Talks

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.