Related papers: Adversary lower bounds for nonadaptive quantum alg…

We theoretically analyse the limits of robustness to test-time adversarial and noisy examples in classification. Our work focuses on deriving bounds which uniformly apply to all classifiers (i.e all measurable functions from features to…

In the circuit model of quantum computing, amplitude amplification techniques can be used to find solutions to NP-hard problems defined on $n$-bits in time $\text{poly}(n) 2^{n/2}$. In this work, we investigate whether such general…

We show that every algorithm for testing $n$-variate Boolean functions for monotonicity must have query complexity $\tilde{\Omega}(n^{1/4})$. All previous lower bounds for this problem were designed for non-adaptive algorithms and, as a…

Large-scale optimization problems are prevalent in several fields, including engineering, finance, and logistics. However, most optimization problems cannot be efficiently encoded onto a physical system because the existing quantum samplers…

Neural networks are getting deeper and more computation-intensive nowadays. Quantization is a useful technique in deploying neural networks on hardware platforms and saving computation costs with negligible performance loss. However, recent…

We derive an analytical lower bound for the concurrence of tripartite quantum mixed states. A functional relation is established relating concurrence and the generalized partial transpositions.

A dynamic algorithm against an adaptive adversary is required to be correct when the adversary chooses the next update after seeing the previous outputs of the algorithm. We obtain faster dynamic algorithms against an adaptive adversary and…

We propose a quantum algorithm to solve systems of nonlinear algebraic equations. In the ideal case the complexity of the algorithm is linear in the number of variables $n$, which means our algorithm's complexity is less than $O(n^{3})$ of…

The Element Distinctness problem is to decide whether each character of an input string is unique. The quantum query complexity of Element Distinctness is known to be $\Theta(N^{2/3})$; the polynomial method gives a tight lower bound for…

Deep neural networks are vulnerable to adversarial examples, i.e., carefully-perturbed inputs aimed to mislead classification. This work proposes a detection method based on combining non-linear dimensionality reduction and density…

Quantum algorithms for Hamiltonian simulation and linear differential equations more generally have provided promising exponential speed-ups over classical computers on a set of problems with high real-world interest. However, extending…

In unitary property testing a quantum algorithm, also known as a tester, is given query access to a black-box unitary and has to decide whether it satisfies some property. We propose a new technique for proving lower bounds on the quantum…

We prove a general relation between adaptive and non-adaptive strategies in the quantum setting, i.e., between strategies where the adversary can or cannot adaptively base its action on some auxiliary quantum side information. Our relation…

Inspired by the Elitzur-Vaidman bomb testing problem [arXiv:hep-th/9305002], we introduce a new query complexity model, which we call bomb query complexity $B(f)$. We investigate its relationship with the usual quantum query complexity…

Quantum phase estimation is one of the most important tools in quantum algorithms. It can be made non-adaptive (meaning all applications of the unitary $U_\phi$ happen simultaneously) without using more applications of $U_\phi$, albeit at…

We provide new lower bounds on the regret that must be suffered by adversarial bandit algorithms. The new results show that recent upper bounds that either (a) hold with high-probability or (b) depend on the total lossof the best arm or (c)…

We present a quantum algorithm for systems of (possibly inhomogeneous) linear ordinary differential equations with constant coefficients. The algorithm produces a quantum state that is proportional to the solution at a desired final time.…

The streams of research on adversarial examples and counterfactual explanations have largely been growing independently. This has led to several recent works trying to elucidate their similarities and differences. Most prominently, it has…

Adversarial examples are a pervasive phenomenon of machine learning models where seemingly imperceptible perturbations to the input lead to misclassifications for otherwise statistically accurate models. In this paper we study how the…

Quantum algorithms for graph problems are considered, both in the adjacency matrix model and in an adjacency list-like array model. We give almost tight lower and upper bounds for the bounded error quantum query complexity of Connectivity,…