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arXiv:0708.1498

Optimizing Optical Quantum Logic Gates using Genetic Algorithms

Zhanghan Wu, Sean D. Huver, Dmitry B. Uskov, Hwang Lee, Jonathan P. Dowling

Published Aug 10, 2007• 0 citations
arXivHTMLPDF

Abstract

We introduce the method of using an annealing genetic algorithm to the numerically complex problem of looking for quantum logic gates which simultaneously have highest fidelity and highest success probability. We first use the linear optical quantum nonlinear sign (NS) gate as an example to illustrate the efficiency of this method. We show that by appropriately choosing the annealing parameters, we can reach the theoretical maximum success probability (1/4 for NS) for each attempt. We then examine the controlled-z (CZ) gate as the first new problem to be solved. We show results that agree with the highest known maximum success probability for a CZ gate (2/27) while maintaining a fidelity of 0.9997. Since the purpose of our algorithm is to optimize a unitary matrix for quantum transformations, it could easily be applied to other areas of interest such as quantum optics and quantum sensors.

DOI
10.48550/arxiv.0708.1498

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We introduce the method of using an annealing genetic algorithm to the numerically complex problem of looking for quantum logic gates which simultaneously have highest fidelity and highest success probability. We first use the linear optical quantum nonlinear sign (NS) gate as an example to illustrate the efficiency of this method. We show that by appropriately choosing the annealing parameters, we can reach the theoretical maximum success probability (1/4 for NS) for each attempt. We then examine the controlled-z (CZ) gate as the first new problem to be solved. We show results that agree with the highest known maximum success probability for a CZ gate (2/27) while maintaining a fidelity of 0.9997. Since the purpose of our algorithm is to optimize a unitary matrix for quantum transformations, it could easily be applied to other areas of interest such as quantum optics and quantum sensors.
Numerical optimization is used to design linear-optical devices that implement a desired quantum gate with perfect fidelity, while maximizing the success rate. For the two-qubit controlled-sign [or controlled NOT (CNOT)] gate, we provide numerical evidence that the maximum success rate is S=2/27S=2/27S=2/27 using two unentangled ancilla resources; interestingly, additional ancilla resources do not increase the success rate. For the three-qubit Toffoli gate, we show that perfect fidelity is obtained with only three unentangled ancilla photons---less than in any existing scheme---with a maximum S=0.003 40S=0.003\text{ }40S=0.003 40. This compares well to $S={(2/27)}^{2}/2\ensuremath{\approx}0.002\text{ }74$, obtainable by combining two CNOT gates and a passive quantum filter [T. C. Ralph, K. J. Resch, and A. Gilchrist, Phys. Rev. A 75, 022313 (2007)]. The general optimization approach can easily be applied to other areas of interest, such as quantum error correction, cryptography, and metrology [M. M. Wilde and D. B. Uskov, Phys. Rev. A 79, 022305 (2009); G. A. Durkin and J. P. Dowling, Phys. Rev. Lett. 99, 070801 (2007)].
We propose a genetic-algorithm-based method to find the unitary transformations for any desired quantum computation. We formulate a simple genetic algorithm by introducing the “genetic parameter vector” of the unitary transformations to be found. In the genetic algorithm process, all components of the genetic parameter vectors are supposed to evolve to the solution parameters of the unitary transformations. We apply our method to find the optimal unitary transformations and to generalize the corresponding quantum algorithms for a realistic problem, the one-bit oracle decision problem, or the often-called Deutsch problem. By numerical simulations, we can faithfully find the appropriate unitary transformations to solve the problem by using our method. We analyze the quantum algorithms identified by the found unitary transformations and generalize the variant models of the original Deutsch’s algorithm.
Recently it was realized that linear optics and photodetectors with feedback can be used for theoretically efficient quantum information processing. The first of three steps toward efficient linear optics quantum computation is to design a simple postselected gate that implements a nonlinear phase shift on one mode. Here a computational strategy is given for finding postselected gates for bosonic qubits with helper photons. A more efficient conditional sign flip gate is obtained. What is the maximum efficiency for such gates? This question is posed and it is shown that the probability of success cannot be 1.
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.
Reversible quantum logic synthesis is to study given quantum gates and quantum circuits of the constraints and limitations and find the smallest or smaller quantum cost to achieve the desired quantum logic circuits.The quantum logic gate functions of the matrix is indicated by the mathematical model. The synthesis and optimization are achieved simultaneously by the genetic algorithm as global search tool. Genetic algorithm is applied to quantum reversible logic synthesis.The fourth-order quantum circuit experiment has achieved good results,and further analysis of this method in high-level synthesis of quantum circuits and its application is completed.
The study of optimal control of quantum annealing by modulating the pace of evolution and by introducing a counterdiabatic potential has gained significant attention in recent times. In this work, we present a numerical approach based on genetic algorithms to improve the performance of quantum annealing, which evades the Landau-Zener transitions to navigate to the ground state of the final Hamiltonian with high probability. We optimize the annealing schedules starting from the polynomial ansatz by treating their coefficients as chromosomes of the genetic algorithm. We also explore shortcuts to adiabaticity by computing a practically feasible kkk-local optimal driving operator, showing that even for k=1k=1k=1 we achieve substantial improvement of the fidelity over the standard annealing solution. With these genetically optimized annealing schedules and/or optimal driving operators, we are able to perform quantum annealing in relatively short timescales and with higher fidelity compared to traditional approaches.