Related papers: Elementary constructive approach to the higher-ran…
Studying the geometry of sets appearing in various problems of quantum information helps in understanding different parts of the theory. It is thus worthwhile to approach quantum mechanics from the angle of geometry -- this has already…
Known quantum error correction schemes are typically able to take advantage of only a limited class of classical error-correcting codes. Entanglement-assisted quantum error correction is a partial solution which made it possible to exploit…
We present methods for the numerical evaluation of the master integrals that appear in the calculation of scattering amplitudes at higher order in perturbative quantum field theory. We follow the general strategy of solving first-order…
Majorization uncertainty relations are derived for arbitrary quantum operations acting on a finite-dimensional space. The basic idea is to consider submatrices of block matrices comprised of the corresponding Kraus operators. This is an…
We investigate the structure of intersecting error-correcting codes, with a particular focus on their connection to matroid theory. We establish properties and bounds for intersecting codes with the Hamming metric and illustrate how these…
We formulate the unitary rational orbifold conformal field theories in the algebraic quantum field theory framework. Under general conditions, we show that the orbifold of a given unitary rational conformal field theories generates a…
Modular tensor categories are generalizations of the representation categories of quantum groups at roots of unity axiomatizing the properties necessary to produce 3-dimensional TQFTs. Although other constructions have since been found,…
We describe new implementations of quantum error correction that are continuous in time, and thus described by continuous dynamical maps. We evaluate the performance of such schemes using numerical simulations, and comment on the…
We consider the problem of joint estimation of structured inverse covariance matrices. We perform the estimation using groups of measurements with different covariances of the same unknown structure. Assuming the inverse covariances to span…
Connecting multiple smaller qubit modules by generating high-fidelity entangled states is a promising path for scaling quantum computing hardware. The performance of such a modular quantum computer is highly dependent on the quality and…
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.
Recent advances in quantum computers are demonstrating the ability to solve problems at a scale beyond brute force classical simulation. As such, a widespread interest in quantum algorithms has developed in many areas, with optimization…
Mapping quantum error correcting codes to classical disordered statistical mechanics models and studying the phase diagram of the latter has proven a powerful tool to study the fundamental error robustness and associated critical error…
Within the general context of the architecture in quantum computer design, this paper aims is to provide a general strategy to obtain a block-matrix representation of quantum gates applied to qubits placed in arbitrary positions over an…
We determine explicit quantum seeds for classes of quantized matrix algebras. Furthermore, we obtain results on centers and block diagonal forms {of these algebras.} In the case where $q$ is {an arbitrary} root of unity, this further…
Let ${\mathbf U}_q^-$ be the negative half of a quantum group of finite type. We construct the canonical basis of ${\mathbf U}_q^-$ by applying the folding theory of quantum groups, and piecewise linear parametrization of canonical basis.…
This guide offers suggestions/insights on uncertainty quantification of nuclear structure models. We discuss a simple approach to statistical error estimates, strategies to assess systematic errors, and show how to uncover…
We develop a layered quantum computer architecture, which is a systematic framework for tackling the individual challenges of developing a quantum computer while constructing a cohesive device design. We discuss many of the prominent…
Topologically quantum error corrected logical gates are complex. Chains of errors can form in space and time and diagonally in spacetime. It is highly nontrivial to determine whether a given logical gate is free of low weight combinations…
One of the main problems in random network coding is to compute good lower and upper bounds on the achievable cardinality of the so-called subspace codes in the projective space $\mathcal{P}_q(n)$ for a given minimum distance. The…