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A powerful method for analyzing quantum error-correcting codes is to map them onto classical statistical mechanics models. Such mappings have thus far mostly focused on static codes, possibly subject to repeated syndrome measurements.…

The main purpose of thispaper is to show that composite quantum-like (QL) systems can closely mimic the separable states of quantum systems, and that suitable physical systems exhibiting these states exist. It is shown that QL graphs can…

We prove that on any two-dimensional lattice of qudits of a prime dimension, every translation invariant Pauli stabilizer group with local generators and with code distance being the linear system size, is decomposed by a local Clifford…

We consider the problem of a generic stabilizer Hamiltonian under local, incoherent Pauli errors. Using two different approaches -- (i) Haah's polynomial formalism arXiv:1204.1063 and (ii) the homological perspective on CSS codes -- we…

We show that real polarization method can be effectively used to geometrically quantize physical systems with compact phase space, like the spin. Our method enables us to construct a wave function of a qubit in both position and momentum…

We discuss phenomena of stabilization for direct images of line bundles over projective curves mapping onto the projective line, for maps of sufficiently big degree.

The various versions of cond-mat/0312353 discuss results obtained by me&coworkers in the last decade. I have received requests to comment on the paper and the comments are collected here, including some that I tried to point in the course…

Quantum error-correcting codes can be used to protect qubits involved in quantum computation. This requires that logical operators acting on protected qubits be translated to physical operators (circuits) acting on physical quantum states.…

The stabiliser fragment of quantum theory is a foundational building block for quantum error correction and the fault-tolerant compilation of quantum programs. In this article, we develop a sound, universal and complete denotational…

We consider the generalization of Haldane's state-counting procedure to describe all possible types of exclusion statistics which are linear in the deformation parameter $g$. The statistics are parametrized by elements of the symmetric…

In several recent papers on entanglement in relativistic quantum systems and relativistic Bell's inequalities, relativistic Bell-type two-particle states have been constructed in analogy to non-relativistic states. These constructions do…

We present a numerical method for the investigation of non-ergodic effects in the Coulomb glass. For that, an almost complete set of low-energy many-particle states is obtained by a new algorithm. The dynamics of the sample is mapped to the…

Paul traps are ion traps that are widely used in spectroscopic experiments to confine and stabilize a charged particle within a small region using oscillating electric fields. The dynamics of the particle inside a Paul trap is described by…

We formulate generalizations of Pauli's theorem on the cases of real and complex Clifford algebras of even and odd dimensions. We give analogues of these theorems in matrix formalism. Using these theorems we present an algorithm for…

We propose a heuristic method to obtain the approximate groundstate for a Hamiltonian in the qubit form, based on the stabilizer formalism. These states may serve as proper initial states for further refined computation. It would be…

We present a theoretical and experimental study of a photonic crystal based optical system in terms of weak values that map polarization states onto longitudinal spatial position and show fast and slow light behavior.

Quantifying experimentally created entanglement could in principle be accomplished by measuring the entire density matrix and calculating an entanglement measure of choice thereafter. Due to the tensor-structure of the Hilbert space, this…

Multipartite entanglement is a natural generalization of bipartite entanglement, but is relatively poorly understood. In this paper, we develop tools to calculate a class of multipartite entanglement measures - known as multi-invariants -…

Protecting information in systems that have more than two basis states (qudits) not only offers a promising route for reducing the number of individual quantum locations that must be protected, while more accurately reflecting the structure…

Quantum squeezing in mechanical systems is not only a key signature of macroscopic quantum effects, but can also be utilized to advance the metrology of weak forces. Here we show that strong mechanical squeezing in the steady state can be…