Related papers: A Block-Sensitivity Lower Bound for Quantum Testin…
Fidelity is a fundamental and ubiquitous concept in quantum information theory. Fuchs-van de Graaf's inequalities deal with bounding fidelity from above and below. In this paper, we give a lower bound on the quantum fidelity between two…
Independent parallel q-ary symmetric channels are a suitable transmission model for several applications. The proposed weighted-Hamming metric is tailored to this setting and enables optimal decoding performance. We show that some…
The hopes for scalable quantum computing rely on the "threshold theorem": once the error per qubit per gate is below a certain value, the methods of quantum error correction allow indefinitely long quantum computations. The proof is based…
The problem of bounding of the distance between the two bodies of volume $\varepsilon$ located inside the $n$-dimensional body $B$ of unit volume where $n \to \infty$ is considered. In some cases such distances are bounded by function…
We study variable time search, a form of quantum search where queries to different items take different time. Our first result is a new quantum algorithm that performs variable time search with complexity $O(\sqrt{T}\log n)$ where…
We study the problem of distinguishing between two symmetric probability distributions over $n$ bits by observing $k$ bits of a sample, subject to the constraint that all $k-1$-wise marginal distributions of the two distributions are…
In this paper we deal with the restricted Block Relocation Problem. We present a new lower bound and a heuristic approach for the problem. The proposed lower bound can be computed in polynomial time and it is provably better than some…
The closest string problem is an NP-hard problem, whose task is to find a string that minimizes maximum Hamming distance to a given set of strings. This can be reduced to an integer program (IP). However, to date, there exists no known…
Different candidates of Quantum Gravity such as String Theory, Doubly Special Relativity, Loop Quantum Gravity and black hole physics all predict the existence of a minimum observable length or a maximum observable momentum which modifies…
Rigorously establishing that the error in an experimental quantum operation is beneath the threshold for fault-tolerant quantum computation currently requires considering the worst-case error, which can be orders of magnitude smaller than…
The asymptotic discrimination problem of two quantum states is studied in the setting where measurements are required to be invariant under some symmetry group of the system. We consider various asymptotic error exponents in connection with…
The expressibility of an ansatz used in a variational quantum algorithm is defined as the uniformity with which it can explore the space of unitary matrices, i.e., its covering number. The expressibility of a particular ansatz has a…
The surface code is a promising candidate for fault-tolerant quantum computation, achieving a high threshold error rate with nearest-neighbor gates in two spatial dimensions. Here, through a series of numerical simulations, we investigate…
The problem of approximate string matching is important in many different areas such as computational biology, text processing and pattern recognition. A great effort has been made to design efficient algorithms addressing several variants…
We consider a hypothesis testing problem where a part of data cannot be observed. Our helper observes the missed data and can send us a limited amount of information about them. What kind of this limited information will allow us to make…
We develop generalized bounds for quantum single-parameter estimation problems for which the coupling to the parameter is described by intrinsic multi-system interactions. For a Hamiltonian with $k$-system parameter-sensitive terms, the…
Consider two problems about an unknown probability distribution $p$: 1. How many samples from $p$ are required to test if $p$ is supported on $n$ elements or not? Specifically, given samples from $p$, determine whether it is supported on at…
We develop a topological framework for proving lower bounds on sign-rank via $\mathbb{Z}_2$-equivariant topology, and use it to resolve the sign-rank of the Gap Hamming Distance problem up to lower-order terms. For every (partial) sign…
The polynomial method by Beals, Buhrman, Cleve, Mosca, and de Wolf (FOCS 1998, J. ACM 2001), the adversary method by Ambainis (STOC 2000, J. Comput. Syst. Sci. 2002), and the compressed oracle method by Zhandry (CRYPTO 2019) have been shown…
It is reasonable to expect the theory of quantum codes to be simplified in the case of codes of minimum distance 2; thus, it makes sense to examine such codes in the hopes that techniques that prove effective there will generalize. With…