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G. P. Berman

Publications and source records attributed to G. P. Berman.

At least 91 records · Page 5Linked to original sources
arXiv2001

Time Scales of Phonon Induced Decoherence of Semiconductor Spin Qubits

Decoherence of a shallow donor electron spin in silicon caused by electron-lattice interaction is studied. We find that there are two time scales associated with the evolution of the electron spin density matrix: the fast but incomplete decay due to the interaction with non-resonant phonons followed by slow relaxation resulting from spin flips accompanied by resonant phonon emission. We estimate both time scales as well as the magnitude of the initial drop of coherence for P donor in Si and argue that the approach used is suitable for evaluation of phonon induced decoherence for a general class of localized spin states in semiconductors.

cond-mat↗
arXiv2001

Perturbation Approach for a Solid-State Quantum Computation

The dynamics of the nuclear-spin quantum computer with large number (L=1000) of qubits is considered using a perturbation approach, based on approximate diagonalization of exponentially large sparse matrices. Small parameters are introduced and used to compute the error in implementation of entanglement between remote qubits, by applying a sequence of resonant radio-frequency pulses. The results of the perturbation theory are tested using exact numerical solutions for small number of qubits.

quant-ph↗
arXiv2001

Magnetic Resonance Force Microscopy Measurement of Entangled Spin States

We simulate magnetic resonance force microscopy measurements of an entangled spin state. One of the entangled spins drives the resonant cantilever vibrations, while the other remote spin does not interact directly with the quasiclassical cantilever. The Schrödinger cat state of the cantilever reveals two possible outcomes of the measurement for both entangled spins.

quant-ph↗
arXiv2001

Quantum Measurement of a Single Spin using Magnetic Resonance Force Microscopy

Single-spin detection is one of the important challenges facing the development of several new technologies, e.g. single-spin transistors and solid-state quantum computation. Magnetic resonance force microscopy with a cyclic adiabatic inversion, which utilizes a cantilever oscillations driven by a single spin, is a promising technique to solve this problem. We have studied the quantum dynamics of a single spin interacting with a quasiclassical cantilever. It was found that in a similar fashion to the Stern-Gerlach interferometer the quantum dynamics generates a quantum superposition of two quasiclassical trajectories of the cantilever which are related to the two spin projections on the direction of the effective magnetic field in the rotating reference frame. Our results show that quantum jumps will not prevent a single-spin measurement if the coupling between the cantilever vibrations and the spin is small in comparison with the amplitude of the radio-frequency external field.

quant-ph↗
arXiv2001

Perturbation Theory and Numerical Modeling of Quantum Logic Operations with a Large Number of Qubits

The perturbation theory is developed based on small parameters which naturally appear in solid state quantum computation. We report the simulations of the dynamics of quantum logic operations with a large number of qubits (up to 1000). A nuclear spin chain is considered in which selective excitations of spins are provided by having a uniform gradient of the external magnetic field. Quantum logic operations are utilized by applying resonant electromagnetic pulses. The spins interact with their nearest neighbors. We simulate the creation of the long-distance entanglement between remote qubits in the spin chain. Our method enables us to minimize unwanted non-resonant effects in a controlled way. The method we use cannot simulate complicated quantum logic (a quantum computer is required to do this), but it can be useful to test the experimental performance of simple quantum logic operations. We show that: (a) the probability distribution of unwanted states has a ``band'' structure, (b) the directions of spins in typical unwanted states are highly correlated, and (c) many of the unwanted states are high-energy states of a quantum computer (a spin chain). Our approach can be applied to simple quantum logic gates and fragments of quantum algorithms involving a large number of qubits.

quant-ph↗
arXiv2001

Multivariable functions approximation using a single quantum neuron

We describe a model element able to perform universal stochastic approximations of continuous multivariable functions in both neuron-like and quantum form. The implementation of this model in the form of a multi-barrier, multiple-slit system is proposed and it is demonstrated that this single neuron-like model is able to perform the XOR function unrealizable with single classical neuron. For the simplified waveguide variant of this model it is proved for different interfering quantum alternatives with no correlated adjustable parameters, that the system can approximate any continuous function of many variables. This theorem is applied to the 2-input quantum neural model based on the use of the schemes developed for controlled nonlinear multiphoton absorption of light by quantum systems. The relation between the field of quantum neural computing and quantum control is discussed.

quant-ph↗
arXiv2001

A Quantum Full Adder for a Scalable Nuclear Spin Quantum Computer

We demonstrate a strategy for implementation a quantum full adder in a spin chain quantum computer. As an example, we simulate a quantum full adder in a chain containing 201 spins. Our simulations also demonstrate how one can minimize errors generated by non-resonant effects.

quant-ph↗
arXiv2001

Delocalization border and onset of chaos in a model of quantum computation

We study the properties of spectra and eigenfunctions for a chain of $1/2- $spins (qubits) in an external time-dependent magnetic field, and under the conditions of non-selective excitation (when the amplitude of the magnetic field is large). This model is known as a possible candidate for experimental realization of quantum computation. We present the theory for finding delocalization transition and show that for the interaction between nearest qubits, the transition is very different from that to quantum chaos. We explain this phenomena by showing that in the considered region of parameters our model is close to an integrable one. According to a general opinion, the threshold for the onset of quantum chaos due to the interqubit interaction decreases with an increase of the number of qubits. Contrary to this expectation, for a magnetic field with constant gradient we have found that chaos border does not depend on the number of qubits. We give analytical estimates which explain this effect, together with numerical data supporting our analysis. Random models with long-range interactions are studied as well. In particular, we show that in this case the delocalization and quantum chaos borders coincide.

quant-ph↗
arXiv2001

Perturbation Theory for Quantum Computation with Large Number of Qubits

We describe a new and consistent perturbation theory for solid-state quantum computation with many qubits. The errors in the implementation of simple quantum logic operations caused by non-resonant transitions are estimated. We verify our perturbation approach using exact numerical solution for relatively small (L=10) number of qubits. A preferred range of parameters is found in which the errors in processing quantum information are small. Our results are needed for experimental testing of scalable solid-state quantum computers.

quant-ph↗
arXiv2001

Control of Non-Resonant Effects in a Nuclear Spin Quantum Computer with a Large Number of Qubits

We discuss how to simulate simple quantum logic operations with a large number of qubits. These simulations are needed for experimental testing of scalable solid-state quantum computers. Quantum logic for remote qubits is simulated in a spin chain. Analytical estimates are presented for possible correlated errors caused by non-resonant transitions. A range of parameters is given in which non-resonant effects can be minimized.

quant-ph↗
arXiv2001

Solid-State Quantum Computer Based on Scanning Tunneling Microscopy

We propose a solid-state nuclear spin quantum computer based on application of scanning tunneling microscopy (STM) and well-developed silicon technology. It requires the measurement of tunneling current modulation caused by the Larmor precession of a single electron spin. Our envisioned STM quantum computer would operate at the high magnetic field ($\sim 10$T) and at low temperature $\sim 1$K.

quant-ph↗
arXiv2001

Formation and Dynamics of a Schrödinger-Cat State in Continuous Quantum Measurement

We consider the process of a single-spin measurement using magnetic resonance force microscopy (MRFM) as an example of a truly continuous measurement in quantum mechanics. This technique is also important for different applications, including a measurement of a qubit state in quantum computation. The measurement takes place through the interaction of a single spin with a quasi-classical cantilever, modeled by a quantum oscillator in a coherent state in a quasi-classical region of parameters. The entire system is treated rigorously within the framework of the Schrödinger equation, without any artificial assumptions. Computer simulations of the spin-cantilever dynamics, where the spin is continuously rotated by means of cyclic adiabatic inversion, show that the cantilever evolves into a Schrödinger-cat state: the probability distribution for the cantilever position develops two asymmetric peaks that quasi-periodically appear and vanish. For a many-spin system our equations reduce to the classical equations of motion, and we accurately describe conventional MRFM experiments involving cyclic adiabatic inversion of the spin system. We surmise that the interaction of the cantilever with the environment would lead to a collapse of the wave function; however, we show that in such a case the spin does not jump into a spin eigenstate.

quant-ph↗
arXiv2000

Avoiding Quantum Chaos in Quantum Computation

We study a one-dimensional chain of nuclear $1/2-$spins in an external time-dependent magnetic field. This model is considered as a possible candidate for experimental realization of quantum computation. According to the general theory of interacting particles, one of the most dangerous effects is quantum chaos which can destroy the stability of quantum operations. According to the standard viewpoint, the threshold for the onset of quantum chaos due to an interaction between spins (qubits) strongly decreases with an increase of the number of qubits. Contrary to this opinion, we show that the presence of a magnetic field gradient helps to avoid quantum chaos which turns out to disappear with an increase of the number of qubits. We give analytical estimates which explain this effect, together with numerical data supporting

quant-ph↗
arXiv2000

Dynamical Stability of an Ion in a Linear Trap as a Solid-State Problem of Electron Localization

When an ion confined in a linear ion trap interacts with a coherent laser field, the internal degrees of freedom, related to the electron transitions, couple to the vibrational degree of freedom of the ion. As a result of this interaction, quantum dynamics of the vibrational degree of freedom becomes complicated, and in some ranges of parameters even chaotic. We analyze the vibrational ion dynamics using a formal analogy with the solid-state problem of electron localization. In particular, we show how the resonant approximation used in analysis of the ion dynamics, leads to a transition from a two-dimensional (2D) to a one-dimensional problem (1D) of electron localization. The localization length in the solid-state problem is estimated in cases of weak and strong interaction between the cites of the 2D cell by using the methods of resonance perturbation theory, common in analysis of 1D time-dependent dynamical systems.

quant-ph↗
arXiv2000

Single-Pulse Preparation of the Uniform Superpositional State used in Quantum Algorithms

We examine a single-pulse preparation of the uniform superpositional wave function, which includes all basis states, in a spin quantum computer. The effective energy spectrum and the errors generated by this pulse are studied in detail. We show that, in spite of the finite width of the energy spectrum bands, amplitude and phase errors can be made reasonably small.

quant-ph↗
arXiv1999

Non-Resonant Effects in Implementation of Quantum Shor Algorithm

We simulate Shor's algorithm on an Ising spin quantum computer. The influence of non-resonant effects is analyzed in detail. It is shown that our ``$2πk$''-method successfully suppresses non-resonant effects even for relatively large values of the Rabi frequency.

quant-ph↗