QuICS Special Seminar

The unprecedented control of synthetic quantum systems allows to tackle outstanding questions from high-energy physics, such as the non-equilibrium dynamics of gauge theories, using quantum simulators. In this talk, I will first discuss dynamical topological transitions in quantum electrodynamics (QED) in one spatial dimension [1], which bear similarities with the physics of topological insulators. This phenomenon is accessible within our proposals to microscopically engineer the Hamiltonian of lattice QED with a mixture of ultracold gases [2].

Quantum technologies fundamentally rely on quantum control, measurement, and feedback; however, a general understanding of many-body quantum dynamics under these conditions remains in its early stages.  Such studies may provide insight into the dynamics of quantum computers undergoing active quantum error correction while running nontrivial quantum algorithms, as well as point to a more general understanding of the transition from quantum to classical physics in many-body systems.  Measurement-induced transitions are a recently uncovered class of critical phenomena that

A long-standing puzzle in quantum complexity theory is to understand the power of the class MIP* of multiprover interactive proofs with shared entanglement. This question is closely related to the study of entanglement through non-local games, which dates back to the pioneering work of Bell. In this work we show that MIP* contains NEEXP (non-deterministic doubly exponential time), exponentially improving the prior lower bound of NEXP due to Ito and Vidick.

I will begin by reviewing general results on the equilibration of isolated quantum systems, including sufficient conditions for equilibration and a discussion of the timescales of this equilibration process. I will then focus on new results on the dynamics of two-point correlation functions. These include conditions under which correlation functions factorize at late times, and bounds on their temporal fluctuations. For auto-correlation functions we provide an upper bound on the timescale at which they reach the factorized late time value.

In this paper, we construct a new scheme for delegating a large circuit family, which we call "C+P circuits". "C+P" circuits are the circuits composed of Toffoli gates and diagonal gates. Our scheme is non-interactive, only requires small quantum resources on the client side, and can be proved secure in the quantum random oracle model, without relying on additional assumptions, for example, the existence of fully homomorphic encryption.

The dihedral hidden subgroup problem is equivalent to the hidden shift problem for a cyclic group, while the hidden shift problem for an arbitrary abelian group is generally similar.   In 2003, I found a subexponential time algorithm for this problem, more precisely stretched exponential time.  Later there were two variations, one due to Regev and the other due to me.   These algorithms became more interesting when Childs, Jao, and Soukharev showed that they yield a quantum algorithm t

Scientific explanation often requires one to make inferences about what
is unobservable based on what is observable.  An important example of
this pattern is to make inferences about causal mechanisms based on
observed correlations. In the context of quantum theory, the problem of
uncovering causal mechanisms is particularly vexing. One of the central
results in the foundations of quantum theory, Bell's theorem, can be

Encoding classical information into a quantum system is one of the most fundamental questions of quantum information theory. Classic results in this area include the Holevo bound and the Holevo-Schumacher-Westmoreland theorem. The setting in the latter can be imagined as a black box which takes a single random variable encoding the information as input and outputs a quantum state. The theorem then states that under appropriate conditions, a decoder exists.

Deciding whether a bipartite mixed state is separable (unentangled) or not is a computationally intractable (NP-hard) problem. In the case of qubits, the partial transpose of density matrices is known as a good candidate to diagnose separable states. In particular, it can be used to define an entanglement measure called the (logarithmic) negativity. Surprisingly, the extension of the partial transpose (and so the negativity) to fermionic systems remained intractable even for the non-interacting Gaussian states.

Applying a chemical potential bias to a conductor drives the system out of equilibrium into a current carrying non-equilibrium state.  This current flow is associated with entropy production in the leads, but it remains poorly understood under what conditions the system is driven to local equilibrium by this process.  We investigate this problem using two toy models for coherent quantum transport of diffusive fermions:  Anderson models in the conducting phase and a class of random quantum circuits acting on a chain of qubits, which exactly maps to an interacting f