Quantum Matter

A device called a ‘Gaussian Boson Sampler’ has initially been proposed as a near-term demonstration of classically intractable quantum computation. But these devices can also be used to decide whether two graphs are similar to each other. In this talk, I will show how to construct a feature map and graph similarity measure (or ‘graph kernel’) using samples from an optical Gaussian Boson Sampler, and how to combine this with a support vector machine to do machine learning on graph-structured datasets. I will present promising benchmarking results and try to motivate why such a continuous-variable quantum computer can actually extract interesting properties from graphs.

Both electrons and nuclei follow the laws of quantum mechanics, and even though classical approximations and/or empirical models can be quite successful in many cases, a full quantum description is needed to achieve predictive simulations of matter. Traditionally, simulations that treat both electrons and nuclei as quantum particles have been prohibitively demanding. I will present several recent algorithmic advances that have increased dramatically the range of systems that are amenable to quantum modeling: on one hand, by using accelerated path integral schemes to treat the nuclear degrees of freedom, and on the other by using machine-learning potentials to reproduce inexpensively high-end electronic-structure calculations. I will give examples of both approaches, and discuss how the two can be used in synergy to make fully quantum modeling affordable.

In this talk I will discuss some of the long-term challenges emerging with the effort of making deep learning a relevant tool for controlled scientific discovery in many-body quantum physics. The current state of the art of deep neural quantum states and learning tools will be discussed in connection with open challenging problems in condensed matter physics, including frustrated magnetism and quantum dynamics.

The appearance of scale invariance and diverging response functions in many-body systems is inseparably linked to the presence of a critical point and spontaneous symmetry breaking. In thermal equilibrium critical points mostly correspond to isolated spots in parameter space, which require rather strong fine tuning of e.g., the temperature of magnetic fields, in order to be reached. Pushing systems away from thermal equilibrium, e.g., by exposing them to external drive fields or dissipation, can give rise to more unconventional forms of criticality. External driving and dissipation may even turn critical points robust and attractive, imposing scale invariance for a large variety of external parameters, a phenomenon known as self-organized criticality (SOC).

I will discuss the manifestation of SOC in driven dissipative cold atom ensembles, for which a direct mapping of their microscopic parameters to an SOC field theory exists. This yields an opportunity to study SOC, typically associated with hard-to-control, large scale non-equilibrium setups, such as earthquakes, solar flares, or neural networks, under very controlled conditions. In addition, I will briefly explain the theoretical challenges for a quantum theory of self-organized criticality and point out current steps towards their realization.

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.