Error mitigation for generative models deployed on noisy intermediate-scale quantum (NISQ) devices

Generative modeling is a method for learning arbitrary distributions. A promising generative model scheme involves the use of a quantum circuit Born machine (QCBM) ¹. This model involves a classical optimizer to perform gradient-based training of QCBM, which utilizes the hardware efficient ansatz to encode the probability distribution in the QCBM’s quantum state. In this work we model the 2x2 BAS dataset on IBM’s superconducting quantum computer, accessed via cloud interface. We map the generative model ansatz circuit directly to the IBM hardware. After training the circuits on a noiseless simulator for 100 steps of ADAM, the Kullback Leiber (KL) divergence and a metric known as the qBAS score, introduced by Benedetti et al.², were used to determine how well the QCBM modeled the distribution. Using the results of these metrics, and assuming a uniform error rate for two qubit gates, we used the error extrapolation method of Li and Benjamin³ to estimate the distribution encoding ability of error-resilient QCBM schemes.

[1] Liu, J. et al. (2018) preprint arXiv:1804.04168v1

[2] Benedetti, M. et al. (2014). arXiv preprint arXiv:1801.07686

[3] Li, Y. and Benjamin, S. (2017). Physical Review X, 7(2)