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IEEE Transactions on Magnetics

A Novel Design of Quantum Multiplexer and its Identity Rules-Based Optimization for the Spin-Torque-Based n-Qubit Architecture

Anant Aravind Kulkarni, S. S. Gayathri, Dev Ranjan Das, Brajesh Kumar Kaushik

Published Oct 1, 2024• 0 citations
Publisher

Abstract

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.

DOI
10.1109/tmag.2024.3471700

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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.
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.
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.
Spin-based quantum architectures offer a promising route toward scalable and practical quantum computing owing to their long coherence times, high-fidelity gate operations, and compatibility with established semiconductor fabrication processes. This work focuses on the design, decomposition, and simulation of fundamental multi-qubit logic gates on spin-based architectures. An optimized CNOT gate decomposition is presented, achieving a 36.36%36.36 \%36.36% reduction in elementary operations, verified through quantum circuit simulation. Furthermore, a resource-efficient Toffoli (CCNOT) gate is developed, yielding a 38%38 \%38% reduction in elementary gates and demonstrating improved T-depth efficiency. Finally, a four-qubit circuit example is presented, illustrating the scalability of the pseudocode and validating the correctness of the proposed approach.
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 requires logic operations to be implemented as reversible transformations. Classical combinational circuits must therefore be redesigned using reversible gate structures when mapped to quantum systems. In this work, fundamental quantum digital circuits are implemented using CNOT and Toffoli gates using the Qiskit framework.In addition, an 8-qubit Quantum Random Number Generator (QRNG) is developed and analyzed. Hadamard operations are applied to an 8-qubit register to produce a uniform superposition over 256 states. Measurement in the computational basis generates an 8-bit result per execution. By repeating the circuit 16 independent times and concatenation of the outputs produce a 128-bit random sequence. The QRNG is evaluated using Dirac notation, density operator representation and entropy analysis to verify uniform probability distribution under ideal simulation conditions.Simulation results confirm the correct logical functionality of the reversible arithmetic circuits and demonstrate high entropy random sequence generation using quantum measurement. The presented framework provides a structured approach for implementing digital logic and randomness generation in Qiskit.
Quantum algorithms on near-term quantum processors are typically executed using shallow quantum circuits composed of one- and two-qubit gates. However, as circuit depth and gate number increase, gate imperfections and qubit decoherence begin to dominate, limiting algorithmic complexity. An alternative approach is to explore gates involving more than two qubits. In previous work (X. Wu et al., Physical Review X 14, 041030 (2024)), we demonstrated a new superconducting qubit architecture with user-selectable two-qubit interactions via a reconfigurable router, used to connect pairs of qubits. Here, we leverage this novel architecture to realize programmable and efficient multi-qubit operations involving more than two qubits, resulting in faster preparation of multi-qubit entangled states with good fidelities. We also successfully apply model-free reinforcement learning to perform multi-qubit gates, including training a two-qubit controlled-Z gate as well as three-qubit controlled-SWAP and controlled-controlled-phase (Fredkin and Toffoli) gates. Higher nnnth-order gates may also be feasible, using our high-connectivity router design. This could provide a more efficient and higher-fidelity implementation of complex quantum algorithms and a more practical approach to quantum computation.