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IEEE AFRICON

Simulating quantum circuits with GNU Octave and Python

Makhamisa Senekane, Lerato Mohapi, Francesco Petruccione

Published Sep 1, 2013• 1 citation
Publisher

Abstract

Quantum algorithms are known to be more powerful than their classical counterparts, in the sense that they offer huge speed-ups as opposed to their classical counterparts. Physical realization of quantum algorithms results in the building of quantum circuits, which are in turn used to build a quantum computer. Unfortunately, a full-scale quantum computer is yet to be realized, hence why quantum algorithms are currently modelled on classical computers. In this work, we report the simulation of quantum circuits using GNU Octave and Python Programming languages. Additionally, performance of these languages on simulating such circuits is compared. Quantum circuits simulated are: the circuit for preparing a two-qubit entanglement (Einstein-Podolsky-Rosen (EPR) state), the one for preparing a three-qubit entanglement (Greenberger-Horne-Zeilinger (GHZ) state), swap circuit and Quantum Fourier Transform (QFT).

DOI
10.1109/afrcon.2013.6757857

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Quantum algorithms are known to be more powerful than their classical counterparts, in the sense that they offer huge speed-ups as opposed to their classical counterparts. Physical realization of quantum algorithms results in the building of quantum circuits, which are in turn used to build a quantum computer. Unfortunately, a full-scale quantum computer is yet to be realized, hence why quantum algorithms are currently modelled on classical computers. In this work, we report the simulation of quantum circuits using GNU Octave and Python Programming languages. Additionally, performance of these languages on simulating such circuits is compared. Quantum circuits simulated are: the circuit for preparing a two-qubit entanglement (Einstein-Podolsky-Rosen (EPR) state), the one for preparing a three-qubit entanglement (Greenberger-Horne-Zeilinger (GHZ) state), swap circuit and Quantum Fourier Transform (QFT).
For many practical applications, Quantum computers offer major speed-ups over traditional machines. The production of quantum chips has recently made tremendous strides, with the quantity of Qubits increasing and fidelity increasing. The smallest unit of information is the binary digit i.e. bit in general computing. In Quantum Computing the term Qubit (Quantum Bit) is used for the same purpose. In order to differentiate between a classical bit and a Qubit, Bra-Ket or Dirac notation is used. So, the Qubits are represented as |0〉 and |1〉 and are often read as Ket 0 for zero state and Ket 1 for one state. In this paper mainly programming and application sides of Quantum Computing are focused. For that, Qiskit module and its tools are used in Python programming language. General circuit optimization scheme is given. The Quantum circuits with the concept of Quantum Gates implemented are stronger compared to the optimizing algorithm and with faster execution time. In addition, for prime factorization, access to IBM's Quantum computer is carried out successfully.
Abstract. We present the basic high-level structures used for developing quantum programming languages. The presented structures are commonly used in many existing quantum programming languages and we use quantum pseudo-code based on QCL quantum programming language to describe them. We also present the implementation of introduced structures in GNU Octave language for scientific computing. Procedures used in the implementation are available as a package quantum-octave providing library of functions, which facilitates the simulation of quantum computing. This package allows also to incorporate high-level programming concepts into the simulation in GNU Octave and Matlab. As such it connects features unique for higl-level quantum programming languages, with the full palette of efficient computational routines commonly available in modern scientific computing systems. To present the major features of the described package we provide the implementation of selected quantum algorithms. We also show how quantum errors can be taken into account during the simulation of quantum algorithms using quantum-octave package. This is possible thanks to the ability to operate on density matrices implemented in quantum-octave. Key words: quantum information, quantum programming, models of quantum computation. 1.
We present a basic high-level structures used for developing quantum programming languages. The presented structures are commonly used in many existing quantum programming languages and we use quantum pseudo-code based on QCL quantum programming language to describe them. We also present the implementation of introduced structures in GNU Octave language for scientific computing. Procedures used in the implementation are available as a package quantum-octave, providing a library of functions, which facilitates the simulation of quantum computing. This package allows also to incorporate high-level programming concepts into the simulation in GNU Octave and Matlab. As such it connects features unique for high-level quantum programming languages, with the full palette of efficient computational routines commonly available in modern scientific computing systems. To present the major features of the described package we provide the implementation of selected quantum algorithms. We also show how quantum errors can be taken into account during the simulation of quantum algorithms using quantum-octave package. This is possible thanks to the ability to operate on density matrices.
In a recent paper [CHIN. PHYS. LETT. Vol.26,No.7(2009)070306 ], DONG et al. proposed a scheme for probabilistic controlled teleportation of a triplet W state using combined non-maximally entangled channel of two Einstein–Podolsky–Rosen (EPR) states and one Greenberger–Horne–Zeilinger (GHZ) state. In this paper ,only using one Einstein–Podolsky–Rosen (EPR) state and one Greenberger–Horne–Zeilinger (GHZ) state,the scheme for probabilistic controlled teleportation of a triplet W state is presented. Furthermore, Comparing with the widely used Bell-State measurement, Alice performs orthogonal complete basis measurement in the current work. Then Bob can faithfully reconstruct the original state by performing relevant unitary transformations. The total probability of successful teleportation is only dependent on channel coefficients of EPR state and GHZ state. DOI:  http://dx.doi.org/10.11591/telkomnika.v10i6.1546 Full Text: PDF
Abstract Currently, there is an ongoing “race” to build the first practically useful quantum computer that provides substantial speed-ups for certain problems compared to conventional computers. In addition to the development of such devices, this also requires the development of automated tools and methods that provide assistance in the simulation and design of corresponding applications. Otherwise, a situation might be reached where we have powerful quantum computers but hardly any proper means to actually use them. This work provides an overview of corresponding solutions for the task of quantum circuit simulation, the task of quantum circuit design, as well as corresponding mapping tasks. The covered solutions utilise expertise on efficient data structures and algorithms gained in the design of conventional circuits and systems over the last decades. While the respective descriptions are kept brief and mainly convey the general ideas, references to further readings are provided for a more detailed treatment.
Quantum computing promises an exponential speedup improvement in the time required to solve certain computational problems by leveraging the principles of quantum mechanics.While the potential power of quantum computers is well-established, their practical implementation poses significant challenges ranging from scalability to decoherence and noise.This paper presents QPy, a Python-based quantum circuit simulator that I programmed and designed to track the quantum state of a model quantum computer through the application of quantum gates to qubits.By performing the requisite matrix calculations, the simulator facilitates the understanding of quantum algorithms through the visualization of the underlying mathematics.This tool enables researchers to explore and implement various quantum protocols efficiently to test and build algorithms.