Related papers: Quantum Field Theory Universality Criterion for La…
Quantum embedding methods enable the study of large, strongly correlated quantum systems by (usually self-consistent) decomposition into computationally manageable subproblems, in the spirit of divide-and-conquer methods. Among these,…
Quantum mechanics/molecular mechanics (QM/MM) hybrid models allow one to address chemical phenomena in complex molecular environments. Whereas this modeling approach can cope with a large system size at moderate computational costs, the…
An arbitrary lossless transformation in high-dimensional quantum space can be decomposed into elementary operations which are easy to implement, and an effective decomposition algorithm is important for constructing high-dimensional…
To generate arbitrary one- and two-qubit gates, the universal decompositions are usually used in quantum computing, and the universality of these decompositions has been demonstrated. However, in realistic experiments, gate errors may…
Decoding algorithms are essential to fault-tolerant quantum-computing architectures. In this perspective we explore decoding algorithms for the surface code; a prototypical quantum low-density parity-check code that underlies many of the…
The Quantum Query Model is a framework that allows us to express most known quantum algorithms. Algorithms represented by this model consist on a set of unitary operators acting over a finite Hilbert space, and a final measurement step…
We discuss the issues with tentative generalisations of the process matrix formalism from finite-dimensional mechanical systems all the way to quantum field theory. We present a detailed overview of possible open problems that arise when…
Many fundamental and key objects in quantum mechanics are linear mappings between particular affine/linear spaces. This structure includes basic quantum elements such as states, measurements, channels, instruments, non-signalling channels…
We calculate the decomposition series of the D-module defined as the push-forward of a rank one linear system on the complement of a normal crossings hyperplane configuration and use data of a resolution of singularities to give a…
We construct and investigate quantum fields induced on a d-dimensional dissipationless defect by bulk fields propagating in a (d+1)-dimensional space. All interactions are localized on the defect. We derive a unitary non-canonical quantum…
A new attempt is demonstrated that QFTs can be UV finite if they are viewed as the low energy effective theories of a fundamental underlying theory (that is complete and well-defined in all respects) according to the modern standard point…
A general theory of preparational uncertainty relations for a quantum particle in one spatial dimension is developed. We derive conditions which determine whether a given smooth function of the particle's variances and its covariance is…
A generalization of the Heisenberg algebra has been recently constructed. This generalized algebra has a characteristic function which depends on one of its generators. When this function is linear, $qJ_0+s$, it is possible to construct a…
Accurate representations of unknown and sub-grid physical processes through parameterizations (or closure) in numerical simulations with quantified uncertainty are critical for resolving the coarse-grained partial differential equations…
The paper proved that every $C^2$-solution of a given first order PDEs system, regarded on the jet fibre bundle of order one $J^1(T,M)$, may be viewed as a "generalized harmonic map", via the least squares variational method. Our ideas are…
We discuss the use of field theory for the exact determination of universal properties in two-dimensional statistical mechanics. After a compact derivation of critical exponents of main universality classes, we turn to the off-critical…
In this article we study the deformation of finite maps and show how to use this deformation theory to construct varieties with given invariants in a projective space. Among other things, we prove a criterion that determines when a finite…
We expect quantum field theories for matter to acquire intricate corrections due to their coupling to quantum fluctuations of the gravitational field. This can be precisely worked out in 3d quantum gravity: after integrating out quantum…
We prove a general decomposition theorem for the modal $\mu$-calculus $L_\mu$ in the spirit of Feferman and Vaught's theorem for disjoint unions. In particular, we show that if a structure (i.e., transition system) is composed of two…
We construct an image formation theory that covers the majority of optical microscopy techniques that use diverse coherent or incoherent light-matter interactions. The theories of individual microscopy methods could not previously be…