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Qcompiler: quantum compilation with CSD method

Y. G. Chena, J. B. Wanga

Published Jan 1, 2014• 0 citations
OpenAlex

Abstract

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

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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
Recent research in generalizing quantum computation from 2-valued qudits to d-valued qudits has shown practical advantages for scaling up a quantum computer. A further generalization leads to quantum computing with hybrid qudits where two or more qudits have different finite dimensions. In both cases, a quantum computation is performed when a unitary evolution operator, acting as a quantum logic gate, transforms the state of qudits in a quantum system. Unitary operators can be represented by unitary matrices, and therefore for a quantum system consists of multiple qudits, a gate may be synthesized by matrix decomposition techniques such as QR factorization and the Cosine-sine Decomposition (CSD). In this article, we present a CSD based synthesis method for n qudit hybrid and d-valued quantum circuits.
A quantum compiler is a software program for decomposing ("compiling") an arbitrary unitary matrix into a sequence of elementary operations (SEO). The author of this paper is also the author of a quantum compiler called Qubiter. Qubiter uses a matrix decomposition called the Cosine-Sine Decomposition (CSD) that is well known in the field of Computational Linear Algebra. One way of measuring the efficiency of a quantum compiler is to measure the number of CNOTs it uses to express an unstructured unitary matrix (a unitary matrix with no special symmetries). We will henceforth refer to this number as εεε. In this paper, we show how to improve εεε for Qubiter so that it matches the current world record for εεε, which is held by another quantum compiling algorithm based on CSD.
The software package \emph{Qcompiler} (CPC, 184 (2013) 853) 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 \emph{OptQC}, which finds permutation matrices PPP and QQQ for a given unitary matrix UUU such that the number of gates in the quantum circuit of U=QTPTU′PQU = Q^TP^TU'PQU=QTPTU′PQ is significantly reduced, where U′U'U′ is equivalent to UUU 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.
We introduce an open source software package UniversalQCompiler written in Mathematica that allows the decomposition of arbitrary quantum operations into a sequence of single-qubit rotations (with arbitrary rotation angles) and controlled-NOT (C-NOT) gates. Together with the existing package QI, this allows quantum information protocols to be analysed and then compiled to quantum circuits. Our decompositions are based on Phys. Rev. A 93, 032318 (2016), and hence, for generic operations, they are near optimal in terms of the number of gates required. UniversalQCompiler allows the compilation of any isometry (in particular, it can be used for unitaries and state preparation), quantum channel, positive-operator valued measure (POVM) or quantum instrument, although the run time becomes prohibitive for large numbers of qubits. The resulting circuits can be displayed graphically within Mathematica or exported to LaTeX. We also provide functionality to translate the circuits to OpenQASM, the quantum assembly language used, for instance, by the IBM Q Experience.
We provide a new algorithm that translates a unitary matrix into a quantum circuit according to the G=KAK theorem in Lie group theory. With our algorithm, any matrix decomposition corresponding to type-AIII KAK decompositions can be derived according to the given Cartan involution. Our algorithm contains, as its special cases, Cosine-Sine decomposition (CSD) and Khaneja-Glaser decomposition (KGD) in the sense that it derives the same quantum circuits as the ones obtained by them if we select suitable Cartan involutions and square root matrices. The selections of Cartan involutions for computing CSD and KGD will be shown explicitly. As an example, we show explicitly that our method can automatically reproduce the well-known efficient quantum circuit for the nnn-qubit quantum Fourier transform.
In this paper, the problem of constructing an efficient quantum circuit for the implementation of an arbitrary quantum computation is addressed. To this end, a basic block based on the cosine-sine decomposition method is suggested which contains lll qubits. In addition, a previously proposed quantum-logic synthesis method based on quantum Shannon decomposition is recursively applied to reach unitary gates over lll qubits. Then, the basic block is used and some optimizations are applied to remove redundant gates. It is shown that the exact value of lll affects the number of one-qubit and CNOT gates in the proposed method. In comparison to the previous synthesis methods, the value of lll is examined consequently to improve either the number of CNOT gates or the total number of gates. The proposed approach is further analyzed by considering the nearest neighbor limitation. According to our evaluation, the number of CNOT gates is increased by at most a factor of 53\frac{5}{3}35​ if the nearest neighbor interaction is applied.