Related papers: Recovery algorithms for Clifford Hayden-Preskill p…
Developing algorithms for solving high-dimensional partial differential equations (PDEs) has been an exceedingly difficult task for a long time, due to the notoriously difficult problem known as the "curse of dimensionality". This paper…
Holonomic quantum computation exploits a quantum state's non-trivial, matrix-valued geometric phase (holonomy) to perform fault-tolerant computation. Holonomies arising from systems where the Hamiltonian traces a continuous path through…
Error correction is generally demanded in large-scale quantum information processing and quantum computation. We provide here a universal and realtime control strategy to dynamically correct the arbitrary type of errors in the system…
Proposals for quantum computing devices are many and varied. They each have unique noise processes that make none of them fully reliable at this time. There are several error correction/avoidance techniques which are valuable for reducing…
The fidelity susceptibility serves as a universal probe for quantum phase transitions, offering an order-parameter-free metric that captures ground-state sensitivity to Hamiltonian perturbations and exhibits critical scaling. Classical…
Recent research has demonstrated that quantum computers can solve certain types of problems substantially faster than the known classical algorithms. These problems include factoring integers and certain physics simulations. Practical…
We propose a variant of consensus-based optimization (CBO) algorithms, controlled-CBO, which introduces a feedback control term to improve convergence towards global minimizers of non-convex functions in multiple dimensions. The feedback…
A wide array of image recovery problems can be abstracted into the problem of minimizing a sum of composite convex functions in a Hilbert space. To solve such problems, primal-dual proximal approaches have been developed which provide…
We study the problem of approximately recovering signals on a manifold from one-bit linear measurements drawn from either a Gaussian ensemble, partial circulant ensemble, or bounded orthonormal ensemble and quantized using Sigma-Delta or…
Building on recent advances in quantum algorithms which measure and reuse qubits and in efficient classical simulation leveraging projective measurements, we extend these frameworks to real-time dynamics of quantum many-body systems…
Numerically locating the critical points of non-convex surfaces is a long-standing problem central to many fields. Recently, the loss surfaces of deep neural networks have been explored to gain insight into outstanding questions in…
We initiate the systematic study of experimental quantum physics from the perspective of computational complexity. To this end, we define the framework of quantum algorithmic measurements (QUALMs), a hybrid of black box quantum algorithms…
We address a wide spectrum of quantum control strategies, including various open-loop protocols and advanced adaptive methods. These methodologies apply to few-qubit scenarios and naturally scale to larger N-qubit systems. We benchmark them…
It is important for performance studies in quantum technologies to analyze quantum circuits in the presence of noise. We introduce an error probability tensor, a tool to track generalized Pauli error statistics of qudits within quantum…
The Clifford group plays a central role in quantum information science. It is the building block for many error-correcting schemes and matches the first three moments of the Haar measure over the unitary group -a property that is essential…
We prove convergence rates of linear sampling recovery of functions in abstract Bochner spaces satisfying weighted summability of their generalized polynomial chaos expansion coefficients. The underlying algorithm is a function-valued…
Quantum error correction is believed to be essential for scalable quantum computation, but its implementation is challenging due to its considerable space-time overhead. Motivated by recent experiments demonstrating efficient manipulation…
In this paper we analyze approximation and recovery properties with respect to systems satisfying universal sampling discretization property and a special incoherence property. We apply a powerful nonlinear approximation method -- the Weak…
In this work, we develop a fully implicit Hybrid High-Order algorithm for the Cahn-Hilliard problem in mixed form. The space discretization hinges on local reconstruction operators from hybrid polynomial unknowns at elements and faces. The…
The physical interpretation and eventual fate of gravitational singularities in a theory surpassing classical general relativity are puzzling questions that have generated a great deal of interest among various quantum gravity approaches.…