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V. I. Tsifrinovich

Publications and source records attributed to V. I. Tsifrinovich.

50 records · Page 3Linked to original sources
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.

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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.

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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.

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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.

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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

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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.

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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.

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arXiv1999

Simulations of Quantum Logic Operations in Quantum Computer with Large Number of Qubits

We report the first simulations of the dynamics of quantum logic operations with a large number of qubits (up to 1000). A nuclear spin chain in which selective excitations of spins is provided by the gradient of the external magnetic field is considered. The spins interact with their nearest neighbors. We simulate the quantum control-not (CN) gate implementation for remote qubits which provides the long-distance entanglement. Our approach can be applied to any implementation of quantum logic gates involving a large number of qubits.

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arXiv1999

Solid-State Nuclear Spin Quantum Computer Based on Magnetic Resonance Force Microscopy

We propose a nuclear spin quantum computer based on magnetic resonance force microscopy (MRFM). It is shown that an MRFM single-electron spin measurement provides three essential requirements for quantum computation in solids: (a) preparation of the ground state, (b) one- and two- qubit quantum logic gates, and (c) a measurement of the final state. The proposed quantum computer can operate at temperatures up to 1K.

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arXiv1999

Influence of Non-Resonant Effects on the Dynamics of Quantum Logic Gates at Room Temperature

We study numerically the influence of non-resonant effects on the dynamics of a single $π$-pulse quantum CONTROL-NOT (CN) gate in a macroscopic ensemble of fo ur-spin molecules at room temperature. The four nuclear spins in each molecule r epresent a four-qubit register. The qubits are ``labeled'' by the characteristic frequencies, $ω_k$, ($k=0$ to 3) due to the Zeeman interaction of the nuclear spins with the magnetic field. The qubits interact with each other through an Ising interaction of strength $J$. T he paper examines the feasibility of implementing a single-pulse quantum CN gate in an ensemble of quantum molecules at room temperature. We determine a paramet er region, $ω_k$ and $J$, in which a single-pulse quantum CN gate can be i mplemented at room temperature. We also show that there exist characteristic cri tical values of parameters, $Δω_{cr}\equiv|ω_{k^\prime}-ω_k|_{cr}$ and $J_{cr}$, such that for $J<J_{cr}$ and $Δω_k\equiv|ω_{k^\prime}-ω_k|<Δω_{cr}$, non-resonant effects are sufficient to d estroy the dynamics required for quantum logic operations.

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arXiv1999

Quantum Computation as a Dynamical Process

In this paper, we discuss the dynamical issues of quantum computation. We demonstrate that fast wave function oscillations can affect the performance of Shor's quantum algorithm by destroying required quantum interference. We also show that this destructive effect can be routinely avoided by using resonant-pulse techniques. We discuss the dynamics of resonant pulse implementations of quantum logic gates in Ising spin systems. We also discuss the influence of non-resonant excitations. We calculate the range of parameters where undesirable non-resonant effects can be minimized. Finally, we describe the ``$2πk$-method'' which avoids the detrimental deflection of non-resonant qubits.

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arXiv1998

Generalized Quantum Control-Not Gate in Two-Spin Ising System

The physical implementation of the quantum Control-Not gate for a two-spin system is investigated numerically. The concept of a generalized quantum Control-Not gate, with arbitrary phase shift, is introduced. It is shown that a resonant $π$-pulse provides a simple example of a generalized quantum Control-Not gate.

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