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EVOLVING QUANTUM ERROR CORRECTION CODES

DANIEL RIBAS TANDEITNIK

Published May 11, 2022• 0 citations
Publisher

Abstract

Computational methods become essential in the face of complex problems where human intuition and traditional methods fail.Recent works present artificial neural networks capable of efficiently performing tasks intractable by conventional algorithms using machine learning, rendering it one of the most popular methods.Concomitantly, genetic algorithms, inspired by the biological processes of natural selection and mutation, have been used as a metaheuristic method to find solutions to optimization problems.We then raise the question of whether genetic algorithms have the potential to solve problems in the context of quantum computing, where human intuition decreases as physical systems grow.Specifically, we focus on the evolution of quantum error-correcting codes within the stabilizer code formalism.By specifying an appropriate fitness function, we show that we can evolve celebrated codes, such as the Perfect and Shor's code with respectively 5 and 9 qubits, in addition to new unanticipated examples.Additionally, we compared it with a brute force random search and verified an increasing superiority of the genetic algorithm as the total number of qubits increases.Given the results, we foresee that genetic algorithms can become valuable tools to perform complex applications in quantum systems and produce tailored circuits that satisfy restrictions imposed by hardware.

DOI
10.17771/pucrio.acad.59800

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Computational methods become essential in the face of complex problems where human intuition and traditional methods fail.Recent works present artificial neural networks capable of efficiently performing tasks intractable by conventional algorithms using machine learning, rendering it one of the most popular methods.Concomitantly, genetic algorithms, inspired by the biological processes of natural selection and mutation, have been used as a metaheuristic method to find solutions to optimization problems.We then raise the question of whether genetic algorithms have the potential to solve problems in the context of quantum computing, where human intuition decreases as physical systems grow.Specifically, we focus on the evolution of quantum error-correcting codes within the stabilizer code formalism.By specifying an appropriate fitness function, we show that we can evolve celebrated codes, such as the Perfect and Shor's code with respectively 5 and 9 qubits, in addition to new unanticipated examples.Additionally, we compared it with a brute force random search and verified an increasing superiority of the genetic algorithm as the total number of qubits increases.Given the results, we foresee that genetic algorithms can become valuable tools to perform complex applications in quantum systems and produce tailored circuits that satisfy restrictions imposed by hardware.
Automatic quantum circuit design is motivated by the difficulties in manual design, because quantum algorithms are highly non-intuitive and practical quantum computer hardware is not yet available. Thus, quantum computers have to be simulated on classical hardware which naturally entails an exponential growth of computational costs and allows only to simulate small quantum systems, i. e., with only few qubits. Huge search spaces render evolutionary approaches nearly unable to achieve breakthrough solutions in the development of new quantum algorithms. Consequently, at present we must be content to evolve essentially already existing (black-box) quantum algorithms. This thesis presents empirical results on the evolution of quantum circuits using genetic programming. For that purpose, a linear and a linear-tree GP system (allowing intermediate measurements) with integrated quantum computer simulator were implemented. Their practicality in evolving quantum circuits is shown in different experiments for 1-SAT (solutions act like Hogg's algorithm) and the Deutsch-Jozsa problem. These experiments confirm that the evolution of quantum circuits is practically feasible only for sufficiently small problem instances. In this context, scalability and the detection of scalability becomes very important. It is shown that scalable quantum circuits are evolvable to a certain degree: a general quantum circuit can be inferred manually from the evolved solutions for small instances of the given problem. Besides, further experiments indicate that 're-evolution' is effective for the evolution of scalable quantum circuits. With this method the start population of a problem instance is inoculated with evolved solutions for a smaller problem instance. Furthermore, investigations of fitness landscapes and selection strategies are made, with the aim of improving the efficiency of evolutionary search. A notable result is that using the crossover operator damages rather than benefits evolution of quantum circuits.
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.
Quantum error correction and the use of quantum error correction codes are likely to be essential for the realization of practical quantum computing. Because the error models of quantum devices vary widely, quantum codes that are tailored for a particular error model may have much better performance. In this work, we present a novel evolutionary algorithm that searches for an optimal stabilizer code for a given error model, number of physical qubits, and number of encoded qubits. We demonstrate an efficient representation of stabilizer codes as binary strings, which allows for random generation of valid stabilizer codes as well as mutation and crossing of codes. Our algorithm finds stabilizer codes whose distance closely matches the best-known-distance codes of Grassl (2007) forn≤20n \leq 20n≤20physical qubits. We perform a search for optimal distance Calderbank–Steane–Shor codes and compare their distance to the best known codes. Finally, we show that the algorithm can be used to optimize stabilizer codes for biased error models, demonstrating a significant improvement in the undetectable error rate for[[12,1]]2[[12,1]]_{2}[[12,1]]2​codes versus the best-known-distance code with the same parameters. As part of this work, we also introduce an evolutionary algorithm QDistEvol for finding the distance of quantum error correction codes.
Multi‐objective optimization in quantum systems poses formidable challenges stemming from the high dimensionality, complex constraints, and conflicting performance metrics inherent to quantum control tasks and circuit synthesis. This study presents a comprehensive exploration of genetic AI algorithms—evolutionary strategies inspired by natural selection—tailored specifically for multi‐objective optimization in quantum computing contexts. We propose a hybrid framework that synergistically combines the elitist, Pareto‐based selection mechanics of NSGA-II with quantum‐inspired crossover and mutation operators designed to preserve entanglement structures and exploit hardware‐specific gate sets. In this framework, candidate solutions encoding circuit topologies or control‐pulse parameters undergo iterative evolution, guided by fitness vectors that balance gate fidelity, circuit depth, and resource overhead. To benchmark performance, we apply the algorithm to canonical quantum computing problems: Fourier transform circuits, QAOA ansätze for MaxCut instances, and random Clifford+T circuits. Through extensive simulation on noise-modelled quantum devices, we evaluate Pareto front coverage, convergence speed, diversity maintenance, and robustness under decoherence. Our results demonstrate that the proposed genetic AI algorithm outperforms classical single‐objective genetic methods and established multi‐objective evolutionary algorithms (e.g., SPEA2) by achieving broader Pareto fronts and faster convergence rates, while maintaining solution diversity. Furthermore, noise-resilience experiments show graceful degradation, indicating practical applicability on near-term quantum hardware. These findings substantiate the potential of evolutionary computation paradigms—augmented with quantum‐inspired operators—to address the intricate trade-off surfaces that define NISQ-era optimization problems, paving the way toward automated quantum circuit design and control parameter tuning for real-world quantum computing applications.
Genetic algorithms are heuristic optimization techniques inspired by Darwinian evolution. Quantum computation is a new computational paradigm which exploits quantum resources to speed up information processing tasks. Therefore, it is sensible to explore the potential enhancement in the performance of genetic algorithms by introducing quantum degrees of freedom. Along this line, a modular quantum genetic algorithm has recently been proposed, with individuals encoded in independent registers comprising exchangeable quantum subroutines [1], which leads to different variants. Here, we address the numerical benchmarking of these algorithms against classical genetic algorithms, a comparison missing from previous literature. To overcome the severe limitations of simulating quantum algorithms, our approach focuses on measuring the effect of quantum resources on the performance. In order to isolate the effect of the quantum resources on the performance, we selected the classical variants to resemble the fundamental characteristics of the quantum genetic algorithms. Under these conditions, we encode an optimization problem in a two-qubit Hamiltonian and face the problem of finding its ground state. A numerical analysis based on a sample of 200 random cases shows that some quantum variants outperform all classical ones in convergence speed towards a near-optimal result. Additionally, we have considered a diagonal Hamiltonian and the Hamiltonian of the hydrogen molecule to complete the analysis with two relevant use-cases. If this advantage holds for larger systems, quantum genetic algorithms would provide a new tool to address optimization problems with quantum computers.
This paper demonstrates an application of an evolutionary approach for solving a class of non-trivial, hardware-design problems. Array processing features of the computer language APL simplify the implementation of an evolutionary solution in which simulation is performed by a genetic algorithm on a population of candidate solutions until one or more are satisfactory quantum algorithms. The objective of the simulation model is the automatic discovery of quantum computer algorithms. The algorithms are expressed in a circuit model that specifies the sequences in which quantum operators are to be applied. The automatically configured circuits operate as quantum computers that for the present have their domains of application limited to evaluation of only a few specific functions. The simulations use a small collection of basic and relatively low-level operators to obtain perfect results for five different target functions. These functions were chosen to demonstrate how, on a personal computer, an evolutionary method is able to discover novel designs of computing hardware. The results establish that it is feasible to use genetic algorithms in an evolutionary method to invent correct hardware designs. The progress of simulated evolution is directed by input/output constraints and a fitness function. Alternative configurations of circuit models can obtain algorithms with promise for future quantum computers. Current simulations yield primitive quantum algorithms with a total of twelve or fewer inputs and outputs. The discovered algorithms produce the correct results for evaluating the five selected logical and arithmetic functions.