Abstract
Hybrid quantum-classical algorithms provide ways to use noisy intermediate-scale quantum computers for practical applications. Expanding the portfolio of such techniques, we propose a quantum circuit learning algorithm that can be used to assist the characterization of quantum devices and to train shallow circuits for generative tasks. The procedure leverages quantum hardware capabilities to its fullest extent by using native gates and their qubit connectivity. We demonstrate that our approach can learn an optimal preparation of the Greenberger-Horne-Zeilinger states, also known as “cat states”. We further demonstrate that our approach can efficiently prepare approximate representations of coherent thermal states, wave functions that encode Boltzmann probabilities in their amplitudes. Finally, complementing proposals to characterize the power or usefulness of near-term quantum devices, such as IBM’s quantum volume, we provide a new hardware-independent metric called the qBAS score. It is based on the performance yield in a specific sampling task on one of the canonical machine learning data sets known as Bars and Stripes. We show how entanglement is a key ingredient in encoding the patterns of this data set; an ideal benchmark for testing hardware starting at four qubits and up. We provide experimental results and evaluation of this metric to probe the trade off between several architectural circuit designs and circuit depths on an ion-trap quantum computer.
Highlights
What is a good metric for the computational power of noisy intermediate-scale quantum[1] (NISQ) devices? Can machine learning (ML) provide ways to benchmark the power and usefulness of NISQ devices? How can we capture the performance scaling of these devices as a function of circuit depth, gate fidelity, and qubit connectivity? In this work, we design a hybrid quantum-classical framework called data-driven quantum circuit learning (DDQCL) and address these questions through simulations and experiments
Other successful hybrid approaches based on genetic algorithms were proposed for approximating quantum adders and training quantum autoencoders.[11,12,13]
We note that one of the quantum representations of Bars and stripes (BAS)(2, 2) found by DDQCL reached a remarkable value of SBAS(2,2) = 1.69989. This shows the power of our framework, in that DDQCL is capable of handling useful quantum states that are rich in entanglement. This is an important observation, since we know, based on our empirical results, that (i) single layer circuits with no entangling gates severely underperform in producing the output state probability distribution that is close to the target data set, and (ii) when inspecting the parameters learned for circuits with all-to-all topology with L = 2 layers, we found that most of the XX gates reached their maximum entangling setting
Summary
We present a hybrid quantum-classical algorithm for the unsupervised machine learning task of approximating an unknown probability distribution from data This task is known as generative modeling. This is true when measurements yield distributions such that Pθ(x(d)) = 0 for any of the x(d) in BAS(n, m) In all these cases, the qBAS score can still be computed and the number of measurequbit-to-qubit connectivity and native set of single and two-qubit ments Nreads necessary for obtaining a robust estimate continues gates. The qBAS score can still be computed and the number of measurequbit-to-qubit connectivity and native set of single and two-qubit ments Nreads necessary for obtaining a robust estimate continues gates It takes classical resources such as the choice of cost to remain relatively small to be practical for intermediate size function, optimizer, and hyper-parameters, into account. The F1 score is a useful measure for the quality of information retrieval and classification algorithms, but for our purposes it has a caveat: the dependence of r on the total number of measure-
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