相关论文: Counterexamples to Kalai's Conjecture C
We provide a proof and a counterexample to two conjectures made by N. Kuznetsov.
I make a rough estimate of the accuracy threshold for fault tolerant quantum computing with concatenated codes. First I consider only gate errors and use the depolarizing channel error model. I will follow P.Shor (quant-ph/9505011) for…
This note reviews prospects for quantum computing. It argues that gates need to be tested for a wide range of probability amplitudes.
we envisage a novel quantum cloning machine, which takes an input state and produces an output state whose success branch can exist in a linear superposition of multiple copies of the input state and the failure branch exist in a…
Robust quantum computation requires encoding delicate quantum information into degrees of freedom that are hard for the environment to change. Quantum encodings have been demonstrated in many physical systems by observing and correcting…
Contextuality provides a unifying paradigm for nonclassical aspects of quantum probabilities and resources of quantum information. Unfortunately, most forms of quantum contextuality remain experimentally unexplored due to the difficulty of…
Quantum computing is a new computational paradigm with the potential to solve certain computationally challenging problems much faster than traditional approaches. Civil engineering encompasses many computationally challenging problems,…
We study analytically and numerically the effects of various imperfections in a quantum computation of a simple dynamical model based on the Quantum Wavelet Transform (QWT). The results for fidelity timescales, obtained for a large range of…
The classical PCP theorem is arguably the most important achievement of classical complexity theory in the past quarter century. In recent years, researchers in quantum computational complexity have tried to identify approaches and develop…
In this extended abstract, we carefully examine a purported counterexample to a postulate of iterated belief revision. We suggest that the example is better seen as a failure to apply the theory of belief revision in sufficient detail. The…
Large-scale computing systems today are assembled by numerous computing units for massive computational capability needed to solve problems at scale, which enables failures common events in supercomputing scenarios. Considering the…
The concept of counterfactual explanations (CE) has emerged as one of the important concepts to understand the inner workings of complex AI systems. In this paper, we translate the idea of CEs to linear optimization and propose, motivate,…
In preparing the paper "Some extensions of Hilbert-Kunz multiplicity", we had occasion to perform an intricate set of computations pertaining to a single illustrative example. In the end, we have decided not to include the computations in…
The CQC conjecture by Schneeloch et al. (Physical Review A 90.6, 2014) asserts that the sum of classical mutual information between two parties obtained by measuring individual systems in two mutually unbiased bases cannot exceed their…
We describe a fault-tolerant one-way quantum computer on cluster states in three dimensions. The presented scheme uses methods of topological error correction resulting from a link between cluster states and surface codes. The error…
We predict credit applications with off-the-shelf, interchangeable black-box classifiers and we explain single predictions with counterfactual explanations. Counterfactual explanations expose the minimal changes required on the input data…
We develop a generalized theory of quantum error correction (QEC) that applies to any linear map, in particular maps that are not completely positive (CP). This theory describes entanglement-assisted QEC for invertible noise maps, which we…
A strong confluence result for Q*, a quantum lambda-calculus with measurements, is proved. More precisely, confluence is shown to hold both for finite and infinite computations. The technique used in the confluence proof is syntactical but…
An alternative computational approach to the Collatz (3n+1) conjecture is presented that may be theoretically capable of confirming the conjecture.
This is a series of two papers in which we solve the Clemens conjecture: there are only finitely many smooth rational curves of each degree in a generic quintic threefold. In this first paper, we deal with a family of smooth Calabi-Yau…