Related papers: A Survey of Quantum Property Testing
A language L has a property tester if there exists a probabilistic algorithm that given an input x only asks a small number of bits of x and distinguishes the cases as to whether x is in L and x has large Hamming distance from all y in L.…
In this paper, we study the following question: given a black box performing some unknown quantum measurement on a multi-qudit system, how do we test whether this measurement has certain property or is far away from having this property. We…
A fundamental problem in statistics and learning theory is to test properties of distributions. We show that quantum computers can solve such problems with significant speed-ups. In particular, we give fast quantum algorithms for testing…
The goal of property testing is to quickly distinguish between objects which satisfy a property and objects that are $\epsilon$-far from satisfying the property. There are now several general results in this area which show that natural…
We describe two procedures which, given access to one copy of a quantum state and a sequence of two-outcome measurements, can distinguish between the case that at least one of the measurements accepts the state with high probability, and…
Understanding the power and limitations of classical and quantum information and how they differ is a fundamental endeavor. In property testing of distributions, a tester is given samples over a typically large domain $\{0,1\}^n$. An…
One of the main subjects of this paper is to study quantum property testing with local measurement. In particular, we establish a novel $\ell_2$ norm connection between quantum property testing problems and the corresponding distribution…
We present several new examples of speed-ups obtainable by quantum algorithms in the context of property testing. First, motivated by sampling algorithms, we consider probability distributions given in the form of an oracle $f:[n]\to[m]$.…
Although classical computing has excelled in a wide range of applications, there remain problems that push the limits of its capabilities, especially in fields like cryptography, optimization, and materials science. Quantum computing…
Property testing has been extensively studied and its target is to determine whether a given object satisfies a certain property or it is far from the property. In this paper, we construct an efficient quantum algorithm which tests if a…
A quantum computer (QC) can solve many computational problems more efficiently than a classic one. The field of QCs is growing: companies (such as DWave, IBM, Google, and Microsoft) are building QC offerings. We position that software…
We construct efficient or query efficient quantum property testers for two existential group properties which have exponential query complexity both for their decision problem in the quantum and for their testing problem in the classical…
Quantum computing offers significant speedups for simulating physical, chemical, and biological systems, and for optimization and machine learning. As quantum software grows in complexity, the classical simulation of quantum computers,…
Property testers are fast, randomized "election polling"-type algorithms that determine if an input (e.g., graph or hypergraph) has a certain property or is $\varepsilon$-far from the property. In the dense graph model of property testing,…
To guarantee the normal functioning of quantum devices in different scenarios, appropriate benchmarking tool kits are quite significant. Inspired by the recent progress on quantum state verification, here we establish a general framework of…
Quantum computers are becoming more mainstream. As more programmers are starting to look at writing quantum programs, they need to test and debug their code. In this paper, we discuss various use-cases for quantum computers, either…
Suppose one has access to oracles generating samples from two unknown probability distributions P and Q on some N-element set. How many samples does one need to test whether the two distributions are close or far from each other in the…
Quantum physics holds the promise of enabling certain tasks with better performance than possible when only classical resources are employed. The quantum phenomena present in many experiments signify nonclassical behavior, but do not always…
We review canonical experiments on systems that have pushed the boundary between the quantum and classical worlds towards much larger scales, and discuss their unique features that enable quantum coherence to survive. Because the types of…
The development of small-scale sensors and actuators enables the construction of smart matter in which physical properties of materials are controlled in a distributed manner. In this paper, we describe how quantum computers could provide…