Machine Learning for Quantum Design

As quantum processors become increasingly refined, benchmarking them in useful ways becomes a critical topic. Traditional approaches to quantum tomography, such as state tomography, suffer from self-consistency problems, requiring either perfectly pre-calibrated operations or measurements. This problem has recently been tackled by explicitly self-consistent protocols such as randomized benchmarking, robust phase estimation, and gate set tomography (GST). An undesired side-effect of self-consistency is the presence of gauge degrees of freedom, arising from the lack fiducial reference frames, and leading to large families of gauge-equivalent descriptions of a quantum gate set which are difficult to interpret. We solve this problem through introducing a gauge-free representation of a quantum gate set inspired by linear inversion GST. This allows for the efficient computation of any experimental frequency without a gauge fixing procedure. We use this approach to implement a Bayesian version of GST using the particle filter approach, which was previously not possible due to the gauge. Within Bayesian GST, the prior information allows for inference on tomographically incomplete data sets, such as Ramsey experiments, without giving up self-consistency. We demonstrate the stability and generality of both our gauge-free representation and Bayesian GST by simulating a number of common characterization protocols, such as randomized benchmarking, as well characterizing a trapped-ion qubit using experimental data. Sandia National Labs is managed and operated by National Technology and Engineering Solutions of Sandia, LLC, a subsidiary of Honeywell International, Inc., for the U.S. Dept. of Energy’s National Nuclear Security Administration under contract DE-NA0003525. The views expressed in this presentation do not necessarily represent the views of the DOE, the ODNI, or the U.S. Government. This material was funded in part by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research Quantum Testbed Program. Olivia Di Matteo, TRIUMF, Vancouver, BC, Canada and Microsoft Research, Redmond, WA, USA John Gamble, Microsoft Research, Redmond, WA, USA Chris Granada, Microsoft Research, Redmond, WA, USA Kenneth Ruddinger, Quantum Performance Laboratory, Sandia National Laboratories, Albuquerque, NM, USA Nathan Wiebe, Microsoft Research, Redmond, WA, USA

Belief-propagation (BP) decoders are responsible for the success of many modern coding schemes. While many classical coding schemes have been generalized to the quantum setting, the corresponding BP decoders are flawed by design in this setting. Inspired by an exact mapping between BP and deep neural networks, we train neural BP decoders for quantum low-density parity-check codes, with a loss function tailored for the quantum setting. Training substantially improves the performance of the original BP decoders. The flexibility and adaptability of the neural BP decoders make them suitable for low-overhead error correction in near-term quantum devices. Reference: arXiv:1811.07835 (to appear in PRL)

Modern Machine Learning (ML) relies on cost function optimization to train model parameters. The non-convexity of cost function landscapes results in the emergence of local minima in which state-of-the-art gradient descent optimizers get stuck. Similarly, in modern Quantum Control (QC), a key to understanding the difficulty of multiqubit state preparation holds the control landscape -- the mapping assigning to every control protocol its cost function value. Reinforcement Learning (RL) and QC strive to find a better local minimum of the control landscape; the global minimum corresponds to the optimal protocol. Analyzing a decrease in the learning capability of our RL agent as we vary the protocol duration, we found rapid changes in the search for optimal protocols, reminiscent of phase transitions. These "control phase transitions" can be interpreted within Statistical Mechanics by viewing the cost function as "energy" and control protocols – as "spin configurations". I will show that optimal qubit control exhibits continuous and discontinuous phase transitions familiar from macroscopic systems: correlated/glassy phases and spontaneous symmetry breaking. I will then present numerical evidence for a universal spin-glass-like transition controlled by the protocol time duration. The glassy critical point is marked by a proliferation of protocols with close-to-optimal fidelity and with a true optimum that appears exponentially difficult to locate. Using a ML inspired framework based on the manifold learning algorithm t-SNE, we visualize the geometry of the high-dimensional control landscape in an effective low-dimensional representation. Across the transition, the control landscape features an exponential number of clusters separated by extensive barriers, which bears a strong resemblance with random satisfiability problems.

Differentiable programming makes the optimization of a tensor network much cheaper (in unit of brain energy consumption) than before [e.g. arXiv: 1903.09650]. This talk mainly focuses on the technical aspects of differentiable programming tensor networks and quantum circuits with Yao.jl (https://github.com/QuantumBFS/Yao.jl). I will also show how quantum circuits can help with contracting and differentiating tensor networks.