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International Conference on Research in Computational Intelligence and Communication Networks (ICRCICN)

Spin-Based Simulation and Optimization of Multi-Qubit Quantum Gates

Dolananda Sri Naga Phani Sarma Mokkapati, V Ramesh Kumar, D. De, Jadav Chandra Das

Published Dec 20, 2025• 0 citations
Publisher

Abstract

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 $36.36 \%$ reduction in elementary operations, verified through quantum circuit simulation. Furthermore, a resource-efficient Toffoli (CCNOT) gate is developed, yielding a $38 \%$ 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.

DOI
10.1109/icrcicn68210.2025.11364889

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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.
Multi-bit Toffoli gates form an essential quantum gate class for quantum algorithms. They should be efficiently decomposed into elementary single- or multi-qubit quantum gates, such as CNOT, T, and Hadarmard, for a scalable implementation of a quantum algorithm. We propose an engineering method for the practical synthesis of a multi-bit Toffoli gate. Two optimization models and their closed-form solutions are presented for optimal decomposition of the multi-bit Toffoli gate. These models are based on linearized multi-objective integer programming with parameters such as the number of target ancillae, ancillae states, and basis gates. The proposed method supports the systematic handling of quantum circuit constraints, including the total number of available qubits and maximum circuit depth, which depend on various quantum hardware specifications. Our approach exhibits promise in the noisy intermediate-scale quantum environment by providing a rapid and optimal method for synthesizing multi-bit Toffoli gates in diverse and unpredictable quantum hardware specifications.
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Pairwise exchange couplings have long been the standard mechanism for entangling spin qubits in semiconductor systems. However, implementing quantum circuits based on pairwise exchange gates often requires a lengthy sequence of elementary gate operations. In this work, we present an alternative approach: multi-qubit entangling gate operations that simultaneously drive the exchange couplings between multiple pairs of spin qubits. We explore three spin qubit systems in linear or triangular configurations. We derive analytical expressions for these multi-exchange entangling operations and demonstrate how to use the resulting three-qubit gates to construct quantum circuits capable of generating standard entangled states such as GHZ and W states, and the Toffoli gate, by optimizing control parameters. Our results show that this multi-qubit strategy significantly reduces the number of required operations, offering a pathway to more efficient, shallower, and more coherent circuits for spin-qubit processors.
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Resource consumption is an important issue in quantum information processing, particularly during the present NISQ era. In this paper, we investigate resource optimization of implementing multiple controlled operations, which are fundamental building blocks in the field of quantum computing and quantum simulation. We design new quantum circuits for the nnn-Toffoli gate and general multi-controlled unitary, which have only O(log⁡n)O(\log n)O(logn)-depth and O(n)O(n)O(n)-size, and only require 111 ancillary qubit. To achieve these results, we explore the potential of ancillary qubits and discover a method to create new conditional clean qubits from existed ancillary qubits. These techniques can also be utilized to construct an efficient quantum circuit for incrementor, leading to an implementation of multi-qubit Toffoli gate with a depth of O(log⁡2n)O(\log^2n)O(log2n) and size of O(n)O(n)O(n) without any ancillary qubits. Furthermore, we explore the power of ancillary qubits from the perspective of resource theory. We demonstrate that without the assistance of ancillary qubit, any quantum circuit implementation of multi-qubit Toffoli gate must employ exponential precision gates. This finding indicates a significant disparity in computational power of quantum circuits between using and not using ancillary qubits. Additionally, we discuss the comparison of the power of ancillary qubits and extra energy levels in quantum circuit design.
We consider the problem of the variational quantum circuit synthesis into a gate set consisting of the CNOT gate and arbitrary single-qubit (1q) gates with the primary target being the minimization of the CNOT count. First we note that along with the discrete architecture search suffering from the combinatorial explosion of complexity, optimization over 1q gates can also be a crucial roadblock due to the omnipresence of local minimums (well known in the context of variational quantum algorithms but apparently underappreciated in the context of the variational compiling). Taking the issue seriously, we make an extensive search over the initial conditions an essential part of our approach. Another key idea we propose is to use parametrized two-qubit (2q) controlled phase gates, which can interpolate between the identity gate and the CNOT gate, and allow a continuous relaxation of the discrete architecture search, which can be executed jointly with the optimization over 1q gates. This coherent optimization of the architecture together with 1q gates appears to work surprisingly well in practice, sometimes even outperforming optimization over 1q gates alone (for fixed optimal architectures). As illustrative examples and applications we derive 8 CNOT and T depth 3 decomposition of the 3q Toffoli gate on the nearest-neighbor topology, rediscover known best decompositions of the 4q Toffoli gate on all 4q topologies including a 1 CNOT gate improvement on the star-shaped topology, and propose decomposition of the 5q Toffoli gate on the nearest-neighbor topology with 48 CNOT gates. We also benchmark the performance of our approach on a number of 5q quantum circuits from the ibm_qx_mapping database showing that it is highly competitive with the existing software. The algorithm developed in this work is available as a Python package CPFlow.