Related papers: Decomposing large unitaries into multimode devices…
We investigate decoupling, one of the most important primitives in quantum Shannon theory, by replacing the uniformly distributed random unitaries commonly used to achieve the protocol, with repeated applications of random unitaries…
World models have been recently proposed as sandbox environments in which AI agents can be trained and evaluated before deployment. While realistic world models often have high computational demands, this can often be alleviated by…
We present a general method for decomposing non-unitary operators into a linear combination of unitary operators, where the approximation error decays exponentially. The decomposition is based on a smooth periodic extension of the identity…
Birkhoff's theorem tells that any doubly stochastic matrix can be decomposed as a weighted sum of permutation matrices. A similar theorem reveals that any unitary matrix can be decomposed as a weighted sum of complex permutation matrices.…
In a previous paper, we described a computer program called Qubiter which can decompose an arbitrary unitary matrix into elementary operations of the type used in quantum computation. In this paper, we describe a method of reducing the…
Having a broad range of methods available for implementing unitary operations is crucial for quantum information tasks. We study a dissipative process commonly used to describe dissipatively coupled systems and show that the process can…
The paper presents two algorithms for finding irreducible decomposition of monomial ideals. The first one is recursive, derived from staircase structures of monomial ideals. This algorithm has a good performance for highly non-generic…
To circumvent the high path loss of mmWave propagation and reduce the hardware cost of massive multiple-input multiple-output antenna systems, full-dimensional hybrid beamforming is critical in 5G and beyond wireless communications.…
The Quantum Fourier Transformation (QFT) is a well-known subroutine for algorithms on qubit-based universal quantum computers. In this work, the known QFT circuit is used to derive an efficient circuit for the multidimensional QFT. The…
Quantum computation promises significant computational advantages over classical computation for some problems. However, quantum hardware suffers from much higher error rates than in classical hardware. As a result, extensive quantum error…
Unitary transformations and density matrices are central objects in quantum physics and various tasks require to introduce them in a parameterized form. In the present article we present a parameterization of the unitary group…
A simple algorithm is presented to decompose any 1-loop amplitude for scattering processes of the class 2 fermions -> 4 fermions into a fixed number of gauge-invariant form factors. The structure of the amplitude is simpler than in the…
We propose an interpretation of quantum separability based on a physical principle: local time reversal. It immediately leads to a simple characterization of separable quantum states that reproduces results known to hold for binary…
In 1994, Reck et al. showed how to realize any unitary transformation on a single photon using a product of beamsplitters and phaseshifters. Here we show that any single beamsplitter that nontrivially mixes two modes, also densely generates…
We introduce a technique to decompose the scattered near field of two-dimensional arbitrary metaatoms into its multipole contributions. To this end we expand the scattered field upon plane wave illumination into cylindrical harmonics as…
Achieving high spectral efficiency in realistic massive multi-user (MU) multiple-input multiple-output (MIMO) wireless systems requires computationally-complex algorithms for data detection in the uplink (users transmit to base-station) and…
We present a new computationally efficient method for multi-beamforming in the broadband setting. Our "fast beamspace transformation" forms $B$ beams from $M$ sensor outputs using a number of operations per sample that scales linearly (to…
Methods to decompose nonlinear optical transformation vary from setting to setting, leading to apparent differences in the treatments used to model photon pair sources, compared to those used to model degenerate down-conversion processes.…
Decomposition is a common tool for synthesis of many physical systems. It is also used for analyzing large scale systems which then known as tearing and reconstruction. On the other hand, commutativity of cascade connected systems have…
The construction of multipartite unextendible product bases (UPBs) is a basic problem in quantum information. We respectively construct two families of $2\times2\times4$ and $2\times2\times2\times4$ UPBs of size eight by using the existing…