QuICS Special Seminar

Demonstrating a superpolynomial quantum speedup using feasible schemes has become a key near-term goal in the field of quantum simulation and computation. The most prominent schemes for "quantum supremacy" such as boson sampling or random circuit sampling are based on the task of sampling from the output distribution of a certain randomly chosen unitary. But to convince a skeptic of a successful demonstration of quantum supremacy, one must verify that the sampling device produces the correct outcomes.

Given the unprecedented effort by academia and industry (e.g., IBM and Google), quantum computers with hundred(s) of qubits are at the brink of existence with the promise of outperforming any classical computer. Demonstration of computational advantages of noisy near-term quantum computers over classical computers is an imperative near-term goal. The foremost candidate task for showing this is Random Circuit Sampling (RCS), which is the task of sampling from the output distribution of a random circuit. This is exactly the task that recently Google experimentally performed on 53-qubits.

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.