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IEEE Transactions on Magnetics

Optimal Boolean Logic Quantum Circuit Decomposition for Spin-Torque-Based $\boldsymbol{n}$ -Qubit Architecture

Anant Aravind Kulkarni, Sanjay Prajapati, Shivam Verma, Brajesh Kumar Kaushik

Published Sep 3, 2018• 5 citations
Publisher

Abstract

The semiconductor industry is facing a twofold challenge at sub-nanometer level; first, the high power dissipation in irreversible computing architectures due to information loss and second, inability to handle large data due to sequential information processing. These issues create obstacles in producing the presumed low-power complex computing outcomes. The heat dissipation can be reduced by utilizing the complementary metal-oxide-semiconductor-based reversible computing architectures. However, these architectures fail to enhance the performance owing to inability to process large data. Quantum computing (QC) can circumvent these problems due to its fundamental ineffaceable characteristics of quantum mechanics-based reversible computing and parallelism. Spin-torque-based physical realization is the most suitable platform for reversible computing due to the electron spin analogous to the qubit. However, optimal quantum circuits are required to physically realize the complex Boolean logic due to spin-qubit decoherence and reduce the number of transistor switching activities for the spin generation and injection required for the spin-qubit rotation. Therefore, in this paper, optimal quantum circuit decompositions are presented with the help of developed elementary quantum library {Ry(θ), Rz(θ), √SWAP for the spin-torque-based QC architecture. The reversible Boolean logic performance is analyzed and compared for the conventional, reduced, and optimal decompositions on the first- and second-order transmission coefficient matrix-based spin-torque QC architecture. The results encourage to set a path toward QC-based reconfigurable complex computing systems in near future.

DOI
10.1109/tmag.2018.2815696

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Optimal Boolean Logic Quantum Circuit Decomposition for Spin-Torque-Based n\boldsymbol{n}n -Qubit Architecture
The semiconductor industry is facing a twofold challenge at sub-nanometer level; first, the high power dissipation in irreversible computing architectures due to information loss and second, inability to handle large data due to sequential information processing. These issues create obstacles in producing the presumed low-power complex computing outcomes. The heat dissipation can be reduced by utilizing the complementary metal-oxide-semiconductor-based reversible computing architectures. However, these architectures fail to enhance the performance owing to inability to process large data. Quantum computing (QC) can circumvent these problems due to its fundamental ineffaceable characteristics of quantum mechanics-based reversible computing and parallelism. Spin-torque-based physical realization is the most suitable platform for reversible computing due to the electron spin analogous to the qubit. However, optimal quantum circuits are required to physically realize the complex Boolean logic due to spin-qubit decoherence and reduce the number of transistor switching activities for the spin generation and injection required for the spin-qubit rotation. Therefore, in this paper, optimal quantum circuit decompositions are presented with the help of developed elementary quantum library {Ry(θ), Rz(θ), √SWAP for the spin-torque-based QC architecture. The reversible Boolean logic performance is analyzed and compared for the conventional, reduced, and optimal decompositions on the first- and second-order transmission coefficient matrix-based spin-torque QC architecture. The results encourage to set a path toward QC-based reconfigurable complex computing systems in near future.
Quantum computing due to its ability of inherent parallel processing is emerged as one of the solutions to the complex computing problems. In connection with this, several proposals have been given for the quantum circuits-based design of the reversible combinational and sequential circuits. However, the implementation of the reversible sequential logic is challenging in comparison to the reversible combinational logic. Spin-torque-based reconfigurable architecture could be utilized to realize the quantum circuits. However, the architecture needs the optimized decomposition of the quantum circuits utilized for the reversible sequential logic due to required number of single qubit rotations and two-qubit entanglements. In this paper, the elementary decomposition of the quantum circuits representing the reversible D-Latch is optimized with the help of elementary quantum library{Ry(θ), Rz(θ), SWAP}\{R_{\mathrm{y}}(\theta),\ R_{\mathrm{z}}(\theta),\ \sqrt{\text{SWAP}}\}{Ry​(θ), Rz​(θ), SWAP​}. The number of elementary operations required to realize the D-Latch over 5 clock cycles is reduced by 43.56%. The average fidelity of the D-Latch considered for the implementation and analysis is obtained at the end of each clock cycle is well above 97%. The fidelity is further improved by approximating the present state output utilized for the next state input.
Quantum computing (QC) provides an efficient platform to solve complex problems such as number factoring and searching. The quantum Fourier transform (QFT) is an integral part of quantum algorithms for integer number factoring, phase estimation, discrete algorithms, interchange of position and momentum states, quantum key distribution protocol, multiparty quantum telecommunication, and quantum arithmetic. The theoretical and experimental implementations of QFT on various platforms have been proposed by researchers. Spin-torque-based qubit(s) manipulation is one of the encouraging solid-state device technologies. However, to date, QFT is not realized by spin-torque-based QC architecture. In this article, the spin-torque-based architecture has been modeled with the help of optimized decomposition of quantum circuits for the QFT. Moreover, an optimal-depth Clifford + T gates set-based quantum circuit is utilized to implement the QFT. The performance analysis in terms of fidelity (>99%), magnitude, and phase difference of respective density matrices for different forms of three-qubit QFT provides a novel way of its physical realization to address the complex problems.
Currently, computing paradigm is ruled by the laws of classical physics and will continue till the dimensions of transistors reaches the size of atomic particles. Quantum computing (QC) is a new technology that employs laws of quantum mechanics to address issues such as irreversibility and power dissipation that are outside the scope of conventional computing models. QC offers a powerful stage for solving complex and compound problems like searching and number factoring. A critical task in utilizing quantum physics in many application fields is circuit design using reversible quantum gates. Unitary decomposition is a popular scheme for mapping quantum algorithms to any set of elementary quantum operations. Using decomposition techniques enables transformation of unitary matrices into fundamental quantum gates, which is critical for running algorithms on prevailing quantum computers. Any 3x3 reversible quantum gate can be decomposed into single-qubit rotation gates and two qubit CNOT gates. This paper is the first to present quantum implementations of FRSG1 and JTF1 gates into CNOT gates and single qubit U3 gates with different optimization levels on a platform provided by IBM. These gates are important in a variety of practical applications like Stochastic computing and parity generation circuits. In FRSG1 the implementation count of single qubit gates decreases by 56% and the count of two qubit gates by 15% after optimization, whereas in JTF1 gate the single qubit gate count reduces by 71% and the number of two qubit gates reduces by 41%.
Quantum computing (QC) imitates particle behavior at the sub-atomic level. Quantum gates are based on quantum mechanical phenomena such as superposition and entanglement. The obstacle to the realization of reversible computing is the huge number of operations in terms of quantum gates. Therefore, novel designs of reversible computing blocks with a minimum number of elementary operations with high fidelity are necessary. Therefore, a novel design of multiplexer is proposed in this article, which is composed of only 1-CNOT and 1-Toffoli gates. Moreover, the reduced decomposition of the multiplexer and its identity rule-based optimization for the spin-torque-based n-qubit architecture is discussed. To validate the design, the QISKIT implementation of the novel design in terms of amplitude, probability, and Q-sphere representation is carried out. The results are encouraging to realize the reversible computing involving quantum multiplexer as one of the building blocks.
Abstract Quantum computing (QC) is suitable for reversible computing due to its inherent parallel processing ability and fast speed. It also helps to address the issue of high-power dissipation in classical computing. Moreover, QC gates are the sequence of elementary operations such as single-qubit rotation and two-qubit entanglement. Elementary quantum operations are required to be reduced for the realization of complex computing. In this paper, optimization of 1-Toffoli gate-based quantum full adders (QFAs) in terms of the number of elementary operations with the help of quantum library {Ry, Rz, SWAP\sqrt{\mathrm{SWAP}}SWAP​ SWAP } is carried out. Moreover, the performance of two different 1-Toffoli QFAs is investigated in terms of execution time, fidelity, and number of electrons required to realize the QFAs. Improvement in fidelity is 0.7% and 0.57% for QFA1 and QFA2, respectively, compared to the fidelity of 2-Toffoli QFA. A 9.97% increase in execution time is mandatory for the QFA2 compared to QFA1. The QFA2 takes 5% more number of electrons in comparison to QFA1.
The quantum computing (QC) is emerging as one of the possibilities to replace the conventional computing to meet the complex computing challenges. Quantum gates are based on the quantum mechanical phenomena such as superposition and entanglement. Moreover, there are several ways to realize the reversible full adder representing one of the building blocks of the reversible computing. One of the ways to realize the reversible full adder is by using the controlled V and V+ gates. Spintronics is one of the quantum technologies to realize the reversible computing physically. Therefore, there is need of spin-torque based modelling of controlled V and V+ gates for the quantum computing applications in the reversible computing domain. In this paper, the controlled V and V+ gates are modelled for the spin-torque based qubit architecture through the optimization at elementary single-qubit rotation and two-qubit entanglement level. Therefore, the key innovation or unique contribution is to realize the controlled V and V+ gates by using the minimum number of the elementary operations (single- and two-qubits). Moreover, a quantum full adder (QFA) composed of controlled V and V+ gates, is optimized and realized with the spin-torque models of the controlled V and V+ gates to achieve fault tolerant fidelity. Therefore, the novelty is that the optimization of the controlled V and V+ gates for the reversible full adders is carried out by using the identity rules.