Related papers: Sphere Valued Noise Stability and Quantum MAX-CUT …

Stable quantum computation requires noisy results to remain bounded even in the presence of noise fluctuations. Yet non-stationary noise processes lead to drift in the varying characteristics of a quantum device that can greatly influence…

In this note we obtain tight bounds on the space-complexity of computing the ergodic measure of a low-dimensional discrete-time dynamical system affected by Gaussian noise. If the scale of the noise is $\varepsilon$, and the function…

In this paper, we prove an almost-optimal hardness for Max $k$-CSP$_R$ based on Khot's Unique Games Conjecture (UGC). In Max $k$-CSP$_R$, we are given a set of predicates each of which depends on exactly $k$ variables. Each variable can…

Noise is the defining feature of the NISQ era, but it remains unclear if noisy quantum devices are capable of quantum speedups. Quantum supremacy experiments have been a major step forward, but gaps remain between the theory behind these…

An uncertainty inequality is presented that establishes a lower limit for the product of the variance of the time-averaged intensity of a mode of a quantized electromagnetic field and the degree of its spatial localization. The lower limit…

Demonstrating quantum supremacy, a complexity-guaranteed quantum advantage against over the best classical algorithms by using less universal quantum devices, is an important near-term milestone for quantum information processing. Here we…

We propose a novel algorithm, termed soft quasi-Newton (soft QN), for optimization in the presence of bounded noise. Traditional quasi-Newton algorithms are vulnerable to such perturbations. To develop a more robust quasi-Newton method, we…

The Standard Simplex Conjecture of Isaksson and Mossel asks for the partition $\{A_{i}\}_{i=1}^{k}$ of $\mathbb{R}^{n}$ into $k\leq n+1$ pieces of equal Gaussian measure of optimal noise stability. That is, for $\rho>0$, we maximize $$…

Assuming the Unique Games Conjecture (UGC), the best approximation ratio that can be obtained in polynomial time for the MAX CUT problem is $\alpha_{\text{CUT}}\simeq 0.87856$, obtained by the celebrated SDP-based approximation algorithm of…

For a quantum computer acting on d-dimensional systems, we analyze the computational power of circuits wherein stabilizer operations are perfect and we allow access to imperfect non-stabilizer states or operations. If the noise rate…

We investigate the ultimate precision achievable in Gaussian quantum metrology. We derive general analytical expressions for the quantum Fisher information matrix and for the measurement compatibility condition, ensuring asymptotic…

In the classical context, the cooperative game theory concept of the Shapley value has been adapted for post hoc explanations of machine learning models. However, this approach does not easily translate to eXplainable Quantum ML (XQML).…

Quantum computation has made considerable progress in the last decade with multiple emerging technologies providing proof-of-principle experimental demonstrations of such calculations. However, these experimental demonstrations of quantum…

We study the sensitivity to noise of |permanent(X)|^2 for random real and complex n x n Gaussian matrices X, and show that asymptotically the correlation between the noisy and noiseless outcomes tends to zero when the noise level is…

To successfully execute large-scale algorithms, a quantum computer will need to perform its elementary operations near perfectly. This is a fundamental challenge since all physical qubits suffer a considerable level of noise. Moreover, real…

The vertex cover problem is one of the most important and intensively studied combinatorial optimization problems. Khot and Regev (2003) proved that the problem is NP-hard to approximate within a factor $2 - \epsilon$, assuming the Unique…

In the simultaneous Max-Cut problem, we are given $k$ weighted graphs on the same set of $n$ vertices, and the goal is to find a cut of the vertex set so that the minimum, over the $k$ graphs, of the cut value is as large as possible.…

We introduce a new technique for reducing the dimension of the ambient space of low-degree polynomials in the Gaussian space while preserving their relative correlation structure, analogous to the Johnson-Lindenstrauss lemma. As…

All metal objects support fluctuating currents that are responsible for evanescent-wave Johnson noise in their vicinity due both to thermal and quantum effects. The noise fields can decohere qubits in their neighborhood. It is quantified by…

We introduce a volumetric benchmark for near-term quantum platforms based on the generation and verification of genuine entanglement across n-qubits using graph states and direct stabilizer measurements. Our benchmark evaluates the…