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Entropy

Adaptive Problem Solving Dynamics in Gate-Model Quantum Computers

László Gyöngyösi

Published Aug 26, 2022• 11 citations
Publisher

Abstract

Gate-model quantum computer architectures represent an implementable model used to realize quantum computations. The mathematical description of the dynamical attributes of adaptive problem solving and iterative objective function evaluation in a gate-model quantum computer is currently a challenge. Here, a mathematical model of adaptive problem solving dynamics in a gate-model quantum computer is defined. We characterize a canonical equation of adaptive objective function evaluation of computational problems. We study the stability of adaptive problem solving in gate-model quantum computers.

DOI
10.3390/e24091196

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Gate-model quantum computer architectures represent an implementable model used to realize quantum computations. The mathematical description of the dynamical attributes of adaptive problem solving and iterative objective function evaluation in a gate-model quantum computer is currently a challenge. Here, a mathematical model of adaptive problem solving dynamics in a gate-model quantum computer is defined. We characterize a canonical equation of adaptive objective function evaluation of computational problems. We study the stability of adaptive problem solving in gate-model quantum computers.
Quantum computers provide a valuable resource to solve computational problems. The maximization of the objective function of a computational problem is a crucial problem in gate-model quantum computers. The objective function estimation is a high-cost procedure that requires several rounds of quantum computations and measurements. Here, we define a method for objective function estimation of arbitrary computational problems in gate-model quantum computers. The proposed solution significantly reduces the costs of the objective function estimation and provides an optimized estimate of the state of the quantum computer for solving optimization problems.
A computational problem fed into a gate-model quantum computer identifies an objective function with a particular computational pathway (objective function connectivity). The solution of the computational problem involves identifying a target objective function value that is the subject to be reached. A bottleneck in a gate-model quantum computer is the requirement of several rounds of quantum state preparations, high-cost run sequences, and multiple rounds of measurements to determine a target (optimal) state of the quantum computer that achieves the target objective function value. Here, we define a method for optimal quantum state determination and computational path evaluation for gate-model quantum computers. We prove a state determination method that finds a target system state for a quantum computer at a given target objective function value. The computational pathway evaluation procedure sets the connectivity of the objective function in the target system state on a fixed hardware architecture of the quantum computer. The proposed solution evolves the target system state without requiring the preparation of intermediate states between the initial and target states of the quantum computer. Our method avoids high-cost system state preparations and expensive running procedures and measurement apparatuses in gate-model quantum computers. The results are convenient for gate-model quantum computations and the near-term quantum devices of the quantum Internet.
Gate-model quantum computers can allow quantum computations in near-term implementations. The stabilization of an optimal quantum state of a quantum computer is a challenge, since it requires stable quantum evolutions via a precise calibration of the unitaries. Here, we propose a method for the stabilization of an optimal quantum state of a quantum computer through an arbitrary number of running sequences. The optimal state of the quantum computer is set to maximize an objective function of an arbitrary problem fed into the quantum computer. We also propose a procedure to classify the stabilized quantum states of the quantum computer into stability classes. The results are convenient for gate-model quantum computations and near-term quantum computers.
Quantum computing holds immense promise for revolutionizing various fields, from drug discovery to materials science. However, current quantum computing architectures face significant challenges related to qubit coherence, gate fidelity, and scalability. This paper introduces a novel quantum computing protocol, termed "Adaptive Quantum State Protocols," that dynamically adjusts the quantum state of qubits to mitigate these challenges, aiming to significantly improve the efficiency and stability of quantum computations. The core of this protocol involves a sophisticated feedback mechanism that leverages continuous state evolution to optimize qubit parameters and minimize decoherence. We explore the design of a robust and adaptable framework for implementing this protocol, demonstrating its potential to overcome current limitations of quantum computing. The proposed method offers a fundamentally new approach to managing quantum states, ultimately paving the way for more practical and reliable quantum technologies.
A technique for simulating quantum dynamics in phase space i discussed. It makes use of ensembles of classical trajectories to approximate the distribution functions and their derivatives by implementing Adaptive Kernel Density Estimation. It is found to improve the accuracy and stability of the simulations compared to more conventional particle methods. Formulation of the method in higher dimensions is straightforward. Complete analytical description of physical systems exist only for the most simple ideal cases. The vast majority of physical problems require the solution of approximate equations most fre- quently by using numerical calculations. To this end, much effort has been devoted to the devel- opment of suitable techniques to be used in computer simulations. The increasing computational power makes possible the description of more complicated, that is, less ideal systems allowing for more precise predictions of their properties as well as for a better understanding of the underlying phenomena. Among the wealth of numerical approaches to solve dynamical equations by means of discretization, particle methods have gained attention in the last few decades as a conceptu- ally appealing alternative. Conventional numerical solvers rely on a regular discretization of the independent variables to facilitate the evaluation of derivatives to a given order of accuracy. As a consequence, a mesh needs to be defined as the base of the simulations, parts of which remain empty at any given simulation time even with the most sophisticated mesh schemes. The cen- tral idea of particle methods consists of representing functions by sets of particles conveniently located and weighted such that the function is appropriately sampled by the particles. Evolution of the functions is then accomplished by an equivalent evolution of the particles. This meshless or Lagrangian type of discretization has some intrinsic computational efficiency advantages because there is no wasted space. The advantage, however, comes at the expense of having to evaluate derivatives of functions on unstructured arrays of sampling points. The issues about convergence and stability of the resulting algorithms have been the subject of active and fruitfull research. Currently there are some well established techniques to solve dynamical equations with particle methods. Our interest is to provide an alternative ingredient to further improve the performance of numerical solutions of dynamical problems of physical relevance. In the present work we discuss, in the context of particle methods, the implementation of a technique for representing functions and derivatives with adaptive parameters. Adaptiveness require the parameters to be automatically ad- justed to optimal values according to the location of the particles. As shown below, the proposed scheme is conceptually simple and has been tested in a number of different situations. In some simple test models the present work focuses on quantum dynamics, previously treated with more
Quantum computing promises revolutionary advancements in computation, offering the potential to solve problems intractable for classical computers. However, realizing this potential requires overcoming significant challenges, particularly in the design and optimization of quantum circuits. This paper proposes a novel optimization algorithm, Adaptive Quantum Potential Optimization via Adaptive Neural Networks (AQPO-AN), which leverages the power of adaptive neural networks to dynamically adjust the quantum potential landscape, thereby enhancing the fidelity and efficiency of quantum computations. We demonstrate the effectiveness of AQPO-AN through rigorous analysis and experimental validation on several benchmark quantum algorithms. The core mechanism centers around employing a dynamically parameterized neural network to refine the quantum potential through a series of iterative adjustments based on the quantum state. We analyze the algorithm's convergence properties and show its superior performance compared to existing optimization techniques. The paper concludes with a detailed discussion of the algorithm's architecture, the rationale behind the adaptive neural network design, and future directions for research.