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International Journal of Parallel Emergent and Distributed Systems

Advanced swarm intelligence algorithms in quantum circuit design

Libuše Horáčková, Ivan Zelinka

Published Oct 15, 2024• 1 citation
Publisher

Abstract

This study explores the potential of employing algorithms like iSOMA, Differential Evolution, Particle Swarm Optimization, Grey Wolf Optimization, and Ant Colony Optimization for the design of quantum computing circuits. Utilizing the Qiskit environment, the research involved simulating a straightforward quantum circuit with variable parameters. To substantiate the effectiveness of these algorithms, three distinct experimental setups were conducted under varying conditions and degrees of freedom. The findings reveal that these algorithms are not only suitable for simulations but also excel in identifying solutions that conserve qubits. A comparative analysis of the methods was performed using the Friedman test, followed by the Nemenyi post-hoc test to evaluate their relative performance.

DOI
10.1080/17445760.2024.2388245

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In the present paper, we demonstrate the possibilities of designing quantum computing circuits using a specific swarm intelligence algorithm — iSOMA in the form of three experiments. All simulations are based on a simple sample of a quantum computing circuit from the Qiskit environment, which was used as a comparison circuit with the results of the three experiments already mentioned. In the first experiment, we try to find an arbitrary functional solution using iSOMA with minimal constraints on this circuit’s design. It can be said that in this experiment, iSOMA showed the highest degree of “creativity”. In the second experiment, we focused on whether iSOMA can be used to find a circuit identical to the one designed by a human or equivalent with the positions of the measurement gates fixed. In the last experiment, we highlight iSOMA’s ability to avoid unnecessary qubit usage by adding redundant qubits to a possible circuit and fixing the measurement gates to the last two qubits in the scheme. In all three experiments, we see that iSOMA can find efficient functional and often astonishing solutions — the proposed method applied to a classical circuit founded a new one preserving required properties while saving one ancilla (redundant, useless, non-used)1 qubit. All computations are implemented in the IBM Qiskit2 environment. Although these are relatively simple experiments, the results show that evolutionary algorithms can successfully design more complex quantum circuits.
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Recent advancements in computing speed and capacity of Artificial Intelligence (AI) algorithms have reached a saturation level in performance due to the continuous application of Moore's law which resulted in the memory wall phenomenon. Quantum computing (QC), based on the principles of quantum mechanics which include superposition and entanglement, has the potential to contribute to the advancements of AI by providing exponential speedup. Quantum computers use quantum bits, also known as qubits, as the metric to demonstrate the power of quantum technology. Qubits, the fundamental unit of quantum information can exist in two states, 0 and 1, simultaneously, leveraging the principle of superposition. Quantum gates are the building blocks of quantum circuits, operating on qubits to transform one quantum state into another, and are comparative to classical logic gates. Designing and simulating quantum circuits can be completed using the Qiskit library design by IBM. Qiskit is a cloud-based, open access platform to real quantum computers with 5 to 16 qubits. This paper offers a straightforward tutorial on implementing one, two and three-qubit quantum gates, as well as designing quantum circuits using the Qiskit library, illustrated with an example of a quantum half adder implementation.
This paper presents a novel adaptive optimization algorithm for quantum circuits, leveraging the inherent properties of these circuits to achieve enhanced circuit optimization and computational efficiency. Traditional optimization algorithms are primarily designed for classical computers, but this work explores the potential of quantum circuits to offer significant advantages in computation. The core mechanism centers around dynamically adjusting quantum circuit parameters to guide the optimization process. The research focuses on a specific non-linear quantum circuit optimization framework, demonstrating significant improvements in performance compared to established methods. This algorithm employs a unique approach to parameter tuning, which is mathematically derived and carefully implemented. We present a comprehensive analysis of the algorithm's effectiveness, highlighting its strengths and limitations. The paper concludes with a discussion of future research directions and potential applications within the field of quantum computing.
Four intelligent optimization algorithms are compared by searching for control pulses to achieve the preparation of target quantum states for closed and open quantum systems, which include differential evolution (DE), particle swarm optimization (PSO), quantum-behaved particle swarm optimization (QPSO), and quantum evolutionary algorithm (QEA). We compare their control performance and point out their differences. By sampling and learning for uncertain quantum systems, the robustness of control pulses found by these four algorithms is also demonstrated and compared. The resulting research shows that the QPSO nearly outperforms the other three algorithms for all the performance criteria considered. This conclusion provides an important reference for solving complex quantum control problems by optimization algorithms and makes the QPSO be a powerful optimization tool.