Conference

Using superconducting parametric cavities, we have demonstrated much of the toolbox of linear quantum optics, but also extended it by taking advantage of the strong nonlinearities of superconducting circuits. In a set of experiments, we have used these parametric cavities as a platform for analog quantum simulation of lattice field theories. Preliminary results already show the promise of the platform for this application. For instance, a single device can simulate a number of different models, including topological and chiral models, in a flexible and programmable way.

Trapped ions are among the most advanced technology platforms for quantum information processing, in particular quantum simulation. However, ions are most readily trapped as a linear chain in radio-frequency traps, limiting their use to simulate higher dimensional quantum systems. In this talk, I'll describe an analog and an analog-digital hybrid [1] quantum simulation protocols to simulate programmable 2D and 3D spin models in a linear ion chain, by manipulating phonon-mediated long-ranged interactions between ion spins. The ability to dynamically engineer lattice geometries enables the investigation of a rich variety of physical phenomena such as spin frustration, topological states, and quantum quenches. [1] Rajabi et al., npj Quantum Information 5:32 (2019)

Coherent errors in a quantum system can, in principle, build up much more rapidly than incoherent errors, accumulating as the square of the number of qubits in the system rather than linearly. I will characterize the types of channels that can exhibit such behavior and present a simple protocol that can detect and characterize coherent errors whenever they are present, no matter what their nature. This allows us to identify coherent errors in gates and measurements to within a constant fraction of the maximum possible sensitivity to such errors.

Tensor networks are powerful computational tools, widely used in condensed matter physics, and increasingly in high-energy physics, with promising applications to machine learning problems. Developed in collaboration with Google and X, we present TensorNetwork: a new software package that makes it easier to code tensor network algorithms and, by using a framework like TensorFlow as a backend, to accelerate computations using specialized hardware (GPUs, TPUs) and integrate tensor networks into machine-learning projects.

I will present an efficient variational approach for preparing highly entangled pure states as well as thermofield double states on a quantum computer. The latter, in addition to being of interest in the holographic correspondence, enables an alternative approach for simulating thermal states without an external heat bath.

I will describe a proposal to simulate MERA on Google's 72 qubit NISQ device known as Bristlecone, and explain how it can be the basis for simulating inflation in an early universe. Other applications of this proposal include benchmarking of the NISQ device, hybrid classical quantum optimizations and quantum machine learning.

Recent experiments in graphene heterostructures have observed Chern insulators - integer and fractional Quantum Hall states made possible by a periodic substrate potential. Here we study theoretically that the competition between different Chern insulators, which can be tuned by the amplitude of the periodic potential, leads to a new family of quantum critical points described by QED3-Chern-Simons theory. At these critical points, Nf flavors of Dirac fermions interact through an emergent U(1) gauge theory at Chern-Simons level K, and remarkably, the entire family (with any Nf or K) can be realized at special values of the external magnetic field. I will talk about the physical properties and microscopic realization of those critical points. We propose experiments on Chern insulators that could resolve open questions in the study of 2+1 dimensional conformal field theories and test recent duality inspired conjectures.

The conventional Euclidean time Monte Carlo approach to Lattice Field Theories faces a major obstacle in the sign problem in certain parameter regimes, such as the presence of a nonzero chemical potential or a topological theta-term. Tensor Network States, a family of ansatzes for the efficient description of quantum many-body states, offer a promising alternative for addressing Lattice Field Theories in the Hamiltonian formulation. In particular, numerical methods based on Tensor Network states do not suffer from the sign problem which makes it possible to study scenarios which are not accessible with standard Monte Carlo methods. In this talk I will present some recent work demonstrating this capability using two (1+1)-dimensional models as a test bed. Studying the O(3) nonlinear sigma model at nonzero chemical potential and the Schwinger model with topological theta-term, I will show how Tensor Networks States accurately describe the low-energy spectrum and that numerical errors can be controlled well enough to make contact with continuum predictions.

We give rigorous analytical results on the temporal behavior of two-point correlation functions (also known as dynamical response functions or Green’s functions) in quantum many body systems undergoing unitary dynamics. Using recent results from large deviation theory, we show that in a large class of models the correlation functions factorize at late times -> , thus proving that dissipation emerges out of the unitary dynamics of the system. We also show that the fluctuations around this late-time value are bounded by the purity of the thermal ensemble, which generally decays exponentially with system size. This conclusion connects the behavior of correlation functions to that of the late-time fluctuations of quenched systems out of equilibrium. For auto-correlation functions such as (as well as the symmetrized and anti-symmetrized versions) we provide an upper bound on the timescale at which they reach that factorized late time value. Remarkably, this bound is a function of local expectation values only, and does not increase with system size. As such it constraints, for instance, the behavior of current auto-correlation functions that appear in quantum transport. We give numerical examples that show that this bound is a good estimate in chaotic models, and argue that the timescale that appears can be understood in terms of an emergent fluctuation-dissipation theorem. Our study extends to further classes of two point functions such as the Kubo function of linear response theory, for which we give an analogous result. Joint work with Luis Pedro Garcia-Pintos and Jonathon Riddell