Related papers: Lower Bounds for Unitary Property Testing with Pro…
The uncertainty principle sets lower bound on the uncertainties of two incompatible observables measured on a particle. The uncertainty lower bound can be reduced by considering a particle as a quantum memory entangled with the measured…
We study quantum algorithms for verifying properties of the output probability distribution of a classical or quantum circuit, given access to the source code that generates the distribution. We consider the basic task of uniformity…
In this paper, we consider lower bounds on the query complexity for testing CSPs in the bounded-degree model. First, for any ``symmetric'' predicate $P:{0,1}^{k} \to {0,1}$ except \equ where $k\geq 3$, we show that every (randomized)…
The most elementary prepare-and-measure scenarios have no independent measurement inputs. No inputs mean that quantum advantages require two indispensable ingredients: shared entanglement and measurements that can be adapted to the…
We consider the problem of testing whether a Boolean function has Fourier degree $\leq k$ or it is $\epsilon$-far from any Boolean function with Fourier degree $\leq k$. We improve the known lower bound of $\Omega(k)$ \cite{BBM11,CGM10}, to…
Many quantitative properties of probabilistic programs can be characterized as least fixed points, but verifying their lower bounds remains a challenging problem. We present a new approach to lower-bound verification that exploits and…
We investigate the structure of quantum proof systems by establishing collapse results that reveal simplifications in their complexity landscape. By extending classical theorems such as the Karp-Lipton theorem to quantum settings and…
Sequential methods for quantum hypothesis testing offer significant advantages over fixed-length approaches, which rely on a predefined number of state copies. Despite their potential, these methods remain underexplored for unambiguous…
We consider the time and space required for quantum computers to solve a wide variety of problems involving matrices, many of which have only been analyzed classically in prior work. Our main results show that for a range of linear algebra…
We show that every construction of one-time signature schemes from a random oracle achieves black-box security at most $2^{(1+o(1))q}$, where $q$ is the total number of oracle queries asked by the key generation, signing, and verification…
The uncertainty principle sets a bound on our ability to predict the measurement outcomes of two incompatible observables which are measured on a quantum particle simultaneously. In quantum information theory, the uncertainty principle can…
We address the problem of checking query containment, a foundational problem in database research. Although extensively studied in theory research, optimization opportunities arising from query containment are not fully leveraged in…
Let a Boolean function be available as a black-box (oracle) and one likes to devise an algorithm to test whether it has certain property or it is $\epsilon$-far from having that property. The efficiency of the algorithm is judged by the…
We show that computational problem of testing the behaviour of quantum circuits is hard for the class of problems known as QMA that can be verified efficiently with a quantum computer. This result is a generalization of the techniques…
Properties of Boolean functions can often be tested much faster than the functions can be learned. However, this advantage usually disappears when testers are limited to random samples of a function $f$--a natural setting for data…
This paper develops general space-efficient methods for error reduction for unitary quantum computation. Consider a polynomial-time quantum computation with completeness $c$ and soundness $s$, either with or without a witness (corresponding…
In an ordinary quantum algorithm the gates are applied in a fixed order on the systems. The introduction of indefinite causal structures allows to relax this constraint and control the order of the gates with an additional quantum state. It…
In this article we give several new results on the complexity of algorithms that learn Boolean functions from quantum queries and quantum examples. Hunziker et al. conjectured that for any class C of Boolean functions, the number of quantum…
Testing can be key to software quality assurance. Automated verification may increase throughput and reduce human fallibility errors. Test scripts supply inputs, run programs and check their outputs mechanically using test oracles. In…
Recent advances in quantum technology have led to the development and manufacturing of experimental programmable quantum annealers that promise to solve certain combinatorial optimization problems of practical relevance faster than their…