QuICS Special Seminar

We develop approximations to a perturbed quantum dynamics beyond the standard approximation based on quantum Zeno dynamics and adiabatic elimination. The effective generators describing the approximate evolutions are endowed with the same block structure as the unperturbed part of the generator, and their adiabatic error is “eternal” - it does not accumulate over time. We show how this gives rise to Schrieffer-Wolff generators in open systems.

Commuting projector models (CPMs) have provided microscopic theories for a host of gauge theories and are the venue for Kitaev’s toric code. An immediate question that arises is whether there exist CPMs for the Hall effect, the discovery of which ignited a revolution in modern condensed matter physics. In fact, a no-go theorem has recently appeared suggesting that no CPM can host a nonzero Hall conductance. In this talk, we present a CPM for just that: U(1) states with nonzero Hall conductance.

Recently, works such as the landmark MIP*=RE paper by Ji et. al. have established deep connections between computability theory and the power of nonlocal games with entangled provers. Many of these works start by establishing compression procedures for nonlocal games, which exponentially reduce the verifier's computational task during a game. These compression procedures are then used to construct reductions from uncomputable languages to nonlocal games, by a technique known as iterated compression.

For non-interacting fermions at zero temperature, it is well established that charge transport is quantized whenever the chemical potential lies in a gap of the single-body Hamiltonian. Proving the same result with interactions was an open problem for nearly 30 years until it was solved a few years ago by Hastings and Michalakis. The solution uses new tools originally developed in the context of the classification of exotic phases of matter, and was used before in the proof of the many-dimensional Lieb-Schultz-Mattis theorem.

In many natural situations where the input consists of n quantum systems, each associated with a state space C^d, we are interested in problems that are symmetric under the permutation of the n systems as well as the application of the same unitary U to all n systems.

Hyperbolic lattices are tessellations of the hyperbolic plane using,for instance, heptagons or octagons. They are relevant for quantumerror correcting codes and experimental simulations of curved spacequantum physics in circuit quantum electrodynamics. Underneath theirperplexing beauty lies a hidden and, perhaps, unexpected periodicitythat allows us to identify the unit cell and Bravais lattice for agiven hyperbolic lattice. This paves the way for applying powerfulconcepts from solid state physics and, potentially, finding a

Fault-tolerant error correction (FTEC), a procedure which suppresses error propagation in a quantum circuit, is one of the most important components for building large-scale quantum computers. One major technique often used in recent works is the flag technique, which uses a few ancillas to detect faults that can lead to errors of high weight and is applicable to various fault-tolerant schemes. In this talk, I will further improve the flag technique by introducing the use of error weight parities in error correction.

Fermionic Linear Optics (FLO) is a restricted model of quantum computation which in its original form is known to be efficiently classically simulable. We show that, when initialized with suitable input states, FLO circuits can be used to demonstrate quantum computational advantage with strong hardness guarantees. Based on this, we propose a quantum advantage scheme which is a fermionic analogue of Boson Sampling: Fermion Sampling with magic input states.

Quantifying quantum states’ complexity is a key problem in various subfields of science, from quantum computing to black-hole physics. We prove a prominent conjecture by Brown and Susskind about how random quantum circuits’ complexity increases. Consider constructing a unitary from Haar-random two-qubit quantum gates. Implementing the unitary exactly requires a circuit of some minimal number of gates - the unitary’s exact circuit complexity.

Abstract: In this talk I will study the extension of fault tolerance techniques to holographic quantum error correcting codes in the context of the ads/cft correspondence. I will seek to argue that the threshold here corresponds to that of the confinement/de confinement phase transition here, analogously to the situation in topological quantum error correcting codes based on Tqft’s.
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https://umd.zoom.us/j/4111099146
Meeting ID: 411 109 9146