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Recent works have independently suggested that Quantum Mechanics might permit for procedures that transcend the power of Turing Machines as well as of `standard' Quantum Computers. These approaches rely on and indicate that Quantum…
Quantum mechanics for a four-state-system is derived from classical statistics. Entanglement, interference, the difference between identical fermions or bosons and the unitary time evolution find an interpretation within a classical…
We present a new approach for numerical solutions of ab initio quantum chemistry systems. The main idea of the approach, which we call canonical diagonalization, is to diagonalize directly the second quantized Hamiltonian by a sequence of…
An example is presented when decoherence and quantum interference gives rise to narrow eigenstates (in coordinate representation) for the reduced density matrix of macroscopic quantum systems. On the basis of modal interpretations this…
Effective classicality of a property of a quantum system can be defined using redundancy of its record in the environment. This allows quantum physics to approximate the situation encountered in the classical world: The information about a…
A theory of transformation is presented for the diagonalization of a Hamiltonian that is quadratic in creation and annihilation operators or in coordinates and momenta. It is the systemization and theorization of Dirac and…
Some physical aspects related to the limit operations of the Thomson lamp are discussed. Regardless of the formally unbounded and even infinite number of "steps" involved, the physical limit has an operational meaning in agreement with the…
A new approach to quantum mechanics based on independence of the Continuum Hypothesis is proposed. In one-dimensional case, it is shown that the properties of the set of intermediate cardinality coincide with quantum phenomenology.
An approach to study a generalization of the classical-quantum transition for general systems is proposed. In order to develop the idea, a deformation of the ladder operators algebra is proposed that contains a realization of the quantum…
A formulation of quantum mechanics with additive and multiplicative (q-)difference operators instead of differential operators is studied from first principles. Borel-quantisation on smooth configuration spaces is used as guiding…
Algorithmic approach is based on the assumption that any quantum evolution of many particle system can be simulated on a classical computer with the polynomial time and memory cost. Algorithms play the central role here but not the…
Quantifying the resources available to a quantum computer appears to be necessary to separate quantum from classical computation. Among them, entanglement, nonstabilizerness and coherence are arguably of great significance. We introduce…
Classical machine learning theory and theory of quantum computations are among of the most rapidly developing scientific areas in our days. In recent years, researchers investigated if quantum computing can help to improve classical machine…
The use of the quantizer-dequantizer formalism to describe the evolution of a quantum system is reconsidered. We show that it is possible to embed a manifold in the space of quantum states of a given auxiliary system by means of an…
We study the entanglement of unitary operators on $d_1\times d_2$ quantum systems. This quantity is closely related to the entangling power of the associated quantum evolutions. The entanglement of a class of unitary operators is quantified…
A hybrid formalism is proposed for interacting classical and quantum sytems. This formalism is mathematically consistent and reduces to standard classical and quantum mechanics in the case of no interaction. However, in the presence of…
Quantum entanglement of identical particles is essential in quantum information theory. Yet, its correct determination remains an open issue hindering the general understanding and exploitation of many-particle systems. Operator-based…
To measure an observable of a quantum mechanical system leaves it in one of its eigenstates and the result of the measurement is one of its eigenvalues. This process is shown to be a computational resource. It allows one, in principle, to…
We consider a set of N linearly coupled harmonic oscillators and show that the diagonalization of this problem can be put in geometrical terms. The matrix techniques developed here allowed for solutions in both the classical and quantum…
We present a novel automated technique for parallelizing quantum circuits via forward and backward translation to measurement-based quantum computing patterns and analyze the trade off in terms of depth and space complexity. As a result we…