Related papers: Quantum Property Testing Algorithm for the Concate…
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 apply our recent work on empirical estimates of quantum speedups to the practical task of community detection in complex networks. We design several quantum variants of a popular classical algorithm -- the Louvain algorithm for community…
Testing the symmetries of quantum states and channels provides a way to assess their usefulness for different physical, computational, and communication tasks. Here, we establish several complexity-theoretic results that classify the…
We study the quantum query complexity of finding a certificate for a d-regular, k-level balanced NAND formula. Up to logarithmic factors, we show that the query complexity is Theta(d^{(k+1)/2}) for 0-certificates, and Theta(d^{k/2}) for…
It is well known that quantum, randomized and deterministic (sequential) query complexities are polynomially related for total boolean functions. We find that significantly larger separations between the parallel generalizations of these…
We consider the problem of implementing two-party interactive quantum communication over noisy channels, a necessary endeavor if we wish to fully reap quantum advantages for communication. For an arbitrary protocol with $n$ messages,…
We study the power of nonadaptive quantum query algorithms, which are algorithms whose queries to the input do not depend on the result of previous queries. First, we show that any bounded-error nonadaptive quantum query algorithm that…
The set equality problem is to tell whether two sets $A$ and $B$ are equal or disjoint under the promise that one of these is the case. This problem is related to the Graph Isomorphism problem. It was an open problem to find any $\omega(1)$…
We present a quantum augmented variant of the dual lattice attack on the Learning with Errors (LWE) problem, using classical memory with quantum random access (QRACM). Applying our results to lattice parameters from the literature, we find…
Machine learning algorithms perform well on identifying patterns in many different datasets due to their versatility. However, as one increases the size of the dataset, the computation time for training and using these statistical models…
This paper shows how a basic property of unitary transformations can be used for meaningful computations. This approach immediately leads to search-type applications, where it improves the number of steps by a square-root - a simple minded…
Property-based testing has been previously proposed for quantum programs in Q# with QSharpCheck; however, this implementation was limited in functionality, lacked extensibility, and was evaluated on a narrow range of programs using a single…
A recent breakthrough by Ambainis, Balodis, Iraids, Kokainis, Pr\=usis and Vihrovs (SODA'19) showed how to construct faster quantum algorithms for the Traveling Salesman Problem and a few other NP-hard problems by combining in a novel way…
The Maximum Matching problem has a quantum query complexity lower bound of $\Omega(n^{3/2})$ for graphs on $n$ vertices represented by an adjacency matrix. The current best quantum algorithm has the query complexity $O(n^{7/4})$, which is…
Linear regression is a basic and widely-used methodology in data analysis. It is known that some quantum algorithms efficiently perform least squares linear regression of an exponentially large data set. However, if we obtain values of the…
Quantum algorithms can deliver asymptotic speedups over their classical counterparts. However, there are few cases where a substantial quantum speedup has been worked out in detail for reasonably-sized problems, when compared with the best…
We present a simple sublinear time algorithm for testing the following geometric property. Let $P_1, ..., P_n$ be $n$ convex sets in $\mathbb{R}^d$ ($n \gg d$), such as polytopes, balls, etc. We assume that the complexity of each set…
We propose a fault-tolerant quantum computation scheme that is broadly applicable to quantum low-density parity-check (qLDPC) codes. The scheme achieves constant qubit overhead and a time overhead of $O(d^{a+o(1)})$ for any $[[n,k,d]]$…
Given a non-negative $n \times n$ matrix viewed as a set of distances between $n$ points, we consider the property testing problem of deciding if it is a metric. We also consider the same problem for two special classes of metrics, tree…
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…