Related papers: An upper bound on the number of frequency hypercub…
The $n$-queens problem is to determine $\mathcal{Q}(n)$, the number of ways to place $n$ mutually non-threatening queens on an $n \times n$ board. We show that there exists a constant $\alpha = 1.942 \pm 3 \times 10^{-3}$ such that…
The $n$-hypercube, denoted by $Q_n$, has a vertex for each bit string of length $n$ with two vertices adjacent whenever their Hamming distance is one. The minimum number of colors needed to color $Q_n$ such that no two vertices at a…
A laser frequency combs is a broad spectrum composed of equidistant narrow lines. Initially invented for frequency metrology, such combs enable new approaches to spectroscopy over broad spectral bandwidths, of particular relevance to…
The repetition code is an important primitive for the techniques of quantum error correction. Here we implement repetition codes of at most $15$ qubits on the $16$ qubit \emph{ibmqx3} device. Each experiment is run for a single round of…
A Cullen number is a number of the form $m2^m+1$, where $m$ is a positive integer. In 2004, Luca and St\u anic\u a proved, among other things, that the largest Fibonacci number in the Cullen sequence is $F_4=3$. Actually, they searched for…
A collection of hyperplanes $\mathcal{H}$ slices all edges of the $n$-dimensional hypercube $Q_n$ with vertex set $\{-1,1\}^n$ if, for every edge $e$ in the hypercube, there exists a hyperplane in $\mathcal{H}$ intersecting $e$ in its…
The Fibonacci cube $\Gamma_n$ is the subgraph of the hypercube induced by the binary strings that contain no two consecutive 1's. The Lucas cube $\Lambda_n$ is obtained from $\Gamma_n$ by removing vertices that start and end with 1. We…
An $(m,n,R)$-de Bruijn covering array (dBCA) is a doubly periodic $M \times N$ array over an alphabet of size $q$ such that the set of all its $m \times n$ windows form a covering code with radius $R$. An upper bound of the smallest array…
Frequency-selective readout for superconducting qubits opens the way towards scaling qubit circuits up without increasing the number of measurement lines. Here we demonstrate the readout of an array of 7 flux qubits located on the same…
Over the last two decades, frequency combs have brought breakthroughs in length metrology with traceability to length standards. In particular, frequency-comb-based spectral interferometry is regarded as a promising technology for…
For any given alphabet of size $q$, a Homopolymer Free code (HF code) refers to an $(n, M, d)_q$ code of length $n$, size $M$ and minimum Hamming distance $d$, where all the codewords are homopolymer free sequences. For any given alphabet,…
First we consider families in the hypercube $Q_n$ with bounded VC dimension. Frankl raised the problem of estimating the number $m(n,k)$ of maximal families of VC dimension $k$. Alon, Moran and Yehudayoff showed that…
We introduce a new analysis technique to derive a single-letter upper bound on the mismatch capacity of a stationary, single-user, memoryless channel with a decoding metric $q$. Our bound is obtained by considering a multicast transmission…
A $\{00,01,10,11\}$-valued function on the vertices of the $n$-cube is called a $t$-resilient $(n,2)$-function if it has the same number of $00$s, $01$s, $10$s and $11$s among the vertices of every subcube of dimension $t$. The Friedman and…
Among the objectives toward large-scale quantum computation is the quantum interconnect: a device which uses photons to interface qubits that otherwise could not interact. However, current approaches require photons indistinguishable in…
The ability of a quantum computer to reproduce or replicate the results of a quantum circuit is a key concern for verifying and validating applications of quantum computing. Statistical variations in circuit outcomes that arise from…
In this paper, we address a particular variation of the Tur\'an problem for the hypercube. Alon, Krech and Szab\'o (2007) asked "In an n-dimensional hypercube, Qn, and for l < d < n, what is the size of a smallest set, S, of Q_l's so that…
We introduce the hemicubic codes, a family of quantum codes obtained by associating qubits with the $p$-faces of the $n$-cube (for $n>p$) and stabilizer constraints with faces of dimension $(p\pm1)$. The quantum code obtained by identifying…
The Quantum-Enhanced Space-Time (QUEST) experiment consists of a pair of co-located Power Recycled Michelson Interferometers, each designed to have a broadband, shot-noise limited displacement sensitivity of $2\times10^{-19}$…
We briefly review known results on upper bounds for the minimal domination number $\gamma_n$ of a hypercube of dimension $n$, then present a new method for constructing dominating sets. Write $n =2^{\hat{n}}-1 +{\check{n}}$ with $0\leq…