring Algorithm

We perform formal verification of quantum circuits by integrating several techniques specialized to particular classes of circuits. Our verification methodology is based on the new notion of a reversible miter that allows one to leverage existing techniques for simplification of quantum circuits. For reversible circuits which arise as runtime bottlenecks of key quantum algorithms, we develop several verification techniques and empirically compare them. We also combine existing quantum verification tools with the use of SAT-solvers. Experiments with circuits for Shor's number-factoring algorithm, containing thousands of gates, show improvements in efficiency by four orders of magnitude.

Formal Verification of Control System Software

2019 ◽  
Author(s):  
Pierre-Loïc Garoche
Keyword(s):  
Control System ◽  
Formal Verification ◽  
Formal Analysis ◽  
Critical Systems ◽  
System Software ◽  
Unified Approach ◽  
Verification Methods ◽  
Autonomous Cars ◽  
Computer Scientists ◽  
Verification Techniques

The verification of control system software is critical to a host of technologies and industries, from aeronautics and medical technology to the cars we drive. The failure of controller software can cost people their lives. This book provides control engineers and computer scientists with an introduction to the formal techniques for analyzing and verifying this important class of software. Too often, control engineers are unaware of the issues surrounding the verification of software, while computer scientists tend to be unfamiliar with the specificities of controller software. The book provides a unified approach that is geared to graduate students in both fields, covering formal verification methods as well as the design and verification of controllers. It presents a wealth of new verification techniques for performing exhaustive analysis of controller software. These include new means to compute nonlinear invariants, the use of convex optimization tools, and methods for dealing with numerical imprecisions such as floating point computations occurring in the analyzed software. As the autonomy of critical systems continues to increase—as evidenced by autonomous cars, drones, and satellites and landers—the numerical functions in these systems are growing ever more advanced. The techniques presented here are essential to support the formal analysis of the controller software being used in these new and emerging technologies.

scholarly journals Approximate Equivalence Checking of Noisy Quantum Circuits

2021 ◽  
Author(s):  
Xin Hong ◽  
Mingsheng Ying ◽  
Yuan Feng ◽  
Xiangzhen Zhou ◽  
Sanjiang Li
Keyword(s):  
Quantum Circuits ◽  
Equivalence Checking

scholarly journals A Formal Verification Methodology for DDD Mode Pacemaker Control Programs

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Sana Shuja ◽  
Sudarshan K. Srinivasan ◽  
Shaista Jabeen ◽  
Dharmakeerthi Nawarathna
Keyword(s):  
Formal Verification ◽  
Control Program ◽  
Formal Specifications ◽  
Object Code ◽  
Correctness Proof ◽  
Safety Critical ◽  
Control Programs ◽  
Control Functions ◽  
Verification Process ◽  
Verification Methodology

Pacemakers are safety-critical devices whose faulty behaviors can cause harm or even death. Often these faulty behaviors are caused due to bugs in programs used for digital control of pacemakers. We present a formal verification methodology that can be used to check the correctness of object code programs that implement the safety-critical control functions of DDD mode pacemakers. Our methodology is based on the theory of Well-Founded Equivalence Bisimulation (WEB) refinement, where both formal specifications and implementation are treated as transition systems. We develop a simple and general formal specification for DDD mode pacemakers. We also develop correctness proof obligations that can be applied to validate object code programs used for pacemaker control. Using our methodology, we were able to verify a control program with millions of transitions against the simple specification with only 10 transitions. Our method also found several bugs during the verification process.

scholarly journals An Innovative Genetic Algorithm for the Quantum Circuit Compilation Problem

2019 ◽  
Vol 33 ◽  
pp. 7707-7714
Author(s):  
Riccardo Rasconi ◽  
Angelo Oddi
Keyword(s):  
Genetic Algorithm ◽  
Nearest Neighbor ◽  
Quantum Algorithms ◽  
Quantum Circuit ◽  
Quantum Circuits ◽  
Heuristic Function ◽  
Circuit Realization ◽  
Benchmark Instances ◽  
Technological Limitations ◽  
Selection Of

Quantum Computing represents the next big step towards speed boost in computation, which promises major breakthroughs in several disciplines including Artificial Intelligence. This paper investigates the performance of a genetic algorithm to optimize the realization (compilation) of nearest-neighbor compliant quantum circuits. Currrent technological limitations (e.g., decoherence effect) impose that the overall duration (makespan) of the quantum circuit realization be minimized, and therefore the makespanminimization problem of compiling quantum algorithms on present or future quantum machines is dragging increasing attention in the AI community. In our genetic algorithm, a solution is built utilizing a novel chromosome encoding where each gene controls the iterative selection of a quantum gate to be inserted in the solution, over a lexicographic double-key ranking returned by a heuristic function recently published in the literature.Our algorithm has been tested on a set of quantum circuit benchmark instances of increasing sizes available from the recent literature. We demonstrate that our genetic approach obtains very encouraging results that outperform the solutions obtained in previous research against the same benchmark, succeeding in significantly improving the makespan values for a great number of instances.

scholarly journals Human-Competitive Evolution of Quantum Computing Artefacts by Genetic Programming

2006 ◽  
Vol 14 (1) ◽  
pp. 21-40 ◽  
Author(s):  
Paul Massey ◽  
John A. Clark ◽  
Susan Stepney
Keyword(s):  
Fourier Transform ◽  
Quantum Computing ◽  
Genetic Programming ◽  
Quantum Algorithms ◽  
Quantum Circuits ◽  
Quantum Fourier Transform ◽  
Competitive Evolution ◽  
Specific Quantum

We show how Genetic Programming (GP) can be used to evolve useful quantum computing artefacts of increasing sophistication and usefulness: firstly specific quantum circuits, then quantum programs, and finally system-independent quantum algorithms. We conclude the paper by presenting a human-competitive Quantum Fourier Transform (QFT) algorithm evolved by GP.

Sign in / Sign up

Export Citation Format

Share Document