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Artificial intelligence for engineering design analysis and manufacturing

Machine invention of quantum computing circuits by means of genetic programming

Lee C. Spector, Jon Klein

Published Jun 12, 2008• 23 citations
Publisher

Abstract

Abstract We demonstrate the use of genetic programming in the automatic invention of quantum computing circuits that solve problems of potential theoretical and practical significance. We outline a developmental genetic programming scheme for such applications; in this scheme the evolved programs, when executed, build quantum circuits and the resulting quantum circuits are then tested for “fitness” using a quantum computer simulator. Using the PushGP genetic programming system and the QGAME quantum computer simulator we demonstrate the invention of a new, better than classical quantum circuit for the two-oracle AND/OR problem.

DOI
10.1017/s0890060408000188

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Abstract We demonstrate the use of genetic programming in the automatic invention of quantum computing circuits that solve problems of potential theoretical and practical significance. We outline a developmental genetic programming scheme for such applications; in this scheme the evolved programs, when executed, build quantum circuits and the resulting quantum circuits are then tested for “fitness” using a quantum computer simulator. Using the PushGP genetic programming system and the QGAME quantum computer simulator we demonstrate the invention of a new, better than classical quantum circuit for the two-oracle AND/OR problem.
Research in quantum technology has shown that quantum computers can provide dramatic advantages over classical computers for some problems. The efficiency of quantum computing is considered to become so significant that the study of quantum algorithms has attracted widespread interest. Development of quantum algorithms and circuits is difficult for a human researcher, so automatic induction of computer programs by means of genetic programming, which uses almost no auxiliary information on the search space, proved to be useful in generating new quantum algorithms. This approach takes advantage of the intrinsic parallelism of the genetic algorithm and quantum computing parallelism. The paper begins with a brief review on some basic concepts in genetic algorithms and quantum computation. Next, it describes an application of genetic programming for evolving quantum computing circuits.
Quantum computers are computational devices that use the dynamics of atomic-scale objects to store and manipulate information.Only a few, small-scale quantum computers have been built to date, but quantum computers can in principle outperform all possible classical computers in significant ways.Quantum computation is therefore a subject of considerable theoretical interest that may also have practical applications in the future.Genetic programming can automatically discover new algorithms for quantum computers [Spector et al., 1998].We describe how to simulate a quantum computer so that the fitness of a quantum algorithm can be determined on classical hardware.We then describe ways in which three different genetic programming approaches can drive the simulator to evolve new quantum algorithms.The approaches are standard tree-based genetic programming, stack-based linear genome genetic programming, and stackless linear genome genetic programming.We demonstrate the techniques on four different problems: the two-bit early promise problem, the scaling majority-on problem, the four-item database search problem, and the two-bit and-or problem.For three of these problems (all but majority-on) the automatically discovered algorithms are more efficient than any possible classical algorithms for the same problems.One of the better-than-classical algorithms (for the two-bit and-or problem) is in fact more efficient than any previously known quantum algorithm for the same problem, suggesting that genetic programming may be a valuable tool in the future study of quantum programming.
Research in quantum technology has shown that quantum computers can provide dramatic advantages over classical computers for some problems. The efficiency of quantum computing is considered to become so significant that the study of quantum algorithms has attracted widespread interest. Development of quantum algorithms and circuits is difficult for a human researcher, so automatic induction of computer programs by means of genetic programming, which uses almost no auxiliary information on the search space, proved to be useful in generating new quantum algorithms. This approach takes advantage of the intrinsic parallelism of the genetic algorithm and quantum computing parallelism. The paper begins with a brief review on some basic concepts in genetic algorithms and quantum computation. Next, it describes an application of genetic programming for evolving quantum computing circuits.
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.
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.
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.