arXiv subjects

V. I. Tsifrinovich

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

At least 37 records · Page 2Linked to original sources

arXiv2003

Analytic solutions for quantum logic gates and modeling pulse errors in a quantum computer with a Heisenberg interaction

We analyze analytically and numerically quantum logic gates in a one-dimensional spin chain with Heisenberg interaction. Analytic solutions for basic one-qubit gates and swap gate are obtained for a quantum computer based on logical qubits. We calculated the errors caused by imperfect pulses which implement the quantum logic gates. It is numerically demonstrated that the probability error is proportional to $ε^4$, while the phase error is proportional to $ε$, where $ε$ is the characteristic deviation from the perfect pulse duration.

quant-ph↗

arXiv2003

Regular and Random Magnetic Resonance Force Microscopy Signal with a Cantilever Oscillating Parallel to a Sample Surface

We study theoretically the magnetic resonance force microscopy (MRFM) in oscillating cantilever-driven adiabatic reversals (OSCAR) technique, for the case when the cantilever tip oscillates parallel to the surface of a sample. The main contribution to the MRFM signal is associated with a part of the resonance slice near the surface of the sample. The regular (approximately exponential) decay of the MRFM signal is followed by the non-dissipating random signal. The Fourier spectrum of the random signal has a characteristic peak which can be used for the identification of the signal.

cond-mat↗

arXiv2003

Minimization of nonresonant effects in a scalable Ising spin quantum computer

The errors caused by the transitions with large frequency offsets (nonresonant transitions) are calculated analytically for a scalable solid-state quantum computer based on a one-dimensional spin chain with Ising interactions between neighboring spins. Selective excitations of the spins are enabled by a uniform gradient of the external magnetic field. We calculate the probabilities of all unwanted nonresonant transitions associated with the flip of each spin with nonresonant frequency and with flips of two spins: one with resonant and one with nonresonant frequencies. It is shown that these errors oscillate with changing the gradient of the external magnetic field. Choosing the optimal values of this gradient allows us to decrease these errors by 50%.

quant-ph↗

arXiv2003

Reduction of Magnetic Noise in Magnetic Resonance Force Microscopy

We study the opportunity to reduce a magnetic noise produced by a uniform cantilever with a ferromagnetic particle in magnetic resonance force microscopy (MRFM) applications. We demonstrate theoretically a significant reduction of magnetic noise and the corresponding increase of the MRFM relaxation time using a nonuniform cantilever.

cond-mat↗

arXiv2003

Neutral Radical Molecules Ordered in Self-Assembled Monolayer Systems for Quantum Information Processing

Implementation of quantum information processing based on spatially localized electronic spins in stable molecular radicals is discussed. The necessary operating conditions for such molecules are formulated in self-assembled monolayer (SAM) systems. As a model system we start with 1, 3 -diketone types of neutral radicals. Using first principles quantum chemical calculations we prove that these molecules have the stable localized electron spin, which may represent a qubit in quantum information processing.

quant-ph↗

arXiv2003

Quantum Dynamics of the Oscillating Cantilever-Driven Adiabatic Reversals in Magnetic Resonance Force Microscopy

We simulated the quantum dynamics for magnetic resonance force microscopy (MRFM) in the oscillating cantilever-driven adiabatic reversals (OSCAR) technique. We estimated the frequency shift of the cantilever vibrations and demonstrated that this shift causes the formation of a Schrodinger cat state which has some similarities and differences from the conventional MRFM technique which uses cyclic adiabatic reversals of spins. The interaction of the cantilever with the environment is shown to quickly destroy the coherence between the two possible cantilever trajectories. We have shown that using partial adiabatic reversals, one can produce a significant increase in the OSCAR signal.

quant-ph↗

arXiv2003

Random Spin Signal in Magnetic Resonance Force Microscopy

We study a random magnetic resonance force microscopy (MRFM) signal caused by the thermal vibrations of high frequency cantilever modes in the oscillating cantilever-driven adiabatic reversals (OSCAR) technique. We show that the regular MRFM signal with a characteristic decay time, $τ_m$, is followed by a non-dissipative random signal with a characteristic time $τ_r$. We present the estimates for the values of $τ_m$ and $τ_r$. We argue that this random MRFM signal can be used for spin detection. It has a ``signature'' of a sharp peak in its Fourier spectrum.

cond-mat↗

arXiv2003

Spin Relaxation Caused by Thermal Excitations of High Frequency Modes of Cantilever Vibrations

We consider the process of spin relaxation in the oscillating cantilever-driven adiabatic reversals technique in magnetic resonance force microscopy. We simulated the spin relaxation caused by thermal excitations of the high frequency cantilever modes in the region of the Rabi frequency of the spin sub-system. The minimum relaxation time obtained in our simulations is greater but of the same order of magnitude as one measured in recent experiments. We demonstrated that using a cantilever with nonuniform cross-sectional area may significantly increase spin relaxation time.

quant-ph↗

arXiv2002

Method for implementation of universal quantum logic gates in a scalable Ising spin quantum computer

We present protocols for implementation of universal quantum gates on an arbitrary superposition of quantum states in a scalable solid-state Ising spin quantum computer. The spin chain is composed of identical spins 1/2 with the Ising interaction between the neighboring spins. The selective excitations of the spins are provided by the gradient of the external magnetic field. The protocols are built of rectangular radio-frequency pulses. The phase and probability errors caused by unwanted transitions are minimized and computed numerically.

quant-ph↗

arXiv2002

Single-Spin Measurement and Decoherence in Magnetic Resonance Force Microscopy

We consider a simple version of a cyclic adiabatic inversion (CAI) technique in magnetic resonance force microscopy (MRFM). We study the problem: What component of the spin is measured in the CAI MRFM? We show that the non-destructive detection of the cantilever vibrations provides a measurement of the spin component along the effective magnetic field. This result is based on numerical simulations of the Hamiltonian dynamics (the Schrodinger equation) and the numerical solution of the master equation.

quant-ph↗

arXiv2002

Transient Dynamics in Magnetic Force Microscopy for a Single-Spin Measurement

We analyze a single-spin measurement using a transient process in magnetic force microscopy (MFM) which could increase the maximum operating temperature by a factor of Q (the quality factor of the cantilever) in comparison with the static Stern-Gerlach effect. We obtain an exact solution of the master equation, which confirms this result. We also discuss the conditions required to create a macroscopic Schrodinger cat state in the cantilever.

quant-ph↗

arXiv2002

Stationary cantilever vibrations in the oscillating cantilever-driven adiabatic reversals -- magnetic resonance force microscopy technique

We consider theoretically the novel technique in magnetic resonance force microscopy which is called ``oscillating cantilever-driven adiabatic reversals''. We present analytical and numerical analysis for the stationary cantilever vibrations in this technique. For reasonable values of parameters we estimate the resonant frequency shift as 6Hz per the Bohr magneton. We analyze also the regime of small oscillations of the paramagnetic moment near the transversal plane and the frequency shift of the damped cantilever vibrations.

quant-ph↗

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

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↗