Related papers: Quantum Relative Entropy Decay Composition Yields …
The compression of quantum circuits is a foundational challenge for near-term quantum computing, yet the principles governing circuit stability remain poorly understood. We investigate this problem through a large-scale numerical analysis…
For certain types of quantum graphs we show that the random-matrix form factor can be recovered to at least third order in the scaled time $\tau$ from periodic-orbit theory. We consider the contributions from pairs of periodic orbits…
In the \emph{$k$-Diameter-Optimally Augmenting Tree Problem} we are given a tree $T$ of $n$ vertices as input. The tree is embedded in an unknown \emph{metric} space and we have unlimited access to an oracle that, given two distinct…
Electron transport through disordered quasi one-dimensional quantum systems is studied. Decoherence is taken into account by a spatial distribution of virtual reservoirs, which represent local interactions of the conduction electrons with…
We investigate the emergence of quantum chaos and unitary T-design behavior in derandomized Clifford+T circuits using causal cover architectures. Motivated by the need for deterministic constructions that can exhibit chaotic behavior across…
A directly measurable correlation length may be defined for systems having a two-step relaxation, based on the geometric properties of density profile that remains after averaging out the fast motion. We argue that the length diverges if…
We prove a general lower bound of quantum decision tree complexity in terms of some entropy notion. We regard the computation as a communication process in which the oracle and the computer exchange several rounds of messages, each round…
The Johnson-Lindenstrauss lemma is a fundamental result in probability with several applications in the design and analysis of algorithms in high dimensional geometry. Most known constructions of linear embeddings that satisfy the…
We present universal properties of anticoncentration in weakly noisy quantum circuits at finite depth. We develop a generic framework for single- and multi-qubit noise channels in the weak-noise limit and introduce an effective description…
Generative modeling is one of the most promising applications of quantum machine learning, yet training and deploying Quantum Generative Models (QGMs) on near-term hardware remains effectively intractable due to prohibitive gradient…
The von Neumann and quantum R\'enyi entropies characterize fundamental properties of quantum systems and lead to theoretical and practical applications in many fields. Quantum algorithms for estimating quantum entropies, using a quantum…
We establish rigorous connections between quantum circuit complexity and approximate quantum error correction (AQEC) capability, two properties of fundamental importance to the physics and practical use of quantum many-body systems,…
We develop a novel parallel decomposition strategy for unweighted, undirected graphs, based on growing disjoint connected clusters from batches of centers progressively selected from yet uncovered nodes. With respect to similar previous…
After quantum quenches in many-body systems, finite subsystems evolve non-trivially in time, eventually approaching a stationary state. In typical situations, the reduced density matrix of a given subsystem begins and ends this endeavour as…
We first propose and study a quantum toy model of black hole dynamics. The model is unitary, displays quantum thermalization, and the Hamiltonian couples every oscillator with every other, a feature intended to emulate the color sector…
With the steady progress in quantum computing over recent years, roadmaps for upscaling quantum processors have relied heavily on the targeted qubit architectures. So far, similarly to the early age of classical computing, these designs…
Estimation of unknown qubit elementary gates and alignment of reference frames are formally the same problem. Using quantum states made out of $N$ qubits, we show that the theoretical precision limit for both problems, which behaves as…
A new description of strange attractor systems through three geometrical and dynamical invariants is provided. They are the correlation dimension ($\mathcal{D}$) and the correlation entropy ($\mathcal{K}$), both having attracted attention…
In local quantum circuits with charge conservation, we initialize the system in random product states and study the dynamics of the Renyi entanglement entropy $R_\alpha$. We rigorously prove that $R_\alpha$ with Renyi index $\alpha>1$ at…
We argue that the requirement of a finite entanglement entropy of quantum degrees of freedom across a boundary surface is closely related to the phenomenon of running spectral dimension, universal in approaches to quantum gravity. If…