Related papers: An upper bound on the number of frequency hypercub…
Quantum error correction is widely believed to be essential for large-scale quantum computation, but the required qubit overhead remains a central challenge. Quantum low-density parity-check codes can substantially reduce this overhead…
Quantum Frequency Conversion (QFC) is a widely used technique to interface atomic systems with the telecom band in order to facilitate propagation over longer distances in fiber. Here we demonstrate the difference-frequency conversion from…
Cluster states with higher-dimensional lattices that cannot be physically embedded in three-dimensional space have important theoretical interest in quantum computation and quantum simulation of topologically ordered condensed-matter…
The {\em Fibonacci cube} of dimension $n$, denoted as $\Gamma\_n$, is the subgraph of the $n$-cube $Q\_n$ induced by vertices with no consecutive 1's. In an article of 2016 Ashrafi and his co-authors proved the non-existence of perfect…
The bandwidth of a graph is the labeling of vertices with minimum maximum edge difference. For many graph families this is NP-complete. A classic result computes the bandwidth for the hypercube. We generalize this result to give sharp lower…
As techniques for fault-tolerant quantum computation keep improving, it is natural to ask: what is the fundamental lower bound on redundancy? In this paper, we obtain a lower bound on the redundancy required for $\epsilon$-accurate…
Mid infrared (MIR) photonics is a key region for molecular physics [1]. High-resolution spectroscopy in the 1--10 {\mu}m region, though, has never been fully tackled for the lack of widely-tunable and practical light sources. Indeed, all…
The fluctuations exhibited by the cross-sections generated in a compound-nucleus reaction or, more generally, in a quantum-chaotic scattering process, when varying the excitation energy or another external parameter, are characterized by…
High-fidelity control of superconducting qubits requires the generation of microwave-frequency pulses precisely tailored on nanosecond timescales. These pulses are most commonly synthesized by up-converting and superimposing two narrow-band…
In multi-qubit superconducting systems utilizing flip-chip technology, achieving high accuracy in resonator frequencies is of paramount importance, particularly when multiple resonators share a common Purcell filter with restricted…
We study subsets of $\mathbb{F}_p^n$ that do not contain progressions of length $k$. We denote by $r_k(\mathbb{F}_p^n)$ the cardinality of such subsets containing a maximal number of elements. In this paper we focus on the case $k=p$ and…
The mds (maximum distance separable) conjecture claims that a nontrivial linear mds $[n,k]$ code over the finite field $GF(q)$ satisfies $n \leq (q + 1)$, except when $q$ is even and $k = 3$ or $k = q- 1$ in which case it satisfies $n \leq…
Flash memory is a non-volatile computer memory comprising blocks of cells, wherein each cell can take on q different values or levels. While increasing the cell level is easy, reducing the level of a cell can be accomplished only by erasing…
Large-scale quantum computation will only be achieved if experimentally implementable quantum error correction procedures are devised that can tolerate experimentally achievable error rates. We describe a quantum error correction procedure…
We consider a molecular channel, in which messages are encoded to the frequency of objects (or concentration of molecules) in a pool, and whose output during reading time is a noisy version of the input frequencies, as obtained by sampling…
Let $Q$ be an ideal (downward-closed set) in the lattice of linear subspaces of $(\mathbb F_q)^n$, ordered by inclusion. For $0 \le k \le n$, let $\mu_k(Q)$ denote the fraction of $k$-dimensional subspaces that belong to $Q$. We show that…
We consider the problem of constructing Latin cubes subject to the condition that some symbols may not appear in certain cells. We prove that there is a constant $\gamma > 0$ such that if $n=2t$ and $A$ is a $3$-dimensional $n\times n\times…
The mid-infrared spectral range (2 to 20 \mu m) is of particular importance for chemistry, biology and physics as many molecules exhibit strong ro-vibrational fingerprints. Frequency combs - broad spectral bandwidth coherent light sources…
The $k$'th frequency moment of a sequence of integers is defined as $F_k = \sum_j n_j^k$, where $n_j$ is the number of times that $j$ occurs in the sequence. Here we study the quantum complexity of approximately computing the frequency…
We describe a possible new technique for precise wavelength calibration of high-resolution astronomical spectrographs using femtosecond-pulsed mode-locked lasers controlled by stable oscillators such as atomic clocks. Such `frequency combs'…