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Alexander I. Nesterov

Publications and source records attributed to Alexander I. Nesterov.

At least 37 records · Page 2Linked to original sources
arXiv2013

Non-Hermitian Quantum Annealing in the Ferromagnetic Ising Model

We developed a non-Hermitian quantum optimization algorithm to find the ground state of the ferromagnetic Ising model with up to 1024 spins (qubits). Our approach leads to significant reduction of the annealing time. Analytical and numerical results demonstrate that the total annealing time is proportional to ln N, where N is the number of spins. This encouraging result is important in using classical computers in combination with quantum algorithms for the fast solutions of NP-complete problems. Additional research is proposed for extending our dissipative algorithm to more complicated problems.

quant-ph↗
arXiv2013

Non-Hermitian Quantum Annealing in the Antiferromagnetic Ising Chain

A non-Hermitian quantum optimization algorithm is created and used to find the ground state of an antiferromagnetic Ising chain. We demonstrate analytically and numerically (for up to N=1024 spins) that our approach leads to a significant reduction of the annealing time that is proportional to $\ln N$, which is much less than the time (proportional to $N^2$) required for the quantum annealing based on the corresponding Hermitian algorithm. We propose to use this approach to achieve similar speed-up for NP-complete problems by using classical computers in combination with quantum algorithms.

quant-ph↗
arXiv2012

Quench dynamics in spin crossover induced by high pressure

In this paper we have studied analytically and numerically dynamics of spin crossover induced by time-dependent pressure. We show that quasi static pressure, with a slow dependence on time, yields a spin crossover leading to transition from the state of quantum system with high spin (HS) to the low spin (LS). However, a quench dynamics under shock-wave load is more complicated. The final state of the system depends on the amplitude and pulse velocity, resulting in the mixture of the HS and LS states.

cond-mat.str-el↗
arXiv2012

Quantum search using non-Hermitian adiabatic evolution

We propose a non-Hermitian quantum annealing algorithm which can be useful for solving complex optimization problems. We demonstrate our approach on Grover's problem of finding a marked item inside of unsorted database. We show that the energy gap between the ground and excited states depends on the relaxation parameters, and is not exponentially small. This allows a significant reduction of the searching time. We discuss the relations between the probabilities of finding the ground state and the survival of a quantum computer in a dissipative environment.

quant-ph↗
arXiv2012

Modeling of Low and High Frequency Noise by Slow and Fast Fluctuators

We study the dynamics of dephasing in a quantum two-level system by modeling both 1/f and high-frequency noise by random telegraph processes. Our approach is based on a so-called spin-fluctuator model in which a noisy environment is modeled by a large number of fluctuators. In the continuous limit we obtain an effective random process (ERP) that is described by a distribution function of the fluctuators. In a simplified model, we reduce the ERP to the two (slow and fast) ensembles of fluctuators. Using this model, we study decoherence in a superconducting flux qubit and we compare our theoretical results with the available experimental data. We demonstrate good agreement of our theoretical predictions with the experiments. Our approach can be applied to many quantum systems, such as biological complexes, semiconductors, superconducting and spin qubits, where the effects of interaction with the environment are essential.

quant-ph↗
arXiv2012

Non-Hermitian approach for modeling of noise-assisted quantum electron transfer in photosynthetic complexes

We model the quantum electron transfer (ET) in the photosynthetic reaction center (RC), using a non-Hermitian Hamiltonian approach. Our model includes (i) two protein cofactors, donor and acceptor, with discrete energy levels and (ii) a third protein pigment (sink) which has a continuous energy spectrum. Interactions are introduced between the donor and acceptor, and between the acceptor and the sink, with noise acting between the donor and acceptor. The noise is considered classically (as an external random force), and it is described by an ensemble of two-level systems (random fluctuators). Each fluctuator has two independent parameters, an amplitude and a switching rate. We represent the noise by a set of fluctuators with fitting parameters (boundaries of switching rates), which allows us to build a desired spectral density of noise in a wide range of frequencies. We analyze the quantum dynamics and the efficiency of the ET as a function of (i) the energy gap between the donor and acceptor, (ii) the strength of the interaction with the continuum, and (iii) noise parameters. As an example, numerical results are presented for the ET through the active pathway in a quinone-type photosystem II RC.

quant-ph↗
arXiv2010

Non-Hermitian description of a superconducting phase qubit measurement

We present an approach based on a non-Hermitian Hamiltonian to describe the process of measurement by tunneling of a phase qubit state. We derive simple analytical expressions which describe the dynamics of measurement, and compare our results with those experimentally available.

quant-ph↗
arXiv2009

Non-Hermitian Adiabatic Quantum Optimization

We propose a novel non-Hermitian adiabatic quantum optimization algorithm. One of the new ideas is to use a non-Hermitian auxiliary "initial'' Hamiltonian that provides an effective level repulsion for the main Hamiltonian. This effect enables us to develop an adiabatic theory which determines ground state much more efficiently than Hermitian methods.

quant-ph↗
arXiv2009

Non-Hermitian Quantum Systems and Time-Optimal Quantum Evolution

Recently, Bender et al. have considered the quantum brachistochrone problem for the non-Hermitian $\cal PT$-symmetric quantum system and have shown that the optimal time evolution required to transform a given initial state $|ψ_i\rangle$ into a specific final state $|ψ_f\rangle$ can be made arbitrarily small. Additionally, it has been shown that finding the shortest possible time requires only the solution of the two-dimensional problem for the quantum system governed by the effective Hamiltonian acting in the subspace spanned by $|ψ_i\rangle$ and $|ψ_f\rangle$. In this paper, we study a similar problem for the generic non-Hermitian Hamiltonian, focusing our attention on the geometric aspects of the problem.

quant-ph↗
arXiv2008

Geometric phases and quantum phase transitions in open systems

The relationship between quantum phase transition and complex geometric phase for open quantum system governed by the non-Hermitian effective Hamiltonian with the accidental crossing of the eigenvalues is established. In particular, the geometric phase associated with the ground state of the one-dimensional dissipative Ising model in a transverse magnetic field is evaluated, and it is demonstrated that related quantum phase transition is of the first order.

quant-ph↗
arXiv2005

Infinite-dimensional representations of the rotation group and Dirac's monopole problem

Within the context of infinite-dimensional representations of the rotation group the Dirac monopole problem is studied in details. Irreducible infinite-dimensional representations, being realized in the indefinite metric Hilbert space, are given by linear unbounded operators in infinite-dimensional topological spaces, supplied with a weak topology and associated weak convergence. We argue that an arbitrary magnetic charge is allowed, and the Dirac quantization condition can be replaced by a generalized quantization rule yielding a new quantum number, the so-called topological spin, which is related to the weight of the Dirac string.

hep-th↗
arXiv2005

Nonassociativity, Dirac monopoles and Aharonov-Bohm effect

The Aharonov-Bohm (AB) effect for the singular string associated with the Dirac monopole carrying an arbitrary magnetic charge is studied. It is shown that the emerging difficulties in explanation of the AB effect may be removed by introducing nonassociative path-dependent wave functions. This provides the absence of the AB effect for the Dirac string of magnetic monopole with an arbitrary magnetic charge.

hep-th↗
arXiv2004

Nonassociative geometry: Friedmann-Robertson-Walker spacetime

In (Phys. Rev. D 62, 081501, 2000) we proposed a unified approach to description of continuous and discrete spacetime based on nonassociative geometry and described nonassociative smooth and discrete de Sitter models. In our paper we give the description of nonassociative Friedmann-Robertson-Walker spacetime.

hep-th↗
arXiv2004

On representations of the rotation group and magnetic monopoles

Recently (Phys. Lett. A302 (2002) 253, hep-th/0208210; hep-th/0403146) employing bounded infinite-dimensional representations of the rotation group we have argued that one can obtain the consistent monopole theory with generalized Dirac quantization condition, $2κμ\in \mathbb Z$, where $κ$ is the weight of the Dirac string. Here we extend this proof to the unbounded infinite-dimensional representations.

hep-th↗
arXiv2004

Topology change in (2+1)-dimensional gravity with non-Abelian Higgs field

We study topology change in (2+1)D gravity coupling with non-Abelian SO(2,1) Higgs field from the point of view of Morse theory. It is shown that the Higgs potential can be identified as a Morse function. The critical points of the latter (i.e. loci of change of the spacetime topology) coincide with zeros of the Higgs field. In these critical points two-dimensional metric becomes degenerate, but the curvature remains bounded.

gr-qc↗
arXiv2004

Quasigroups, Asymptotic Symmetries and Conservation Laws in General Relativity

A new quasigroup approach to conservation laws in general relativity is applied to study asymptotically flat at future null infinity spacetime. The infinite-parametric Newman-Unti group of asymptotic symmetries is reduced to the Poincaré quasigroup and the Noether charge associated with any element of the Poincaré quasialgebra is defined. The integral conserved quantities of energy-momentum and angular momentum are linear on generators of Poincaré quasigroup, free of the supertranslation ambiguity, posess the flux and identically equal to zero in Minkowski spacetime.

gr-qc↗
arXiv2004

On angular momentum of gravitational radiation

The quasigroup approach to the conservation laws (Phys. Rev. D56, R7498 (1997)) is completed by imposing new gauge conditions for asymptotic symmetries. Noether charge associated with an arbitrary element of the Poincaré quasialgebra is free from the supertranslational ambiquity and identically vanishes in a flat spacetime

gr-qc↗