Related papers: Variations on Quantum Adversary
We show how an algorithm for the problem of inverting a permutation may be used to design one for the problem of unordered search (with a unique solution). Since there is a straightforward reduction in the reverse direction, the problems…
In the permutation inversion problem, the task is to find the preimage of some challenge value, given oracle access to the permutation. This is a fundamental problem in query complexity, and appears in many contexts, particularly…
Quantum machine learning explores the interplay between machine learning and quantum physics, which may lead to unprecedented perspectives for both fields. In fact, recent works have shown strong evidences that quantum computers could…
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…
Quantum adversarial machine learning is an emerging field that studies the vulnerability of quantum learning systems against adversarial perturbations and develops possible defense strategies. Quantum universal adversarial perturbations are…
We describe new lower bounds for randomized communication complexity and query complexity which we call the partition bounds. They are expressed as the optimum value of linear programs. For communication complexity we show that the…
This paper employs a powerful argument, called an algorithmic argument, to prove lower bounds of the quantum query complexity of a multiple-block ordered search problem in which, given a block number i, we are to find a location of a target…
In the search with wildcards problem [Ambainis, Montanaro, Quantum Inf.~Comput.'14], one's goal is to learn an unknown bit-string $x \in \{-1,1\}^n$. An algorithm may, at unit cost, test equality of any subset of the hidden string with a…
We establish a lower bound of $\Omega{(\sqrt{n})}$ on the bounded-error quantum query complexity of read-once Boolean functions, providing evidence for the conjecture that $\Omega(\sqrt{D(f)})$ is a lower bound for all Boolean functions.…
We show that almost all n-bit Boolean functions have bounded-error quantum query complexity at least n/2, up to lower-order terms. This improves over an earlier n/4 lower bound of Ambainis, and shows that van Dam's oracle interrogation is…
The recently introduced quantum antibracket is further generalized allowing for the defining odd operator Q to be arbitrary. We give exact formulas for higher quantum antibrackets of arbitrary orders and their generalized Jacobi identities.…
We derive rigorous bounds on corrections to Einstein gravity using unitarity and analyticity of graviton scattering amplitudes. In $D\geq 4$ spacetime dimensions, these consistency conditions mandate positive coefficients for certain…
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…
Access to the time-reverse $U^{-1}$ of an unknown quantum unitary process $U$ is widely assumed in quantum learning, metrology, and many-body physics. The fundamental task of unitary time-reversal dictates implementing $U^{-1}$ to within…
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…
The entanglement content of superpositions of quantum states is investigated based on a measure called {\it concurrence}. Given a bipartite pure state in arbitrary dimension written as the quantum superposition of two other such states, we…
By leveraging the principles of quantum mechanics, QML opens doors to novel approaches in machine learning and offers potential speedup. However, machine learning models are well-documented to be vulnerable to malicious manipulations, and…
Quantum discord quantifies quantum correlations beyond entanglement and assumes nonzero values, which are notoriously hard to compute, for almost all quantum states. Here we provide computable tight bounds for the quantum discord for…
We developed new concentration inequalities for a quantum state on an $N$-qudit system or measurement outcomes on it that apply to an adversarial setup, where an adversary prepares the quantum state. Our one-sided concentration inequalities…
Recent progress in quantum field theory and quantum gravity relies on mixed boundary conditions involving both normal and tangential derivatives of the quantized field. In particular, the occurrence of tangential derivatives in the boundary…