Related papers: Unitarization of Pseudo-Unitary Quantum Circuits i…
We study bipartite unitary operators which stay invariant under the local actions of diagonal unitary and orthogonal groups. We investigate structural properties of these operators, arguing that the diagonal symmetry makes them suitable for…
We present an algorithm to solve the Simultaneous Unitary Similarity(S.U.S) problem which is to check if there exists a Similarity transformation determined by a Unitary $U$ s.t $UA_lU^*=B_l$, $l \in \{1,...,p\}$, where $A_l$ and $B_l$ are…
A phenomenological Hamiltonian of a closed (i.e., unitary) quantum system is assumed to have an $N$ by $N$ real-matrix form composed of a unperturbed diagonal-matrix part $H^{(N)}_0$ and of a tridiagonal-matrix perturbation…
In this short note, we prove a formula for the group inverse of a block matrix and consider the pseudo principal pivot transform expressed in terms of group inverses. Extensions of the usual principal pivot transform, where the usual…
We study implications of unitarity for pseudo-orbit expansions of the spectral determinants of quantum maps and quantum graphs. In particular, we advocate to group pseudo-orbits into sub-determinants. We show explicitly that the…
The design and optimization of quantum circuits is central to quantum computation. This paper presents new algorithms for compiling arbitrary 2^n x 2^n unitary matrices into efficient circuits of (n-1)-controlled single-qubit and…
A set of four factorizable non-relativistic S-matrices for a multiplet of fundamental particles are defined based on the R-matrix of the quantum group deformation of the centrally extended superalgebra su(2|2). The S-matrices are a function…
A systematic approach to dualities in symmetric (1+1)d quantum lattice models has recently been proposed in terms of module categories over the symmetry fusion categories. By characterizing the non-trivial way in which dualities intertwine…
In this work, we investigate the consistency of a perturbative definition of the S-matrix in a particular class of non-Lagrangian theories. We focus on the $p$-form theories proposed in \cite{Broccoli:2021pvv}, which are fully defined by…
The work proposes an extension of the quantum circuit formalism where qubits (wires) are circular instead of linear. The left-to-right interpretation of a quantum circuit is replaced by a circular representation which allows to select the…
The implementation of physical symmetries into problem descriptions allows for the reduction of parameters and computational complexity. We show the integration of the permutation symmetry as the most restrictive discrete symmetry into…
By studying the minimum resources required to perform a unitary transformation, families of metrics and pseudo-metrics on unitary matrices that are closely related to a recently reported quantum speed limit by the author are found.…
One-way measurement based quantum computations (1WQC) may describe unitary transformations, via a composition of CPTP maps which are not all unitary themselves. This motivates the following decision problems: Is it possible to determine…
The development of large-scale, programmable photonic circuits capable of performing generic matrix-vector multiplication is essential for both classical and quantum information processing. However, this goal is hindered by high losses,…
Near-term quantum devices generally suffer from shallow circuit depth and hence limited expressivity due to noise and decoherence. To address this, we propose tensor-network-assisted parametrized quantum circuits, which concatenate a…
In this work, we study distributions of unitaries generated by random quantum circuits containing only symmetry-respecting gates. We develop a unified approach applicable to all symmetry groups and obtain an equation that determines the…
We consider the effects of plane-wave states scattering off finite graphs, as an approach to implementing single-qubit unitary operations within the continuous-time quantum walk framework of universal quantum computation. Four semi-infinite…
The subject of this thesis is the rigorous construction of QFT models with nontrivial interaction. Two different approaches in the framework of AQFT are discussed. On the one hand, an inverse scattering problem is considered. A given…
Random matrices in the large N expansion and the so-called double scaling limit can be used as toy models for quantum gravity: 2D quantum gravity coupled to conformal matter. This has generated a tremendous expansion of random matrix…
While quantum circuits built from two-particle dual-unitary (maximally entangled) operators serve as minimal models of typically nonintegrable many-body systems, the construction and characterization of dual-unitary operators themselves are…