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NASA/DoD Conference on Evolvable Hardware

Evolving quantum circuits using genetic algorithm

M. Lukac, Marek A. Perkowski

Published Jun 25, 2003• 77 citations
Publisher

Abstract

In this paper we focus on a general approach of using genetic algorithm (GA) to evolve Quantum circuits (QC). We propose a generic GA to evolve arbitrary quantum. circuit specified by a (target) unitary matrix as well as a specific encoding that reduces the time of calculating the resultant unitary matrices of chromosomes. We demonstrate that, in contrast to previous approaches, our encoding allows synthesis of small quantum circuits of arbitrary type, using standard genetic operators.

DOI
10.1109/eh.2002.1029883

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In this paper we focus on a general approach of using genetic algorithm (GA) to evolve Quantum circuits (QC). We propose a generic GA to evolve arbitrary quantum. circuit specified by a (target) unitary matrix as well as a specific encoding that reduces the time of calculating the resultant unitary matrices of chromosomes. We demonstrate that, in contrast to previous approaches, our encoding allows synthesis of small quantum circuits of arbitrary type, using standard genetic operators.
Genetic algorithms were among the early choices for quantum circuit synthesis, because of their ability to evolve a given starting circuit towards one of the possible solutions. The synthesis method presented here is the first GA-based approach that dynamically adjusts its control parameters. The adaptive parameter control takes into account the analysis performed on each genetic operator, in order to automatically find an acceptable tradeoff between runtime and appropriate exploration. The experimental results prove that this method improves the synthesis runtime and the size of the circuit to be handled up to 7 qubits (previous GA-based techniques are effective only for 3-4 qubit circuits).
The developments in the area of Evolvable Quantum Hardware (QEHW) are based on successful quantum genetic algorithms (QGAs) that take advantage of both the Genetic Algorithms (GAs) and Quantum Computation (QC) parallelism. This paper presents a new Quantum Inspired Genetic Algorithm (QIGA) based on the evolution of a single chromosome. A simple combinational circuit has been implemented using a conventional GA (CGA), a single chromosome QGA (SCQGA), and the new QIGA. In the last case, the total evolution time has been considerably reduced, by changing the population size used in the evolution.
Due to the non- intuitive nature of Quantum algorithms, it becomes difficult for a classically trained person to efficiently construct new ones. So rather than designing new algorithms manually, lately, Genetic algorithms (GA) are being implemented for this purpose. GA is a technique to automatically solve a problem using principles of Darwinian evolution. This has been implemented to explore the possibility of evolving an n-qubit circuit when the circuit matrix has been provided using a set of single, two and three qubit gates. Using a variable length population and universal stochastic selection procedure, a number of possible solution circuits, with different number of gates can be obtained for the same input matrix during different runs of GA. The given algorithm has also been successfully implemented to obtain two and three qubit Boolean circuits using Quantum gates. The results demonstrate the effectiveness of the GA procedure even when the search spaces are large.
In this paper we present an evolutionary approach to the quantum symbolic logic synthesis. We use a genetic algorithm to synthesize quantum circuits from examples, allowing to synthesize functions that are both completely and incompletely specified. The symbolic synthesis is implemented in the GA so as to verify our approach. The Occam Razor principle, fundamental to inductive learning as well as to logic synthesis, is satisfied in this approach by seeking circuits of reduced complexity. The GA is tested on a set of benchmark functions representing single output quantum circuits as well as multiple entangled-qubit state generators.
Quantum algorithms will likely play a key role in future high-performance-computing (HPC) environments. These algorithms are typically expressed as quantum circuits composed of arbitrary gates or as unitary matrices. Executing these on physical devices, however, requires translation to device-compatible circuits, in a process called quantum compilation or circuit synthesis, since these devices support a limited number of native gates. Moreover, these devices typically have specific qubit topologies, which constrain how and where gates can be applied. Consequently, logical qubits in input circuits and unitaries may need to be mapped to and routed between physical qubits. Furthermore, current Noisy Intermediate-Scale Quantum (NISQ) devices present additional constraints. They are vulnerable to errors during gate application and their short decoherence times lead to qubits rapidly succumbing to accumulated noise and possibly corrupting computations. Therefore, circuits synthesized for NISQ devices need to minimize gates and execution times. The problem of synthesizing device-compatible circuits, while optimizing for low gate count and short execution times, can be shown to be computationally intractable using analytical methods. Therefore, interest has grown towards heuristics-based synthesis techniques, which are able to produce approximations of the desired algorithm, while optimizing depth and gate-count. In this work, we investigate using genetic algorithms (GA)—a proven gradient-free optimization technique based on natural selection—for circuit synthesis. In particular, we formulate the quantum synthesis problem as a multi-objective optimization (MOO) problem, with the objectives of minimizing the approximation error, number of multi-qubit gates, and circuit depth. We also employ fuzzy logic for runtime parameter adaptation of GA to enhance search efficiency and solution quality in our proposed method.