Seminar

Competition between unitary dynamics that scrambles quantum information non-locally and local measurements that probe and collapse the quantum state can result in a measurement-induced entanglement phase transition. Here we introduce analytically tractable models of measurement-induced criticality in large-N Brownian hybrid circuit model composed of qubits [1]. The system is initially entangled with an equal sized reference, and the subsequent hybrid system dynamics either partially preserves or totally destroys this entanglement depending on the measurement rate.

The integer quantum Hall states, the quantum spin Hall insulator, and the (2+1)D p-wave topological superconductor each have an important place in condensed matter physics due to their quantized symmetry-protected topological invariants. These systems have a unique ground state on any closed manifold in (2+1) dimensions, and are examples of 'invertible' topological phases of fermions. Here I will describe a general theory which fully encodes the universal properties of such invertible phases, and classifies them based on their symmetries.

In 2019, Google announced that they had achieved quantum supremacy: they performed a task on their newly constructed quantum device that could not be accomplished using classical computers in a reasonable amount of time.  In this talk, we present the mathematics and statistics involved in the set-up and analysis of the experiment, sampling from random quantum circuits.  We start with the theory of random matrices and explain how to produce a sequence of (pseudo) random unitary matrices using quantum circuits.  We then discuss how the Google team compares quantum and cla

Quantum mechanics allows for a consistent formulation of particles that are neither bosons nor fermions. In this talk, I’ll present a particular example of those particles, the so-called para-particles, which arise as a generalization of the usual bosons and fermions. Even though these particles are unlikely to be present in nature, a quantum system involving a spin-½ degree of freedom coupled to two bosonic modes yields a Hamiltonian that describes para-bosons and para-fermions.

A group 2-design is a unitary 2-design arising via the image of a suitable compact group under a projective unitary representation in dimension d.  The Clifford group in dimension d is the quotient of the normalizer of the Weyl-Heisenberg group in dimension d, by its centre: namely U(1).  In this talk, we prove that the Clifford group is not a group 2-design when d is not prime. Our main proofs rely, primarily, on elementary representation theory, and so we review the essentials. We also discuss the general structure of group 2-designs.

Calculating quantities such as the quantum or private capacity of a quantum channel is a fundamental, but unfortunately a generally very hard, problem. A well known class of channels for which the task simplifies is that of degradable channels, and it was later shown that the same also holds for a potentially bigger class of channels, the so called less noisy channels. Based on the former, the concept of approximately degradable channels was introduced to find bounds on capacities for general channels.

Many-body open quantum systems balance internal dynamics against decoherence from interactions with an environment. In this talk, I describe an experiment that explores this balance via random quantum circuits implemented on a trapped-ion quantum computer, where the system evolution is represented by unitary gates with interspersed projective measurements. As the measurement rate is varied, a purification phase transition is predicted to emerge at a critical point akin to a fault-tolerant threshold.

We derive a family of optimal protocols, in the sense of saturating the quantum Cramér-Rao bound, for measuring a linear combination of d field amplitudes with quantum sensor networks, a key subprotocol of general quantum sensor networks applications. We demonstrate how to select different protocols from this family under various constraints via linear programming. Focusing on entanglement-based constraints, we prove the surprising result that highly entangled states are not necessary to achieve optimality for many problems.

In this talk, I will discuss chaotic billiard systems subject to a rapid periodic driving force, with driving frequency ω. Classically, the energy of such systems changes by small, effectively random increments associated with collisions with the billiard wall, leading to a random walk in energy space, or “energy diffusion.” I will present a Fokker-Planck description of this process. This model displays several notable features, including a 1/ω² scaling of the energy absorption rate, and (in certain special cases) an exact analytical solution.

Recent years have seen the development of isolated quantum simulator platforms capable of exploring interesting questions at the frontiers of many-body physics. We describe our platform, based on a chain of Ytterbium ions in a linear trap, and describe its capabilities, which include long-range spin-spin interactions and single-site manipulation and readout. We then describe some recent studies undertaken with this machine, focusing on two.