Related papers: Sphere Valued Noise Stability and Quantum MAX-CUT …
For an $n$-dimensional real-valued centered Gaussian random vector $(X_1,\ldots,X_n)$ with any covariance matrix, the following moment product conjecture is proved in this paper \[ \mathbb{E}\prod_{j=1}^nX_j^{2m_j}\geq…
Assuming the Unique Games Conjecture, we show that existing approximation algorithms for some Boolean Max-2-CSPs with cardinality constraints are optimal. In particular, we prove that Max-Cut with cardinality constraints is UG-hard to…
Inertial particles in 2D driven by a Gaussian white noise forcing are considered. For two examples of the forcing (compressible and incompressible) upper and lower bounds are found for the mean number of caustics as a function of Stokes…
This paper considers the decidability of fully quantum nonlocal games with noisy maximally entangled states. Fully quantum nonlocal games are a generalization of nonlocal games, where both questions and answers are quantum and the referee…
In the present paper we give proof that the information-transmission capacity of the approximate position measurement with the oscillator energy constraint, which underlies noisy Gaussian homodyning in quantum optics, is attained on…
Variational Quantum Eigensolvers (VQEs) are a powerful class of hybrid quantum-classical algorithms designed to approximate the ground state of a quantum system described by its Hamiltonian. VQEs hold promise for various applications,…
Parameter estimation is of fundamental importance in areas from atomic spectroscopy and atomic clocks to gravitational wave detection. Entangled probes provide a significant precision gain over classical strategies in the absence of noise.…
A sharp isoperimetric inequality for the Hamming cube is proved at the critical exponent $\beta=\frac12$. This follows up on previous work, where such bounds were established for $\beta$ near $\frac12$. As a consequence, this result settles…
Quantum algorithms face significant challenges due to qubit susceptibility to environmental noise, and quantum error correction typically requires prohibitive resource overhead. This paper proposes that quantum algorithms may possess…
Quantum gravity is a challenge in physics, and the existence of graviton is the prime question at present. We study the detectability of the quantum noise induced by gravitons in this letter. The correlation of the quantum noise in the…
A novel algorithm is proposed for quantitative comparisons between compact surfaces embedded in the three-dimensional Euclidian space. The key idea is to identify those objects with the associated surface measures and compute a weak…
A canonical feature of the constraint satisfaction problems in NP is approximation hardness, where in the worst case, finding sufficient-quality approximate solutions is exponentially hard for all known methods. Fundamentally, the lack of…
There is a strong interest in finding challenging instances of NP-hard problems, from the perspective of showing quantum advantage. Due to the limits of near-term NISQ devices, it is moreover useful if these instances are small. In this…
We describe a web of connections between the following topics: the mathematical theory of voting and social choice; the computational complexity of the Maximum Cut problem; the Gaussian Isoperimetric Inequality and Borell's generalization…
In previous studies, we have explored the ansatz that the volume elements of the Bures metrics over quantum systems might serve as prior distributions, in analogy to the (classical) Bayesian role of the volume elements ("Jeffreys' priors")…
In this paper, we explore the impact of noise on quantum computing, particularly focusing on the challenges when sampling bit strings from noisy quantum computers as well as the implications for optimization and machine learning…
Too much noise kills entanglement. This is the main problem in its production and transmission. We use a handy approach to indicate noise resistance of entanglement of a bi-partite system described by $d\times d$ Hilbert space. Our analysis…
The Betke-Henk-Wills conjecture proposes a sharp upper bound for the lattice point enumerator $G(K, \Lambda)$ of a convex body in terms of its successive minima. While the conjecture remains open for general convex bodies in dimensions $d…
Noisy, intermediate-scale quantum (NISQ) computing devices offer opportunities to test the principles of quantum computing but are prone to errors arising from various sources of noise. Fluctuations in the noise itself lead to unstable…
Quantum technologies exploit entanglement to enhance various tasks beyond their classical limits including computation, communication and measurements. Quantum metrology aims to increase the precision of a measured quantity that is…