Related papers: Robust and Space-Efficient Dual Adversary Quantum …
We show that any boolean function can be evaluated optimally by a quantum query algorithm that alternates a certain fixed, input-independent reflection with a second reflection that coherently queries the input string. Originally introduced…
We study dynamic algorithms robust to adaptive input generated from sources with bounded capabilities, such as sparsity or limited interaction. For example, we consider robust linear algebraic algorithms when the updates to the input are…
We give a new version of the adversary method for proving lower bounds on quantum query algorithms. The new method is based on analyzing the eigenspace structure of the problem at hand. We use it to prove a new and optimal strong direct…
Adversarial training is a standard defense against malicious input perturbations in security-critical machine-learning systems. Its main burden is structural: before every parameter update, the current model must first be attacked to find a…
The quantum adversary method is a versatile method for proving lower bounds on quantum algorithms. It yields tight bounds for many computational problems, is robust in having many equivalent formulations, and has natural connections to…
We describe a method to upper bound the quantum query complexity of Boolean formula evaluation problems, using fundamental theorems about the general adversary bound. This nonconstructive method can give an upper bound on query complexity…
We present a quantum algorithmic routine that extends the realm of Grover-based heuristics for tackling combinatorial optimization problems with arbitrary efficiently computable objective and constraint functions. Building on previously…
The general adversary bound is a semi-definite program (SDP) that lower-bounds the quantum query complexity of a function. We turn this lower bound into an upper bound, by giving a quantum walk algorithm based on the dual SDP that has query…
Many quantum algorithms can be analyzed in a query model to compute Boolean functions where input is given by a black box. As in the classical version of decision trees, different kinds of quantum query algorithms are possible: exact,…
The polynomial and the adversary methods are the two main tools for proving lower bounds on query complexity of quantum algorithms. Both methods have found a large number of applications, some problems more suitable for one method, some for…
Machine learning algorithms are powerful tools for data driven tasks such as image classification and feature detection, however their vulnerability to adversarial examples - input samples manipulated to fool the algorithm - remains a…
This note complements the paper "One-Way Ticket to Las Vegas and the Quantum Adversary" (arxiv:2301.02003). I develop the ideas behind the adversary bound - universal algorithm duality therein in a different form, using the same perspective…
Despite their ever more widespread deployment throughout society, machine learning algorithms remain critically vulnerable to being spoofed by subtle adversarial tampering with their input data. The prospect of near-term quantum computers…
Given the widespread use of deep learning models in safety-critical applications, ensuring that the decisions of such models are robust against adversarial exploitation is of fundamental importance. In this thesis, we discuss recent…
The quantum adversary method is one of the most successful techniques for proving lower bounds on quantum query complexity. It gives optimal lower bounds for many problems, has application to classical complexity in formula size lower…
We propose a new method for proving lower bounds on quantum query algorithms. Instead of a classical adversary that runs the algorithm with one input and then modifies the input, we use a quantum adversary that runs the algorithm with a…
In the thesis, we use a recently developed tight characterisation of quantum query complexity, the adversary bound, to develop new quantum algorithms and lower bounds. Our results are as follows: * We develop a new technique for the…
Quantum algorithms can be analyzed in a query model to compute Boolean functions where input is given in a black box, but the aim is to compute function value for arbitrary input using as few queries as possible. In this paper we…
Quantum query complexity is known to be characterized by the so-called quantum adversary bound. While this result has been proved in the standard discrete-time model of quantum computation, it also holds for continuous-time (or…
Artificial Intelligence has achieved remarkable success across diverse application domains. However, its vulnerability to adversarial attacks poses significant challenges to reliability, security, and trustworthiness. Adversarial machine…