Seminar

The fundamental assumption of statistical mechanics is that the long-time average of any observable is equal to its average over the microcanonical ensemble. In classical mechanics, this stems from Boltzmann’s ergodic hypothesis, by which a generic initial state in an ergodic system visits the neighborhood of all states in phase space with the same energy. However, wavelike effects in quantum mechanics have made it difficult to identify what it even means for a quantum system to be ergodic, except on a case-by-case basis for individual observables.

Quantum measurements are critical to virtually any aspect of quantum information processing--for example: quantum error correction, distillation protocols, or state preparation.  We discuss the evolution of quantum information under Pauli measurement circuits.  We define "local reversibility" in context of measurement circuits, which guarantees that quantum information is preserved and remain "localized" after measurement.  We find that measurement circuits can exhibit a richer set of behaviour in comparison to their unitary counterparts.  For example, a finite depth me

A key goal in modern quantum science is to harness the complex behavior of quantum systems to develop new technologies. While precisely engineered platforms with ultracold atoms and trapped ions have emerged as powerful tools for this task, our limited ability to theoretically and computationally probe these systems poses immense challenges for their improved control and characterization.

In this session, new and current QuICS members will introduce themselves and their research. Organized by Yi-Kai Liu.

Quantum cryptography leverages unique features of quantum mechanics in order to construct cryptographic primitives which are oftentimes impossible for digital computers. Cryptographic applications of quantum computers therefore have the potential for useful quantum advantage – entirely without computational speed-ups. In this talk, I will focus on two fundamental questions: First, is it possible to certify that private data has been deleted? And second, is it possible to revoke a cryptographic key?

In this talk, I will first provide an overview of an ongoing project on symmetric quantum circuits and then discuss two related recent results from this year. The overarching goal of this project is to investigate the properties of quantum circuits constructed from k-local gates that all respect a global symmetry, such as U(1) or SU(d).

In this talk, I will present a theory of interaction-induced band-flattening in strongly correlated electron systems. I will begin by illustrating an inherent connection between flat bands and index theorems and presenting a generic prescription for constructing flat bands by periodically repeating local Hamiltonians with topological zero modes. Specifically, a Dirac particle in an external, spatially periodic magnetic field can be cast in this form.

Optical experiments utilize excitons (electron-hole bound states) in moir ́e transition metal dichalcogenide bilayers as a quantum simulator of the Bose-Hubbard model. Nevertheless, we show that these excitations possess nonbosonic commutation relations due to their composite nature, limiting the size of phase space for them to occupy. Such an effect manifests at weak electron-hole correlation, and restricts the number of excitons to be less than 4 per site and valley for three different bilayers.

Concatenating bosonic error-correcting codes with qubit codes can substantially boost the error-correcting power of the original qubit codes. It is not clear how to concatenate optimally, given that there are several bosonic codes and concatenation schemes to choose from, including the recently discovered Gottesman-Kitaev-Preskill (GKP) – stabilizer codes [Phys. Rev. Lett. 125, 080503 (2020)] that allow protection of a logical bosonic mode from fluctuations of the conjugate variables of the mode.

The noncommutative sum-of-squares (ncSoS) hierarchy was introduced by Navascues--Pironio--Acin as a sequence of semidefinite programming relaxations for approximating values of "noncommutative polynomial optimization problems," which were originally intended to generalize quantum values of nonlocal games. Recent work has started to analyze the hierarchy for approximating ground energies of local Hamiltonians, initially through rounding algorithms which output product states for degree-2 ncSoS.