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Experimental pairwise entanglement estimation for an N-qubit system

Elizabeth Behrman, Nathan Thompson, Nam Nguyen, James E. Steck

Published Dec 27, 2019• 0 citations
Publisher

Abstract

Designing and implementing algorithms 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 algorithm design difficulty. This works quite well for small systems. But the goal is macroscopic physical computation. Here, we implement our learned pairwise entanglement witness on Microsoft’s Q\#, one of the commercially available gate model quantum computer simulators; we perform statistical analysis to determine reliability and reproducibility; and we show that after training the system in stages for an incrementing number of qubits (2, 3, 4, \ldots) we can infer the pattern for mesoscopic $N$ from simulation results for three-, four-, five-, six-, and seven-qubit systems. Our results suggest a fruitful pathway for general quantum computer algorithm design and for practical computation on noisy intermediate scale quantum devices.

DOI
10.36227/techrxiv.11398401.v1

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Designing and implementing algorithms 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 algorithm design difficulty. This works quite well for small systems. But the goal is macroscopic physical computation. Here, we implement our learned pairwise entanglement witness on Microsoft's Q\#, one of the commercially available gate model quantum computer simulators; we perform statistical analysis to determine reliability and reproducibility; and we show that after training the system in stages for an incrementing number of qubits (2, 3, 4, \ldots) we can infer the pattern for mesoscopic NNN from simulation results for three-, four-, five-, six-, and seven-qubit systems. Our results suggest a fruitful pathway for general quantum computer algorithm design and for practical computation on noisy intermediate scale quantum devices.
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.
Major obstacles remain to the implementation of macroscopic quantum computing: hardware problems of noise, decoherence, and scaling; software problems of error correction; and, most important, algorithm construction. Finding truly quantum algorithms is quite difficult, and many of these genuine quantum algorithms, like Shor's prime factoring or phase estimation, require extremely long circuit depth for any practical application, which necessitates error correction. In contrast, we show that machine learning can be used as a systematic method to construct algorithms, that is, to non-algorithmically “program” quantum computers. Quantum machine learning enables us to perform computations without breaking down an algorithm into its gate “building blocks”, eliminating that difficult step and potentially increasing efficiency by simplifying and reducing unnecessary complexity. In addition, our non-algorithmic machine learning approach is robust to both noise and to decoherence, which is ideal for running on inherently noisy NISQ devices which are limited in the number of qubits available for error correction. We demonstrate this using a fundamentally nonclassical calculation: experimentally estimating the entanglement of an unknown quantum state. Results from this have been successfully ported to the IBM hardware and trained using a hybrid reinforcement learning method.
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.
Learning compressed, latent representations of quantum states can help us understand and simulate the natural world. To this end, one needs devices that can capture and reliably process information using quantum-mechanical effects. Whilst we currently lack a device that can achieve this goal, we are well into the era of noisy, intermediate-scale quantum (NISQ) computers—quantum machines with 50−10050{-}10050−100 noisy qubits—which have catalysed machine learning applications. This chapter provides the main ideas underpinning learning with NISQ machines. It also provides insight into the architectures and training schemes currently in use, as well as the limitations and potential futures of the field.