Machine Learning for Quantum Design

Various optimization problems that arise naturally in science are frequently solved by heuristic algorithms. Recently, multiple quantum enhanced algorithms have been proposed to speed up the optimization process, however a quantum speed up on practical problems has yet to be observed. One of the most promising candidates is the Quantum Approximate Optimization Algorithm (QAOA), introduced by Farhi et al. I will then discuss numerical and exact results we have obtained for the quantum Ising chain problem and compare the performance of the QAOA and the Quantum Annealing algorithm. I will also briefly describe the landscape that emerges from the optimization problem and how techniques borrowed from machine learning can be used to improve the optimization process.

In the first half, I will demonstrate an efficient and general approach for realizing non-trivial quantum states, such as quantum critical and topologically ordered states, in quantum simulators. In the second half, I will present a related variational ansatz for many-body quantum systems that is remarkably efficient. In particular, representing the critical point of the one-dimensional transverse field Ising model only requires a number of variational parameters scaling logarithmically with system size. Though optimizing the ansatz generally requires Monte Carlo sampling, our ansatz potentially enables a partial mitigation of the sign problem at the expense of having to optimize a few parameters.

Quantum anomalies are violations of classical scaling symmetries caused by quantum fluctuations. Although they appear prominently in quantum field theory to regularize divergent physical quanti- ties, their influence on experimental observables is difficult to discern. Here, we discovered a striking manifestation of a quantum anomaly in the momentum-space dynamics of a 2D Fermi superfluid of ultracold atoms. We measured the position and pair momentum distribution of the superfluid during a breathing mode cycle for different interaction strengths across the BEC-BCS crossover. Whereas the system exhibits self-similar evolution in the weakly interacting BEC and BCS limits, we found a violation in the strongly interacting regime. The signature of scale-invariance breaking is enhanced in the first-order coherence function. In particular, the power-law exponents that char- acterize long-range phase correlations in the system are modified due to this effect, indicating that the quantum anomaly has a significant influence on the critical properties of 2D superfluids.

Computer simulations are extremely useful in providing insight on the physical and chemical processes taking places in nature. Very often simulations are complementary to experimental investigations, providing the interpretations and the molecular level understanding that experiments struggle to deliver. Yet, simulations are useful only when their results may be relied upon, that is, when they can accurately model the physical system and the forces therein. Thriving nanotechnologies and exciting experiments pose a big challenge to computational approaches, especially when dealing with solid-liquid interfaces. On the one hand, the systems to be simulated are large and often long molecular dynamics simulations are needed. On the other hand, extremely high accuracy is required. We discuss here an approach to deliver high accuracy at low computational cost using quantum Monte Carlo and Machine Learning.

Variational algorithms for a gate-based quantum computer, like the QAOA, prescribe a fixed circuit ansatz --- up to a set of continuous parameters --- that is designed to find a low-energy state of a given target Hamiltonian. After reviewing the relevant aspects of the QAOA, I will describe attempts to make the algorithm more efficient. The strategies I will explore are 1) tuning the variational objective function away from the energy expectation value, 2) analytical estimates that allow elimination of some of the gates in the QAOA circuit, and 3) using methods of machine learning to search the design space of nearby circuits for improvements to the original ansatz. While there is evidence of room for improvement in the circuit ansatz, finding an ML algorithm to effect that improvement remains an outstanding challenge.

High-dimensional quantum systems are vital for quantum technologies and are essential in demonstrating practical quantum advantage in quantum computing, simulation and sensing. Since dimensionality grows exponentially with the number of qubits, the potential power of noisy intermediate-scale quantum (NISQ) devices over classical resources also stems from entangled states in high dimensions. An important family of quantum protocols that can take advantage of high-dimensional Hilbert space are classification tasks. These include quantum machine learning algorithms, witnesses in quantum information processing and certain decision problems. However, due to counter-intuitive geometrical properties emergent in high dimensions, classification problems are vulnerable to adversarial attacks. We demonstrate that the amount of perturbation needed for an adversary to induce a misclassification scales inversely with dimensionality. This is shown to be a fundamental feature independent of the details of the classification protocol. Furthermore, this leads to a trade-off between the security of the classification algorithm against adversarial attacks and quantum advantages we expect for high-dimensional problems. In fact, protection against these adversarial attacks require extra resources that scale at least polynomially with the Hilbert space dimension of the system, which can erase any significant quantum advantage that we might expect from a quantum protocol. This has wide-ranging implications in the use of both near-term and future quantum technologies for classification.

Prospective near-term applications of early quantum devices rely on accurate estimates of expectation values to become relevant. Decoherence and gate errors lead to wrong estimates. This problem was, at least in theory, remedied with the advent of quantum error correction. However, the overhead that is needed to implement a fully fault-tolerant gate set with current codes and current devices seems prohibitively large. In turn, steady progress is made in improving the quality of the quantum hardware, which leads to the believe that in the foreseeable future machines could be build that cannot be emulated by a conventional computer. In light of recent progress mitigating the effect of decoherence on expectation values, it becomes interesting to ask what these noisy devices can be used for. In this talk we will present our advances in finding quantum machine learning applications for noisy quantum computers.

In the first part of this presentation, I will present supervised machine-learning studies of the low-lying energy levels of disordered quantum systems. We address single-particle continuous-space models that describe cold-atoms in speckle disorder, and also 1D quantum Ising glasses. Our results show that a sufficiently deep feed-forward neural network (NN) can be trained to accurately predict low-lying energy levels. Considering the long-term prospect of using cold-atoms quantum simulator to train neural networks to solve computationally intractable problems, we consider the effect of random noise in the training data, finding that the NN model is remarkably resilient. We explore the use of convolutional NN to build scalable models and to accelerate the training process via transfer learning. In the second part, I will discuss how generative stochastic NN, specifically, restricted and unrestricted Boltzmann machines, can be used as variational Ansatz for the ground-state many-body wave functions. In particular, we show how to employ them to boost the efficiency of projective quantum Monte Carlo (QMC) simulations, and how to automatically train them within the projective QMC simulation itself. SP, P. Pieri, Scientific Reports 9, 5613 (2019) E. M. Inack, G. Santoro, L. Dell’Anna, SP, Physical Review B 98, 235145 (2018)

Density functional theory is a widely used electronic structure method for simulating and designing nanoscale systems based on first principles. I will outline our recent efforts to improve density functionals using deep learning. Improvement would mean achieving higher accuracy, better scaling (with respect to system size), improved computational parallelizability, and achieving reliable performance transferability across different electronic environments. To this end, we have generated a large and diverse dataset of 2d simulations of electrons (http://clean.energyscience.ca/datasets) with a varying number of electrons in confining potentials for several (approximate) density functionals. As a proof-of-principal, we have used extensive deep neural networks to reproduce the results of these simulations to high accuracy at significantly reduced computational cost. By learning the screening length-scale of the electrons directly from the data, we are able to train on small-scale calculations, yet perform inference at effectively arbitrary length-scales at only O(N) cost. This overcomes a key-scaling limitation of Kohn-Sham DFT (which scales as O(N^3)), paving the way for accurate, large scale ab initio enabled design of nanoscale components and devices.

For the past decade, there has been a new major architectural fad in deep learning every year or two. One such fad for the past two years has been the transformer model, an implementation of the attention method which has superseded RNNs in most sequence learning applications. I'll give an overview of the model, with some discussion of non-physics applications, and intimate some possibilities for physics.

Inspired by the "third wave" of artificial intelligence (AI), machine learning has found rapid applications in various topics of physics research. Perhaps one of the most ambitious goals of machine learning physics is to develop novel approaches that ultimately allows AI to discover new concepts and governing equations of physics from experimental observations. In this talk, I will present our progress in applying machine learning technique to reveal the quantum wave function of Bose-Einstein condensate (BEC) and the holographic geometry of conformal field theories. In the first part, we apply machine translation to learn the mapping between potential and density profiles of BEC and show how the concept of quantum wave function can emerge in the latent space of the translator and how the Schrodinger equation is formulated as a recurrent neural network. In the second part, we design a generative model to learn the field theory configuration of the XY model and show how the machine can identify the holographic bulk degrees of freedom and use them to probe the emergent holographic geometry.

Site resolution in quantum gas microscopes for ultracold atoms in optical lattices have transformed quantum simulations of many-body Hamiltonians. Statistical analysis of atomic snapshots can produce expectation values for various charge and spin correlation functions and have led to new discoveries for the Hubbard model in two dimensions. Conventional approaches, however, fail in general when the order parameter is not known or when an expected phase has no clear signatures in the density basis. In this talk, I will introduce our efforts in using machine learning techniques to overcome this challenge with snapshots of fermionic atoms. Collaborators: Richard Scalettar (UC Davis), Waseem Bakr (Princeton), and Juan Carrasquilla (Vector Institute)