We consider a family of Gaussian and non-Gaussian continuous-variable (CV) circuits, suitable to describe state-of-the-art photonic processors, and evaluate its learning capabilities.
We consider measurement disturbance tradeoffs in quantum machine learning protocols which seek to learn about quantum data. We study the simplest example of a binary classification task in the unsupervised regime. Primarily, we investigate how a classification of two qubits, that can each be in one of two unknown states, affects our ability to perform a subsequent classification on three qubits when a third is added. Surprisingly, we find a range of strategies in which a nontrivial first classification does not affect the success rate of the second classification.
We develop the p-adic quantum mechanics introduced by Volovich, where physics takes place in three-dimensional p-adic space rather than Euclidean space.
We study the p-adic rotation group SO(3)ₚ, and we outline a program to classify its continuous complex unitary projective representations.
These can be interpreted as a theory of p-adic angular momentum, where the p-adic qubit arises from those two-dimensional irreducible representations.
Entanglement detection with imprecise measurements
[ Based on Phys. Rev. Lett. 128, 250501 (2022)]
Dual unitaries are four-legged tensors which satisfy the unitarity condition across the time as well as the space direction. These have attracted a lot of attention in the last three years. One reason being that they allow for the construction of many-body models which display quantum chaos and are analytically tractable. In this talk will present a family of dual-unitary circuits in 1+1 dimensions which constitute discrete analogs of conformal field theories. In other words, these are quantum cellular automata which are scale and Lorentz invariant.
Chaotic systems are highly sensitive to small perturbation, be they biological, chemical, classical, ecological, political, or quantum. Taking this as the underlying principle, we construct an operational notion for quantum chaos. Namely, we demand that the whole future state of a large system is highly sensitive to past operations on a small subpart of that system. This immediately leads to a direct link between quantum chaos and volumetric spatiotemporal entanglement.
Many applications of the emerging quantum technologies, such as quantum teleportation and quantum key distribution, require singlets, maximally entangled states of two quantum bits. It is thus of utmost importance to develop optimal procedures for establishing singlets between remote parties. As has been shown very recently, singlets can be obtained from other quantum states by using a quantum catalyst, an entangled quantum system which is not changed in the procedure. We put this idea further, investigating properties of entanglement catalysis and its role for quantum communication.
Landauer's principle states that a minimum amount of dissipation is required to erase one bit of information. Reaching this bound in practice requires infinite resources (either infinite time or infinite energy), a fact that is intimately connected to the second and third laws of thermodynamics. In the presence of finite resources, it becomes a challenging problem to identify optimal erasure processes that minimize the generation of dissipation. In this talk, I will present progress in this question based on a geometric approach to finite-time thermodynamics [1].
In this talk I will provide a high level overview of the various modules that go into the design of a fault-tolerant quantum computer. I will use photonic quantum computers as a working example. Processes include state preparation, choice of computing model, quantum error correction, to list a few. I will also highlight some of the pressing open problems and challenges that lie ahead even from a theoretical point of view. Building low-error logical qubits in a scalable (modular) way remains the single core challenge impeding the deployment of usable quantum computing.
