Annual review of condensed matter physics

Classical machine learning (ML) provides a potentially powerful approach to solving challenging quantum many-body problems in physics and chemistry. However, the advantages of ML over traditional methods have not been firmly established. In this work, we prove that classical ML algorithms can efficiently predict ground-state properties of gapped Hamiltonians after learning from other Hamiltonians in the same quantum phase of matter. By contrast, under a widely accepted conjecture, classical algorithms that do not learn from data cannot achieve the same guarantee. We also prove that classical ML algorithms can efficiently classify a wide range of quantum phases. Extensive numerical experiments corroborate our theoretical results in a variety of scenarios, including Rydberg atom systems, two-dimensional random Heisenberg models, symmetry-protected topological phases, and topologically ordered phases. 

/pdf/provably-efficient-machine-learning-for-quantum-many-body-1gxa5z2e.pdf

Provably efficient machine learning for quantum many-body problems

The future development of quantum technologies relies on creating and manipulating quantum systems of increasing complexity, with key applications in computation, simulation and sensing. This poses severe challenges in the efficient control, calibration and validation of quantum states and their dynamics. Although the full simulation of large-scale quantum systems may only be possible on a quantum computer, classical characterization and optimization methods still play an important role. Here, we review different approaches that use classical post-processing techniques, possibly combined with adaptive optimization, to learn quantum systems, their correlation properties, dynamics and interaction with the environment. We discuss theoretical proposals and successful implementations across different multiple-qubit architectures such as spin qubits, trapped ions, photonic and atomic systems, and superconducting circuits. This Review provides a brief background of key concepts recurring across many of these approaches with special emphasis on the Bayesian formalism and neural networks. Although the complexity of quantum systems scales exponentially with their size, classical algorithms and optimization strategies can still play an important role in the characterization of quantum states, their dynamics and the detection process. 

/pdf/learning-quantum-systems-2tbhywdt.pdf

Learning quantum systems

Classical machine learning (ML) provides a potentially powerful approach to solving challenging quantum many-body problems in physics and chemistry. However, the advantages of ML over more traditional methods have not been firmly established. In this work, we prove that classical ML algorithms can efficiently predict ground state properties of gapped Hamiltonians in finite spatial dimensions, after learning from data obtained by measuring other Hamiltonians in the same quantum phase of matter. In contrast, under widely accepted complexity theory assumptions, classical algorithms that do not learn from data cannot achieve the same guarantee. We also prove that classical ML algorithms can efficiently classify a wide range of quantum phases of matter. Our arguments are based on the concept of a classical shadow, a succinct classical description of a many-body quantum state that can be constructed in feasible quantum experiments and be used to predict many properties of the state. Extensive numerical experiments corroborate our theoretical results in a variety of scenarios, including Rydberg atom systems, 2D random Heisenberg models, symmetry-protected topological phases, and topologically ordered phases.

Provably efficient machine learning for quantum many-body problems.

Performing electronic structure calculations is a canonical many-body problem that has recently emerged as a challenging new paradigm for neural network quantum states (NNQS). Here, we parameterise the electronic wavefunction with a novel autoregressive neural network (ARN) that permits highly efficient and scalable sampling, whilst also embedding physical priors that reflect the structure of molecular systems without sacrificing expressibility. This allows us to perform electronic structure calculations on molecules with up to 30 spin-orbitals - which consider multiple orders of magnitude more Slater determinants than previous applications of conventional NNQS - and we find that our ansatz can outperform the de-facto gold-standard coupled cluster methods even in the presence of strong quantum correlations. With a highly expressive neural network for which sampling is no longer a computational bottleneck, we conclude that the barriers to further scaling are not associated with the wavefunction ansatz itself, but rather are inherent to any variational Monte Carlo approach.

Autoregressive neural-network wavefunctions for ab initio quantum chemistry.

Generative models are a promising technology for the enhancement of quantum simulators. These machine learning methods are capable of reconstructing a quantum state from experimental measurements, and can aid in the calculation of physical observables. In this paper, we employ a recurrent neural network (RNN) to reconstruct the ground state of the spin-1/2 $XY$ model, a prototypical Hamiltonian explored in trapped ion simulators. We explore its performance after enforcing a U(1) symmetry, which was recently shown by Hibat-Allah et al. [Phys. Rev. Res. 2, 023358 (2020)] to preserve the autoregressive nature of the RNN. By studying the reconstruction of the $XY$ model ground state from projective measurement data, we show that imposing U(1) symmetry on the RNN significantly increases the efficiency of learning, particularly in the early epoch regime. We argue that this performance increase may result from the tendency of the enforced symmetry to alleviate vanishing and exploding gradients, which helps stabilize the training process. Thus, symmetry-enforced RNNs may be particularly useful for applications of quantum simulators where a rapid feedback between optimization and circuit preparation is necessary, such as in hybrid classical-quantum algorithms.

U(1)-symmetric recurrent neural networks for quantum state reconstruction

Electroless nickel plating is an established industrial process that provides a robust and relatively low-cost coating suitable for transporting and storing ultracold neutrons (UCN). Using roughness measurements and UCN-storage experiments we characterized UCN guides made from polished aluminum or stainless-steel tubes plated by several vendors. All electroless nickel platings were similarly suited for UCN storage with an average loss probability per wall bounce of $2.8\cdot10^{-4}$ to $4.1\cdot10^{-4}$ for energies between 90 neV and 190 neV, or a ratio of imaginary to real Fermi potential $\eta$ of $1.7\cdot10^{-4}$ to $3.3\cdot10^{-4}$. Measurements at different elevations indicate that the energy dependence of UCN losses is well described by the imaginary Fermi potential. Some special considerations are required to avoid an increase in surface roughness during the plating process and hence a reduction in UCN transmission. Increased roughness had only a minor impact on storage properties. Based on these findings we chose a vendor to plate the UCN-production vessel that will contain the superfluid-helium converter for the new TRIUMF UltraCold Advanced Neutron (TUCAN) source, achieving acceptable UCN-storage properties with ${\eta=3.5(5)\cdot10^{-4}}$. 

/pdf/characterization-of-electroless-nickel-phosphorus-plating-2782q3xt.pdf

Characterization of electroless nickel-phosphorus plating for ultracold-neutron storage

Artificial neural networks have been widely adopted as ansatzes to study classical and quantum systems. However, for some notably hard systems, such as those exhibiting glassiness and frustration, they have mainly achieved unsatisfactory results, despite their representational power and entanglement content, thus suggesting a potential conservation of computational complexity in the learning process. We explore this possibility by implementing the neural annealing method with autoregressive neural networks on a model that exhibits glassy and fractal dynamics: the two-dimensional Newman–Moore model on a triangular lattice. We find that the annealing dynamics is globally unstable because of highly chaotic loss landscapes. Furthermore, even when the correct ground-state energy is found, the neural network generally cannot find degenerate ground-state configurations due to mode collapse. These findings indicate that the glassy dynamics exhibited by the Newman–Moore model caused by the presence of fracton excitations in the configurational space likely manifests itself through trainability issues and mode collapse in the optimization landscape.

/pdf/neural-annealing-and-visualization-of-autoregressive-neural-1vprnpin.pdf

Neural Annealing and Visualization of Autoregressive Neural Networks in the Newman–Moore Model

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U(1)-symmetric recurrent neural networks for quantum state reconstruction

Characterization of electroless nickel-phosphorus plating for ultracold-neutron storage

Neural Annealing and Visualization of Autoregressive Neural Networks in the Newman–Moore Model