Recently, the quantum computer (QC) using the nano‐devices have significantly attracted attention, because a large‐scale extention of the qubits could be easily realized in the nano‐devices. However, some problems for the realization of the QC with nano‐devices arise from the short decoherence time and the interaction of qubits only between nearest‐neighbor qubits. Therefore, we try to design the optimal quantum circuit of the quantum Fourier transform in various network system by means of the genetic algorithm (GA).
Recently, the quantum computer (QC) using the nano‐devices have significantly attracted attention, because a large‐scale extention of the qubits could be easily realized in the nano‐devices. However, some problems for the realization of the QC with nano‐devices arise from the short decoherence time and the interaction of qubits only between nearest‐neighbor qubits. Therefore, we try to design the optimal quantum circuit of the quantum Fourier transform in various network system by means of the genetic algorithm (GA).
Although quantum computing has made tremendous progress in last couple of years and technologies like NMR, Ion Trap, superconducting qubits have come out as promising platforms to implement quantum computing devices, such technologies are facing several design constraints. One such constraint is the Nearest Neighbor (NN) property, which demands the adjacency of logical qubits. Aiming to contribute to this cause, here we are proposing an improved design approach for transforming quantum circuits for NN-based architectures using genetic algorithms. In this work, our primary objective remains to form efficient NN structures by restricting the SWAP usage. In the design phase, initially, we use the k-means clustering scheme for partitioning the qubits into separate objects and, then, a genetic algorithm is applied that eventually fixes the order of qubits for each individual cluster. In the final phase, all these local solutions are combined and, again, a genetic algorithm is employed to obtain a global solution. We have tested our approach over a large spectrum of benchmarks and improvements are registered over some state-of-the-art design works.
Recently, researchers have applied genetic algorithms (GAs) to address some problems in quantum computation. Also, there has been some works in the designing of genetic algorithms based on quantum theoretical concepts and techniques. The so called Quantum Evolutionary Programming has two major sub-areas: Quantum Inspired Genetic Algorithms (QIGAs) and Quantum Genetic Algorithms (QGAs). The former adopts qubit chromosomes as representations and employs quantum gates for the search of the best solution. The later tries to solve a key question in this field: what GAs will look like as an implementation on quantum hardware? As we shall see, there is not a complete answer for this question. An important point for QGAs is to build a quantum algorithm that takes advantage of both the GA and quantum computing parallelism as well as true randomness provided by quantum computers. In the first part of this paper we present a survey of the main works in GAs plus quantum computing including also our works in this area. Henceforth, we review some basic concepts in quantum computation and GAs and emphasize their inherent parallelism. Next, we review the application of GAs for learning quantum operators and circuit design. Then, quantum evolutionary programming is considered. Finally, we present our current research in this field and some perspectives.
Quantum Computing represents the next big step towards speed boost in computation, which promises major breakthroughs in several disciplines including Artificial Intelligence. This paper investigates the performance of a genetic algorithm to optimize the realization (compilation) of nearest-neighbor compliant quantum circuits. Currrent technological limitations (e.g., decoherence effect) impose that the overall duration (makespan) of the quantum circuit realization be minimized, and therefore the makespanminimization problem of compiling quantum algorithms on present or future quantum machines is dragging increasing attention in the AI community. In our genetic algorithm, a solution is built utilizing a novel chromosome encoding where each gene controls the iterative selection of a quantum gate to be inserted in the solution, over a lexicographic double-key ranking returned by a heuristic function recently published in the literature.Our algorithm has been tested on a set of quantum circuit benchmark instances of increasing sizes available from the recent literature. We demonstrate that our genetic approach obtains very encouraging results that outperform the solutions obtained in previous research against the same benchmark, succeeding in significantly improving the makespan values for a great number of instances.
In many candidate designs of solid-state quantum computers, interactions between qubits are limited to a small number of neighboring qubits. Taking into account this limitation we describe how quantum algorithms can be executed efficiently on these designs. We illustrate our results with the quantum Fourier transform for which linear depth networks are obtained. The concepts presented in this work can be applied to all quantum algorithms to reduce considerably the coherence time needed for their execution.
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.
In the paper, we consider quantum circuits for the Quantum Fourier Transform (QFT) algorithm. The QFT algorithm is a very popular technique used in many quantum algorithms. We present a generic method for constructing quantum circuits for this algorithm implementing on quantum devices with restrictions. Many quantum devices (for example, based on superconductors) have restrictions on applying two-qubit gates. These restrictions are presented by a qubit connectivity graph. Typically, researchers consider only the linear nearest neighbor (LNN) architecture of the qubit connection, but current devices have more complex graphs. We present a method for arbitrary connected graphs that minimizes the number of CNOT gates in the circuit for implementing on such architecture. We compare quantum circuits built by our algorithm with existing quantum circuits optimized for specific graphs that are Linear-nearest-neighbor (LNN) architecture, ``sun'' (a cycle with tails, presented by the 16-qubit IBMQ device) and ``two joint suns'' (two joint cycles with tails, presented by the 27-qubit IBMQ device). Our generic method gives similar results with existing optimized circuits for ``sun'' and ``two joint suns'' architectures, and a circuit with slightly more CNOT gates for the LNN architecture. At the same time, our method allows us to construct a circuit for arbitrary connected graphs.