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arXiv:0808.1558 · Quantum Information and Computation

Quantum algorithm design using dynamic learning

Elizabeth Behrman, James E. Steck, Preethika Kumar, K. A. Walsh

Published Jan 1, 2008• 41 citations
arXivHTMLPDF

Abstract

We present a dynamic learning paradigm for ``programming'' a general quantum computer. A learning algorithm is used to find the control parameters for a coupled qubit system, such that the system at an initial time evolves to a state in which a given measurement corresponds to the desired operation. This can be thought of as a quantum neural network. We first apply the method to a system of two coupled superconducting quantum interference devices (SQUIDs), and demonstrate learning of both the classical gates XOR and XNOR. Training of the phase produces a gate similar to the CNOT. Striking out for somewhat more interesting territory, we attempt learning of an entanglement witness for a two qubit system. Simulation shows a reasonably successful mapping of the entanglement at the initial time onto the correlation function at the final time for both pure and mixed states. For pure states this mapping requires knowledge of the phase relation between the two parts; however, given that knowledge, this method can be used to measure the entanglement of an otherwise unknown state. The method is easily extended to multiple qubits or to quNits.

DOI
10.26421/qic8.1-2-2

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We present a dynamic learning paradigm for ``programming'' a general quantum computer. A learning algorithm is used to find the control parameters for a coupled qubit system, such that the system at an initial time evolves to a state in which a given measurement corresponds to the desired operation. This can be thought of as a quantum neural network. We first apply the method to a system of two coupled superconducting quantum interference devices (SQUIDs), and demonstrate learning of both the classical gates XOR and XNOR. Training of the phase produces a gate similar to the CNOT. Striking out for somewhat more interesting territory, we attempt learning of an entanglement witness for a two qubit system. Simulation shows a reasonably successful mapping of the entanglement at the initial time onto the correlation function at the final time for both pure and mixed states. For pure states this mapping requires knowledge of the phase relation between the two parts; however, given that knowledge, this method can be used to measure the entanglement of an otherwise unknown state. The method is easily extended to multiple qubits or to quNits.
We present a dynamic learning paradigm for "programming" a general quantum computer. A learning algorithm is used to find the control parameters for a coupled qubit system, such that the system at an initial time evolves to a state in which a given measurement corresponds to the desired operation. We apply the method to a system of coupled superconducting quantum interference devices (SQUIDs), and demonstrate learning of the XOR, XNOR, Toffoli, and Fredkin gates. Striking out for more interesting territory, we attempt learning of an entanglement witness for a two qubit system. Simulation shows a reasonably successful mapping of the entanglement at the initial time onto the correlation function at the final time for both pure and mixed states. For pure states this mapping requires knowledge of the phase relation between the parts; however, given that knowledge, this method can be used to measure the entanglement of an unknown state.
In previous work, we have developed a dynamic learning paradigm for "programming" a general quantum computer. A learning algorithm is used to find a set of parameters for a coupled qubit system such that the system at an initial time evolves to a state in which a given measurement results in the desired calculation value. This can be thought of as a quantum neural network (QNN). Here, we apply our method to a system of three qubits, and demonstrate training the quantum computer to estimate both pairwise and three-way entanglement.
In previous work, we have developed a dynamic learning paradigm for “programming” a general quantum computer. A learning algorithm is used to find a set of parameters for a coupled qubit system such that the system at an initial time evolves at the final time to a state in which a given measurement results in the desired calculation value. This can be thought of as a quantum neural network (QNN). Here, we apply our method to a system of three qubits, and demonstrate training the quantum computer to estimate both pairwise and three-way entanglement of the initial state.
Designing for medium and large scale quantum computers is not easy. In previous work we have suggested, and developed, the idea of using machine learning techniques to train a quantum system such that the desired process is learned, thus obviating the design difficulty. This works quite well. But it is also of interest to explore what exactly these learned algorithms are. Here, we take a step towards answering that question, by looking at a learned entanglement witness for a two-qubit system, and find its decomposition in terms of elementary quantum gates such as can be implemented on one of the commercially available gate model quantum computer simulators. The learned algorithm generalizes easily to three-, four-, five-, six-, and seven-qubit systems, and we infer a result for mesoscopic N. We successfully implement our witness on Microsoft's Q\#. Our results suggest a fruitful pathway for general quantum computer design.
Measurement of entanglement remains an important problem for quantum information. We present the design and simulation of an experimental method for an entanglement indicator for a general multiqubit state. The system can be in a pure or a mixed state, and it need not be ``close'' to any particular state. The system contains information about its own entanglement; we use dynamic learning methods to map this information onto a single experimental measurement which is our entanglement indicator. Our method does not require prior state reconstruction or lengthy optimization. An entanglement witness emerges from the learning process, beginning with two-qubit systems, and extrapolating this to three, four, and five qubit systems where the entanglement is not well understood. Our independently learned measures for three-qubit systems compare favorably with known entanglement measures. As the size of the system grows the amount of additional training necessary diminishes, raising hopes for applicability to large computational systems.
This paper investigates the potential of quantum machine learning to revolutionize the field of machine learning through adaptive learning algorithms. Traditional machine learning algorithms often rely on static parameter settings, limiting their adaptability and potentially hindering optimal performance. We propose a novel quantum learning framework that leverages quantum entanglement and quantum computation to dynamically adjust model parameters during the learning process, resulting in enhanced learning efficiency and generalization capabilities. The core mechanism centers around utilizing quantum entanglement to create a dynamic feedback loop that continuously refines the model's parameters based on its internal state. We present a detailed theoretical analysis and preliminary experimental validation demonstrating the effectiveness of this approach in a simplified learning scenario. The study explores the potential advantages of quantum-enhanced learning over classical methods.