Quantum Compilation Research Articles

OptQC v1.3: An (updated) optimized parallel quantum compiler

We present a revised version of the OptQC program of Loke et al. (2014) [1]. We have removed the simulated annealing process in favour of a descending random walk. We have also introduced a new method for iteratively generating permutation matrices during the random walk process, providing a reduced total cost for implementing the quantum circuit. Lastly, we have also added a synchronization mechanism between threads, giving quicker convergence to more optimal solutions. New version program summaryProgram title: OptQC v1.3Catalogue identifier: AEUA_v1_3Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEUA_v1_3.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 240903No. of bytes in distributed program, including test data, etc.: 632395Distribution format: tar.gzProgramming language: Fortran, MPI.Computer: Any computer with Fortran compiler (not gfortran4.9 or earlier) and MPI library.Operating system: Linux.Classification: 4.15.Catalogue identifier of previous version: AEUA_v1_3Journal reference of previous version: Comput. Phys. Comm. 185(2014)3307External routines: Intel MKL LAPACK routines and MPI routines.Does the new version supersede the previous version?: YesNature of problem:It aims to minimize the number of quantum gates required to implement a given unitary operation.Solution method:It utilizes a descending random walk to select permutation matrices P and Q for a given unitary matrix U such that the number of gates in the quantum circuit of U=QTPTU′PQ is minimized, where U′ is equivalent to U up to a permutation. The decomposition of a unitary operator is performed by recursively applying the cosine–sine decomposition.Reasons for new version:Simulated annealing process was found to give suboptimal results compared to a normal descending random walk. Computation time was also bloated by the necessity of running the CS decomposition thrice (for U′,P and PT) for each iteration of the optimization process.Summary of revisions:•Simulated annealing process was replaced by a descending random walk (equivalent to setting the threshold value β to 0), due to poor convergence of the simulated annealing process, and due to the lack of pathological instances of local minima in this particular search space.•Introduced an iterative method for generating the general permutation matrix P, in which we start with P=I and build up the quantum circuit (and modify P correspondingly) by adding gates onto the existing circuit. This removes the requirement of running the CS decomposition on P and PT to find the quantum circuit implementation, since it is already known by construction.•Added a synchronization mechanism between threads (after some prescribed number of iterations) in which the current state of the top 10% processes with the fittest solutions is copied over to the remaining 90%. This works so as to discard the less fit solutions and focuses the searching algorithm in the state space with the fittest solutions.Additional comments:The program contains some Fortran2003 features and will not compile with gcc4.9 or earlier.Running time:As before, running time increases with the size of the unitary matrix, as well as the prescribed maximum number of iterations for qubit permutation selection and the descending random walk. All simulation results presented in this paper are obtained from running the program on the Fornax supercomputer managed by iVEC@UWA with Intel Xeon X5650 CPUs. A comparison of running times is also given in Table 1.

OptQC: An optimized parallel quantum compiler

The software package Qcompiler (Chen and Wang 2013) provides a general quantum compilation framework, which maps any given unitary operation into a quantum circuit consisting of a sequential set of elementary quantum gates. In this paper, we present an extended software OptQC, which finds permutation matrices P and Q for a given unitary matrix U such that the number of gates in the quantum circuit of U=QTPTU′PQ is significantly reduced, where U′ is equivalent to U up to a permutation and the quantum circuit implementation of each matrix component is considered separately. We extend further this software package to make use of high-performance computers with a multiprocessor architecture using MPI. We demonstrate its effectiveness in reducing the total number of quantum gates required for various unitary operators. Program summaryProgram title: OptQCCatalogue identifier: AEUA_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEUA_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 178435No. of bytes in distributed program, including test data, etc.: 491574Distribution format: tar.gzProgramming language: Fortran, MPI.Computer: Any computer with Fortran compiler and MPI library.Operating system: Linux.Classification: 4.15.Nature of problem: It aims to minimize the number of quantum gates required to implement a given unitary operation.Solution method: It utilizes a threshold-based acceptance strategy for simulated annealing to select permutation matrices P and Q for a given unitary matrix U such that the number of gates in the quantum circuit of U=QTPTU′PQ is minimized, where U′ is equivalent to U up to a permutation. The decomposition of a unitary operator is performed by recursively applying the cosine–sine decomposition.Running time: Running time increases with the size of the unitary matrix, as well as the prescribed maximum number of iterations for qubit permutation selection and the subsequent simulated annealing algorithm. Running time estimates are provided for each example in Section 4. All simulation results presented in this paper are obtained from running the program on the Fornax supercomputer managed by iVEC@UWA with Intel Xeon X5650 CPUs.

FTQLS: Fault-Tolerant Quantum Logic Synthesis

Quantum computation can solve certain problems much faster than classical computation. However, quantum computations are more susceptible to errors than conventional digital computations. Thus, a fault-tolerant (FT) quantum circuit design is required for a practical implementation. Quantum circuits consist of a cascade of quantum gates. These gates are themselves realized using primitive quantum operations that are supported by the quantum physical machine description (PMD). As different quantum systems are associated with different Hamiltonians, they have different PMDs. In addition, the quantum cost for implementing a quantum operation may differ from one PMD to another. Thus, a quantum logic circuit needs to be realized with and optimized for the set of primitive quantum operations supported by the given PMD. In this paper, an FT quantum logic synthesis (FTQLS) methodology and tool is described for six different PMDs. A methodology, such as this, which can be targeted at multiple PMDs, has not been attempted before, to the best of our knowledge. The input to FTQLS is an unoptimized quantum circuit realized using a set of commonly used gates and its output is an optimized FT quantum circuit that only comprises of primitive quantum operations supported by the given PMD. FTQLS does technology mapping for different PMDs and then converts non-FT circuits to FT circuits. For technology mapping, it utilizes an optimized quantum gate library targeted at various PMDs that decomposes gates into primitive operations. Efficient conversion to FT circuits is done by integrating two quantum compilers and an FT cache table into FTQLS. For improving the synthesis results, an FT set of gates that is directly supported by each PMD is proposed. Quantum circuit optimization is done by utilizing quantum identity rules. The performance of FTQLS is evaluated using two cost metrics: number of primitive operations (#ops) and execution cycles on the critical path (#cycles). Experiment results show that the decrease in #ops varies between 58.1% and 87.0% and in #cycles between 42.8% and 76.4%, on an average, depending on the PMD.

Qcompiler: Quantum compilation with the CSD method

In this paper, we present a general quantum computation compiler, which maps any given quantum algorithm to a quantum circuit consisting a sequential set of elementary quantum logic gates based on recursive cosine–sine decomposition. The resulting quantum circuit diagram is provided by directly linking the package output written in LaTeX to Qcircuit.tex <http://www.cquic.org/Qcircuit >. We illustrate the use of the Qcompiler package through various examples with full details of the derived quantum circuits. Besides its accuracy, generality and simplicity, Qcompiler produces quantum circuits with significantly reduced number of gates when the systems under study have a high degree of symmetry. Program summaryProgram title: QcompilerCatalogue identifier: AENX_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AENX_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 4321No. of bytes in distributed program, including test data, etc.: 50943Distribution format: tar.gzProgramming language: Fortran.Computer: Any computer with a Fortran compiler.Operating system: Linux, Mac OS X 10.5 (and later).RAM: Depends on the size of the unitary matrix to be decomposedClassification: 4.15.External routines: Lapack (http://www.netlib.org/lapack/)Nature of problem:Decompose any given unitary operation into a quantum circuit with only elementary quantum logic gates.Solution method:This package decomposes an arbitrary unitary matrix, by applying the CSD algorithm recursively, into a series of block-diagonal matrices, which can then be readily associated with elementary quantum gates to form a quantum circuit.Restrictions:The only limitation is imposed by the available memory on the user’s computer.Additional comments:This package is applicable for any arbitrary unitary matrices, both real and complex. If the unitary matrix is real, its corresponding quantum circuit is much simpler, with only half the number of quantum gates in comparison with complex matrices of the same size.Running time:Memory and CPU time requirements depend critically on the size of the unitary matrix to be decomposed. Run-time is dominated by the recursive CSD. Most examples presented in this paper require a few minutes of CPU time on Intel Pentium Dual Core 2 Duo E2200 2.2 GHz.

A Flowchart Language for Quantum Programming

Several high-level quantum programming languages have been proposed in the previous research. In this paper, we define a low-level flowchart language for quantum programming, which can be used in implementation of high-level quantum languages and in design of quantum compilers. The formal semantics of the flowchart language is given, and the notion of correctness for programs written in this language is introduced. A structured quantum programming theorem is presented, which provides a technique of translating quantum flowchart programs into programs written in a high-level language, namely, a quantum extension of the while-language.

Topological Quantum Hashing with the Icosahedral Group

We study an efficient algorithm to hash any single-qubit gate into a braid of Fibonacci anyons represented by a product of icosahedral group elements. By representing the group elements by braid segments of different lengths, we introduce a series of pseudogroups. Joining these braid segments in a renormalization group fashion, we obtain a Gaussian unitary ensemble of random-matrix representations of braids. With braids of length O(log2(1/epsilon)), we can approximate all SU(2) matrices to an average error epsilon with a cost of O(log(1/epsilon)) in time. The algorithm is applicable to generic quantum compiling.

Matrix Computations (Gene H. Golub And Charles F. van Loan)

Previous article Next article Matrix Computations (Gene H. Golub And Charles F. van Loan)James W. DemmelJames W. Demmelhttps://doi.org/10.1137/1028073PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout Previous article Next article FiguresRelatedReferencesCited byDetails Robust quantum compilation and circuit optimisation via energy minimisation24 January 2022 | Quantum, Vol. 6 Cross Ref 2D PET Image Reconstruction Using Robust L1 Estimation of the Gaussian Mixture Model2 May 2022 | Informatica, Vol. 1 Cross Ref Personalized intervention cardiology with transcatheter aortic valve replacement made possible with a non-invasive monitoring and diagnostic framework25 May 2021 | Scientific Reports, Vol. 11, No. 1 Cross Ref Towards a non-invasive computational diagnostic framework for personalized cardiology of transcatheter aortic valve replacement in interactions with complex valvular, ventricular and vascular diseaseInternational Journal of Mechanical Sciences, Vol. 202-203 Cross Ref A Novel Approach for Solving the BMI Problem in Barrier Certificates Generation14 July 2020 Cross Ref Cross - Language Information Retrieval Using Two Methods: LSI via SDD and LSI via SVD30 May 2018 Cross Ref Flow-based dissimilarity measures for reservoir models: a spatial-temporal tensor approach8 April 2017 | Computational Geosciences, Vol. 21, No. 4 Cross Ref Matrix Computations; Second Edition (Gene Golub and Charles F. Van Loan)James W. Demmel18 July 2006 | SIAM Review, Vol. 32, No. 4PDF (345 KB)Matrix computationsLinear Algebra and its Applications, Vol. 141 Cross Ref Volume 28, Issue 2| 1986SIAM Review History Published online:18 July 2006 InformationCopyright © 1986 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1028073Article page range:pp. 252-255ISSN (print):0036-1445ISSN (online):1095-7200Publisher:Society for Industrial and Applied Mathematics