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In a recent paper, PNAS, 118, e1921529118 (2021), it was argued that while the standard definition of conservation laws in quantum mechanics, which is of a statistical character, is perfectly valid, it misses essential features of nature…
Up to now every good quantum error-correcting code discovered has had the structure of an eigenspace of an Abelian group generated by tensor products of Pauli matrices; such codes are known as stabilizer or additive codes. In this letter we…
Adiabatic quantum computing (AQC) can be protected against thermal excitations via an encoding into error detecting codes, supplemented with an energy penalty formed from a sum of commuting Hamiltonian terms. Earlier work showed that it is…
We calculated ab initio the three-fold differential cross section of a double single-photon Helium photoionization at equal energy sharing, and obtained from one the Gaussian width parameter, describing the angular interelectron…
A possible solution to the observed baryon asymmetry in the universe is described, based on the physics of the standard model of electroweak interactions. At temperatures high enough electroweak physics provides violation of baryon number,…
We study energy scaling laws for a simplified, singularly perturbed, double-well nucleation problem confined in a half-space, in the absence of gauge invariance and for an inclusion of fixed volume. Motivated by models for boundary…
The GW approximation for the electronic self-energy is an important tool for the quantitative prediction of excited states in solids, but its mathematical exploration is hampered by the fact that it must, in general, be evaluated…
We provide state-dependent error bounds for strongly continuous unitary representations of connected Lie groups. That is, we bound the difference of two unitaries applied to a state in terms of the energy with respect to a reference…
We prove a general lower bound to the spectral gap of the Davies generator for Hamiltonians that can be written as the sum of commuting Pauli operators. These Hamiltonians, defined on the Hilbert space of $N$-qubits, serve as one of the…
We study the quantum mechanical many-body problem of $N$ nonrelativistic electrons interacting with their self-generated classical electromagnetic field and $K$ static nuclei. The system of coupled equations governing the dynamics of the…
We develop an analytical expression for the self-energy of the infinite-dimensional Hubbard model that is correct in a number of different limits. The approach represents a generalization of the iterative perturbation theory to arbitrary…
Current approaches for building quantum computing devices focus on two-level quantum systems which nicely mimic the concept of a classical bit, albeit enhanced with additional quantum properties. However, rather than artificially limiting…
We treat a quantum mechanical system with certain general properties which are expected to be common in macroscopic quantum systems. Starting from a PURE initial state (which may not describe an equilibrium) in which energy is mildly…
We define and investigate a notion of entropy for quantum error correcting codes. The entropy of a code for a given quantum channel has a number of equivalent realisations, such as through the coefficients associated with the Knill-Laflamme…
In this article, we study the impact of self-interaction and multiparticle states on sustaining negative energies in relativistic quantum systems. For physically reasonable models, one usually requires bounds on both magnitude and duration…
The energy correction associated with the self-energy diagram is the leading (in magnitude) and fundamental (in significance) contribution to the Lamb shift in highly charged ions. Conventional approaches to this correction rely on…
One version of the energy-time uncertainty principle states that the minimum time $T_{\perp}$ for a quantum system to evolve from a given state to any orthogonal state is $h/(4 \Delta E)$ where $\Delta E$ is the energy uncertainty. A…
A solution to the quantum Zermelo problem for control Hamiltonians with general energy resource bounds is provided. Interestingly, the energy resource of the control Hamiltonian and the control time define a pair of conjugate variables that…
We show a practical application of the Jarzynski equality in quantum computation. Its implementation may open a way to solve combinatorial optimization problems, minimization of a real single-valued function, cost function, with many…
In this work, we present a general theoretical framework for the study of autonomously corrected quantum devices. First, we identify a necessary and sufficient revised version of the Knill-Laflamme conditions for the existence of an…