Condensed Matter

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.

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.

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.

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.

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.

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.

Successful implementation of error correction is imperative for fault-tolerant quantum computing. At present, the toric code, surface code and related stabilizer codes are state of the art techniques in error correction. Standard decoders for these codes usually assume uncorrelated single qubit noise, which can prove problematic in a general setting. In this work, we use the knowledge of topological phases of modified toric codes to identify the underlying Hamiltonians for certain types of imperfections. The Hamiltonian learning is employed to adiabatically remove the underlying noise and approach the ideal toric code Hamiltonian. This approach can be used regardless of correlations. Our method relies on a neural network reconstructing the Hamiltonian given as input a linear amount of expectation values. The knowledge of the Hamiltonian offers significant improvement of standard decoding techniques Eliska Greplova, Agnes Valenti, Evert van Nieuwenburg, Sebastian Huber

In this talk I will discuss how (unsupervised) machine learning methods can be useful for quantum experiments. Specifically, we will consider the use of a generative model to perform quantum many-body (pure) state reconstruction directly from experimental data. The power of this machine learning approach enables us to trade few experimentally complex measurements for many simpler ones, allowing for the extraction of sophisticated observables such as the Rényi mutual information. These results open the door to integration of machine learning architectures with intermediate-scale quantum hardware.

The sign structure of quantum states - the appearance of “probability” amplitudes with negative sign - is one of the most striking contrasts between the classical and the quantum world, with far-reaching implications in condensed matter physics and quantum information science. Because it is a basis-dependent property, one may wonder: is a given sign structure truly intrinsic, or can it be removed by a local change of basis? In this talk, I will present an algorithm based on automatic differentiation of tensor networks for discovering non-negative representations of many-body wavefunctions. I will show some numerical results for ground states of a two-leg triangular Heisenberg ladder, including an exotic Bose-metal phase.