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Proceedings - Asian Test Symposium/Proceedings

An Optimization Problem for Topological Quantum Computation

Shigeru Yamashita

Published Nov 1, 2012• 4 citations
Publisher

Abstract

This paper formulates the logic level circuit optimization problem for topological quantum computation. Observing the properties of brading operations in topological quantum computation, we formulate our problem as to find a good gate order and a good initial qubit order. For the problem, we propose an efficient method by utilizing an algorithm for clique finding. Our experimental result shows the effectiveness of our proposed method.

DOI
10.1109/ats.2012.45

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This paper formulates the logic level circuit optimization problem for topological quantum computation. Observing the properties of brading operations in topological quantum computation, we formulate our problem as to find a good gate order and a good initial qubit order. For the problem, we propose an efficient method by utilizing an algorithm for clique finding. Our experimental result shows the effectiveness of our proposed method.
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This paper introduces a novel approach to quantum computation topology optimization based on dynamic topology. Traditional topology optimization methods often require manual design, which is challenging for complex quantum computing environments. Our method leverages dynamic topology to automatically optimize the quantum computation's topology, leading to improved computational efficiency and stability. We propose a framework that dynamically adjusts the quantum circuit's topology during the optimization process, resulting in a more robust and efficient solution. This paper presents a detailed analysis of the proposed algorithm and its implementation, demonstrating its effectiveness in optimizing quantum circuits for specific scenarios. The core of the method lies in the utilization of self-similarity properties within the topological landscape, allowing for a streamlined and adaptive optimization process. We discuss the challenges and benefits of this approach, highlighting its potential to advance quantum computation.
This paper formulates the qubit layout problem for ICM representation which is favorable for topological quantum computation. Observing the properties of braiding operations in a logic circuit model of ICM, we study the potential usefulness of two-dimensional qubit layouts based on this model. We compare and contrast the efficiency of one- and two-dimensional qubit layouts in reducing the logical time steps for topological quantum circuits. This leads us to an approach to find a good gate order for two-dimensional qubit layouts. Indeed, our preliminary experimental results show the effectiveness of two-dimensional qubit layouts.
The development of efficient quantum algorithms is a significant challenge in the field of quantum computing. This paper introduces a novel approach to quantum algorithm design, employing a topological adaptive framework. We propose a method that leverages the inherent topological properties of quantum systems to optimize the performance of existing quantum algorithms. This framework aims to enhance the efficiency of quantum computation by systematically manipulating the quantum state to achieve optimal results. The core mechanism involves utilizing topological transformations to guide the evolution of the quantum state, thereby improving the algorithm's convergence and fidelity. This research explores the potential of topological optimization to significantly advance the capabilities of quantum algorithms. This work presents a framework with a strong theoretical foundation and initial experimental validation demonstrating its effectiveness. The ultimate goal is to contribute to the creation of robust and versatile quantum algorithms capable of solving complex problems.
Quantum circuit synthesis, the process of mapping logical operations onto a quantum hardware architecture, presents a significant bottleneck in the development of practical quantum computers. Traditional methods often suffer from exponential computational complexity, rendering them unsuitable for circuits of even moderate size. This work introduces a novel approach to quantum circuit synthesis leveraging topological optimization, a technique rooted in condensed matter physics. We represent quantum circuits as topological phases on a graph, where gate operations are encoded as transitions between these phases. An iterative optimization process then refines the graph structure, minimizing circuit complexity (represented as energy) while maintaining the desired quantum operations. The core of our method lies in the application of gradient-based optimization algorithms to this topological graph, driving the system towards a low-energy state representing an optimal quantum circuit. Preliminary results demonstrate the potential of this approach to significantly reduce gate count and improve fidelity compared to conventional synthesis methods. The proposed framework offers a scalable solution to the challenges inherent in quantum circuit design, paving the way for more efficient and reliable quantum computation.