Related papers: An upper bound on the number of frequency hypercub…
Frameproof codes are used to fingerprint digital data. It can prevent copyrighted materials from unauthorized use. In this paper, we study upper and lower bounds for $w$-frameproof codes of length $N$ over an alphabet of size $q$. The upper…
The advancement of technologies for the precise interrogation of molecules offers exciting possibilities for new studies in the realms of precision spectroscopy and quantum technologies. Experiments in these domains often address molecular…
Inspired by the coupled-layer construction of the X-Cube model, we introduce the X-Cube Floquet code, a dynamical quantum error-correcting code where the number of encoded logical qubits grows with system size. The X-Cube Floquet code is…
This paper is the first part of a two-part series in which we present results from an experimental demonstration of frequency regulation in a commercial building test facility. In Part I, we introduce the test facility and develop relevant…
Several upper bounds on the size of quantum codes are derived using the linear programming approach. These bounds are strengthened for the linear quantum codes.
How many edges can a quadrilateral-free subgraph of a hypercube have? This question was raised by Paul Erd\H{o}s about $27$ years ago. His conjecture that such a subgraph asymptotically has at most half the edges of a hypercube is still…
Scaling superconducting quantum processors is fundamentally limited by the escalating complexity of cryogenic wiring and the debilitating effects of microwave crosstalk and Purcell decay. This paper proposes the concept of…
The $n$-dimensional hypercube has $n+1$ distinct eigenvalues $n-2i$, $0\leq i\leq n$, with corresponding eigenspaces $U_i(n)$. In 2021 it was proved by the author that if a function with non-empty support belongs to the direct sum…
In this paper we provide explicit constructions of digital sequences over the finite field of order 2 in the infinite dimensional unit cube whose first $N$ points projected onto the first $s$ coordinates have $\mathcal{L}_q$ discrepancy…
High-coherence, fault-tolerant and scalable quantum computing architectures with unprecedented long coherence times, faster gates, low losses and low bit-flip errors may be one of the only ways forward to achieve the true quantum advantage.…
Frequency-multiplexing is an effective method to achieve resource-efficient superconducting qubit readout. Allowing multiple resonators to share a common feedline, the number of cables and passive components involved in the readout of a…
We consider the restricted subsets of $\mathbb{N}_n=\{1,2,\ldots,n\}$ with $q\geq1$ being the largest member of the set $\mathcal{Q}$ of disallowed differences between subset elements. We obtain new results on various classes of problem…
The optical microresonator-based frequency comb (microcomb) provides a versatile platform for nonlinear physics studies and has wide applications ranging from metrology to spectroscopy. Deterministic quantum regime is an unexplored aspect…
Let \mathbb{F}_q^{n+l} denote the (n+l)-dimensional singular linear space over a finite field \mathbb{F}_q. For a fixed integer m\leq\min\{n,l\}, denote by \mathcal{L}^m_o(\mathbb{F}_q^{n+l}) the set of all subspaces of type (t,t_1), where…
The Fourier transform of the observed magnetic quantum oscillations (MQO) in YBa$_{2}$Cu$_{3}$O$_{6+\delta }$ high-temperature superconductors has a prominent low-frequency peak with two smaller neighbouring peaks. The separation and…
Optical frequency combs are key to optical precision measurements. While most frequency combs operate in the near-infrared regime, many applications require combs at mid-infrared, visible or even ultra-violet wavelengths. Frequency combs…
The network paradigm for quantum computing involves interconnecting many modules to form a scalable machine. Typically it is assumed that the links between modules are prone to noise while operations within modules have significantly higher…
We derive a universal performance limit for coherent quantum control in the presence of modeled and unmodeled uncertainties. For any target unitary $W$ that is implementable in the absence of error, we prove that the worst-case (and hence…
We establish general limits on how precise a parameter, e.g. frequency or the strength of a magnetic field, can be estimated with the aid of full and fast quantum control. We consider uncorrelated noisy evolutions of N qubits and show that…
A perfect $k$-coloring of the Boolean hypercube $Q_n$ is a function from the set of binary words of length $n$ onto a $k$-set of colors such that for any colors $i$ and $j$ every word of color $i$ has exactly $S(i,j)$ neighbors (at Hamming…