**Collection Number**S006

**Collection Type**Series

## Oscillator-to-oscillator codes do not have a threshold

It is known that continuous variable quantum information cannot be protected against naturally occurring noise using Gaussian states and operations only. Noh et al. (PRL 125:080503, 2020) proposed bosonic oscillator-to-oscillator codes relying on non-Gaussian resource states as an alternative, and showed that these encodings can lead to a reduction of the effective error strength at the logical level as measured by the variance of the classical displacement noise channel.

## Time-efficient learning of quantum Hamiltonians from high-temperature Gibbs states

We study the problem of learning a Hamiltonian given copies of its Gibbs state at a known inverse temperature. Anshu et al. recently studied the sample complexity (number of copies of the Gibbs state needed) of this problem for geometrically local Hamiltonians. In the high-temperature regime, their algorithm has sample complexity polynomial in the system size, temperature, and accuracy. Their algorithm can also be implemented with polynomial, but suboptimal, time complexity.

## Why supervised learning with quantum circuits reduces to kernel methods

With the race for quantum computers in full swing, researchers became interested in the question of what happens if we replace a supervised machine learning model with a quantum circuit. While such "supervised quantum models" are sometimes called "quantum neural networks", their mathematical structure reveals that they are in fact kernel methods with kernels that measure the distance between data embedded into quantum states. This talk gives an informal overview of the link, and discusses the far-reaching consequences for quantum machine learning.

## The power of random quantum circuits

In recent years, random quantum circuits have played a central role in the theory of quantum computation. Much of this prominence is due to recent random quantum circuit sampling experiments which have constituted the first claims of "quantum supremacy". While random quantum circuits enjoy certain advantages that make them ideal for implementation by near-term quantum experiments, it is unclear a priori why they should be difficult to simulate classically.

## Fault-tolerant logical gates in holographic stabilizer codes are severely restricted

We evaluate the usefulness of holographic stabilizer codes for practical purposes by studying their allowed sets of fault-tolerantly implementable gates. We treat them as subsystem codes and show that the set of transversally implementable logical operations is contained in the Clifford group for sufficiently localized logical subsystems. As well as proving this concretely for several specific codes, we argue that this restriction naturally arises in any stabilizer subsystem code that comes close to capturing certain properties of holography.

## Fault-tolerant qubit from a constant number of components

With gate error rates in multiple technologies now below the threshold required for fault-tolerant quantum computation, the major remaining obstacle to useful quantum computation is scaling, a challenge greatly amplified by the huge overhead imposed by quantum error correction itself. I’ll discuss a new fault-tolerant quantum computing scheme that can nonetheless be assembled from a small number of experimental components, potentially dramatically reducing the engineering challenges associated with building a large-scale fault-tolerant quantum computer.

## General conditions for universality of Quantum Hamiltonians

Recent work has defined what it means for one quantum system to simulate the full physics of another, and demonstrated that—within a very demanding definition of simulation —there exist families of local Hamiltonians that are universal, in the sense that they can simulate all other quantum Hamiltonians. This rigorous mathematical framework of Hamiltonian simulation not only gave a theoretical foundation for describing analogue Hamiltonian simulation. It also unified many previous Hamiltonian complexity results, and implied new ones.

## Multipartite entanglement: combinatorics, topology, and ... astronomy

A brief introduction to entanglement of multipartite pure quantum states will be given. As the Bell states are known to be maximally entangled among all two-qubit quantum states, a natural question arises: What is the most entangled state for the quantum system consisting of N sub-systems with d levels each? The answer depends on the entanglement measure selected, but already for four-qubit system, there is no state which displays maximal entanglement with respect to all three possible splittings of the systems into two pairs of qubits.

## Fast estimation of outcome probabilities for quantum circuits

We present two classical algorithms for the simulation of universal quantum circuits on n qubits constructed from c instances of Clifford gates and t arbitrary-angle Z-rotation gates such as T gates. Our algorithms complement each other by performing best in different parameter regimes. The Estimate algorithm produces an additive precision estimate of the Born rule probability of a chosen measurement outcome with the only source of run-time inefficiency being a linear dependence on the stabilizer extent (which scales like ≈1.17^t for T gates).

## Speck of Chaos

It has been shown that, despite being local, a perturbation applied to a single site of the one-dimensional XXZ model is enough to bring this interacting integrable spin-1/2 system to the chaotic regime. In this talk, we show that this is not unique to the XXZ model, but happens also to the spin-1/2 Ising model in a transverse field and to the spin-1 Lai-Sutherland chain. The larger the system is, the smaller the amplitude of the local perturbation for the onset of chaos.