Efficient Quantum-enabled Monte Carlo sampling for training neural network quantum states

Neural-network quantum states have proven in the past to be a viable alternative to traditional variational ansatz for representing quantum data in a wide variety of tasks. A particularly promising candidate are energy-based models like Hopfield networks and Restricted Boltzmann Machines [1–3] which combines statistical physical insight to represent accessible states on an energy landscape thereby forming a descriptor for associative memory. In this work, we show that arbitrary such energy based models can be trained using Monte Carlo techniques assisted by a quantum device. Unlike previous variants, this algorithm is linearly scaling in circuit width, circuit depth and measurement counts leading to optimal efficiency. We show compared to other classical variants, sampling from a quantum device is efficient in terms of lowered convergence time of the underlying Markov Chain. We exemplify the protocol to learn ground states of not only local spin models in quantum magnetism but also on non-local electronic structure hamiltonians even in the limit of strong multi-reference correlation. Results so obtained are benchmarked against other standard techniques and are found to be in reasonable agreement. This highlights the versatility of our method, employing only noisy near-term devices, for accurately learning quantum states in a wide variety of quantum systems - a task central to applications in theoretical chemistry and condensed matter physics.

References

(1) Sajjan, M.; Sureshbabu, S. H.; Kais, S. Quantum machine-learning for eigenstate filtration in two-dimensional materials. Journal of the American Chemical Society 2021, 143, 18426–18445.

(2) Sajjan, M.; Singh, V.; Selvarajan, R.; Kais, S. Imaginary components of out-of-time order correlator and information scrambling for navigating the learning landscape of a quantum machine learning model. Physical Review Research 2023, 5, 013146.

(3) Sajjan, M.; Alaeian, H.; Kais, S. Magnetic phases of spatially modulated spin-1 chains in Rydberg excitons: Classical and quantum simulations. The Journal of Chemical Physics, 2022, 157.