arXiv subjects

Yuriy Makhlin

Publications and source records attributed to Yuriy Makhlin.

At least 37 records · Page 2Linked to original sources

arXiv2006

Tunable coupling of qubits: nonadiabatic corrections

We analyze the coupling of qubits mediated by a tunable and fast element beyond the adiabatic approximation. The nonadiabatic corrections are important and even dominant in parts of the relevant parameter range. As an example, we consider the tunable capacitive coupling between two charge qubits mediated by a gated Josephson junction, as suggested by Averin and Bruder. The nonadiabatic, inductive contribution persists when the capacitive coupling is tuned to zero. On the other hand, the total coupling can be turned off (in the rotating wave approximation) if the qubits are operated at symmetry points.

cond-mat.mes-hall↗

arXiv2005

Decoherence from ensembles of two-level fluctuators

1/f noise, the major source of dephasing in Josephson qubits, may be produced by an ensemble of two-level systems. Depending on the statistical properties of their distribution, the noise distribution can be Gaussian or non-Gaussian. The latter situation is realized, for instance, when the distribution of coupling strengths has a slowly decaying power-law tail. In this regime questions of self-averaging and sample-to-sample fluctuations become crucial. We study the dephasing process for a class of distribution functions and analyze the self-averaging properties of the results.

cond-mat.mes-hall↗

arXiv2005

Landau-Zener interferometry with superconducting qubits

Quantum-mechanical systems having two discrete energy levels are ubiquitous in nature. For crossing energy levels, depending on how fast they approach each other, there is a possibility of a transition between them. This phenomenon is known as Landau-Zener tunneling and it forms the physical basis of the Zener diode, for example. The traditional treatment of the Landau-Zener tunneling, however, ignores quantum-mechanical interference. Here we report an observation of phase-sensitive interference between consecutive Landau-Zener tunneling attempts in an artificial two-level system formed by a Cooper-pair-box qubit. We interpret the experiment in terms of a multi-pass analog to the well-known optical Mach-Zehnder interferometer. In our case, the beam splitting occurs by Landau-Zener tunneling at the charge degeneracy, while the arms of the Mach-Zehnder interferometer in energy space are represented by the ground and excited state. Our Landau-Zener interferometer can be used as a high-resolution detector for phase and charge owing to interferometric sensitivity-enhancement. The findings also demonstrate new methods for qubit manipulations.

cond-mat.mes-hall↗

arXiv2005

Geometric nature of the environment-induced Berry phase and geometric dephasing

We investigate the geometric phase or Berry phase (BP) acquired by a spin-half which is both subject to a slowly varying magnetic field and weakly-coupled to a dissipative environment (either quantum or classical). We study how this phase is modified by the environment and find that the modification is of a geometric nature. While the original BP (for an isolated system) is the flux of a monopole-field through the loop traversed by the magnetic field, the environment-induced modification of the BP is the flux of a quadrupole-like field. We find that the environment-induced phase is complex, and its imaginary part is a geometric contribution to dephasing. Its sign depends on the direction of the loop. Unlike the BP, this geometric dephasing is gauge invariant for open paths of the magnetic field.

cond-mat.mes-hall↗

arXiv2005

Low- and high-frequency noise from coherent two-level systems

Recent experiments indicate a connection between the low- and high-frequency noise affecting superconducting quantum systems. We explore the possibilities that both noises can be produced by one ensemble of microscopic modes, made up, e.g., by sufficiently coherent two-level systems (TLS). This implies a relation between the noise power in different frequency domains, which depends on the distribution of the parameters of the TLSs. We show that a distribution, natural for tunneling TLSs, with a log-uniform distribution in the tunnel splitting and linear distribution in the bias, accounts for experimental observations.

cond-mat.mes-hall↗

arXiv2004

Berry phase with environment: classical versus quantum

We discuss the concept of the Berry phase in a dissipative system. We show that one can identify a Berry phase in a weakly-dissipative system and find the respective correction to this quantity, induced by the environment. This correction is expressed in terms of the symmetrized noise power and is therefore insensitive to the nature of the noise representing the environment, namely whether it is classical or quantum mechanical. It is only the spectrum of the noise which counts. We analyze a model of a spin-half (qubit) anisotropically coupled to its environment and explicitly show the coincidence between the effect of a quantum environment and a classical one.

cond-mat.mes-hall↗

arXiv2003

Dephasing of solid-state qubits at optimal points

Motivated by recent experiments with Josephson-junction circuits, we analyze the influence of various noise sources on the dynamics of two-level systems at optimal operation points where the linear coupling to low-frequency fluctuations is suppressed. We study the decoherence due to nonlinear (quadratic) coupling, focusing on the experimentally relevant 1/f and Ohmic noise power spectra. For 1/f noise strong higher-order effects influence the evolution.

cond-mat.mes-hall↗

arXiv2003

Dephasing of qubits by transverse low-frequency noise

We analyze the dissipative dynamics of a two-level quantum system subject to low-frequency, e.g. 1/f noise, motivated by recent experiments with superconducting quantum circuits. We show that the effect of transverse linear coupling of the system to low-frequency noise is equivalent to that of quadratic longitudinal coupling. We further find the decay law of quantum coherent oscillations under the influence of both low- and high-frequency fluctuations, in particular, for the case of comparable rates of relaxation and pure dephasing.

cond-mat.mes-hall↗

arXiv2003

Quantum Zeno effect in the Cooper-pair transport through a double-island Josephson system

Motivated by recent experiments, we analyze transport of Cooper pairs through a double-island Josephson qubit. At low bias in a certain range of gate voltages coherent superpositions of charge states play a crucial role. Analysis of the evolution of the density matrix allows us to cover a wide range of parameters, incl. situations with degenerate levels, when dissipation strongly affects the coherent eigenstates. At high noise levels the so-called Zeno effect can be observed, which slows down the transport. Our analysis explains certain features of the I-V curves, in particular the visibility and shape of resonant peaks and lines.

cond-mat.mes-hall↗

arXiv2003

Dissipation in Josephson qubits

We discuss the dissipative dynamics of superconducting qubits in the applicability range of the Bloch equations and beyond.

cond-mat.mes-hall↗

arXiv2003

Spin-spin correlators in Majorana representation

In the Majorana representation of a spin 1/2 we find an identity which relates spin-spin correlators to one-particle fermionic correlators. This should be contrasted with the straightforward approach in which two-particle (four-fermion) correlators need to be calculated. We discuss applications to the analysis of the dynamics of a spin coupled to a dissipative environment and of a quantum detector performing a continuous measurement of a qubit's state.

cond-mat.mes-hall↗

arXiv2002

Noise and decoherence in quantum two-level systems

Motivated by recent experiments with Josephson-junction circuits we reconsider decoherence effects in quantum two-level systems (TLS). On one hand, the experiments demonstrate the importance of 1/f noise, on the other hand, by operating at symmetry points one can suppress noise effects in linear order. We, therefore, analyze noise sources with a variety of power spectra, with linear or quadratic coupling, which are longitudinal or transverse relative to the eigenbasis of the unperturbed Hamiltonian. To evaluate the dephasing time for transverse 1/f noise second-order contributions have to be taken into account. Manipulations of the quantum state of the TLS define characteristic time scales. We discuss the consequences for relaxation and dephasing processes.

cond-mat.mes-hall↗

arXiv2001

Counting statistics for arbitrary cycles in quantum pumps

Statistics of charge transport in an adiabatic pump are determined by the dynamics of the scattering matrix S(t). We show that, up to an integer offset, the statistics depend only on the corresponding path N(t)=S^\daggerσ_3 S in the coset space (the sphere for a single channel). For a general loop S(t) we solve for the noise-minimizing pumping strategy. The average current is given by the area enclosed by N(t) in the coset space; its minimal noise by the area of a minimal surface (soap film) spanned by N(t) in the space of all matrices. We formulate conditions for quantization of the pumped charge.

cond-mat.mes-hall↗

arXiv2000

Quantum state engineering with Josephson-junction devices

We review recent theoretical and experimental progress in quantum state engineering with Josephson junction devices. The concepts of quantum computing have stimulated an increased activity in the field. Either charges or phases (fluxes) of the Josephson systems can be used as quantum degrees of freedom, and their quantum state can be manipulated coherently by voltage and current pulses. They thus can serve as qubits, and quantum logic gates can be performed. Their phase coherence time, which is limited, e.g., by the electromagnetic fluctuations in the control circuit, is long enough to allow a series of these manipulations. The quantum measurement process performed by a single-electron transistor, a SQUID, or further nanoelectronic devices is analyzed in detail.

cond-mat.mes-hall↗

arXiv2000

Nonlocal properties of two-qubit gates and mixed states and optimization of quantum computations

Entanglement of two parts of a quantum system is a non-local property unaffected by local manipulations of these parts. It is described by quantities invariant under local unitary transformations. Here we present, for a system of two qubits, a set of invariants which provides a complete description of non-local properties. The set contains 18 real polynomials of the entries of the density matrix. We prove that one of two mixed states can be transformed into the other by single-bit operations if and only if these states have equal values of all 18 invariants. Corresponding local operations can be found efficiently. Without any of these 18 invariants the set is incomplete. Similarly, non-local, entangling properties of two-qubit unitary gates are invariant under single-bit operations. We present a complete set of 3 real polynomial invariants of unitary gates. Our results are useful for optimization of quantum computations since they provide an effective tool to verify if and how a given two-qubit operation can be performed using exactly one elementary two-qubit gate, implemented by a basic physical manipulation (and arbitrarily many single-bit gates).

quant-ph↗

arXiv2000

Statistics and noise in a quantum measurement process

The quantum measurement process by a single-electron transistor or a quantum point contact coupled to a quantum bit is studied. We find a unified description of the statistics of the monitored quantity, the current, in the regime of strong measurement and expect this description to apply for a wide class of quantum measurements. We derive the probability distributions for the current and charge in different stages of the process. In the parameter regime of the strong measurement the current develops a telegraph-noise behavior which can be detected in the noise spectrum.

cond-mat.mes-hall↗

arXiv1999

Nano-electronic Realizations of Quantum Bits

Quantum computers could perform certain tasks which no classical computer can perform in acceptable times. Josephson junction circuits can serve as building blocks of quantum computers. We discuss and compare two designs, which employ charge or magnetic flux degrees of freedom to process quantum information. In both cases, elementary single-qubit and two-qubit logic gates can be performed by voltage or flux pulses. The coherence time is long enough to allow a series of such operations. We also discuss the read-out, i.e., a quantum measurement process. In the charge case it is accomplished by coupling a single-electron transistor to the qubit.

cond-mat.mes-hall↗

arXiv1999

Josephson-Junction Qubits and the Readout Process by Single-Electron Transistors

Several physical realizations of quantum bits have been proposed. Of those, nano-electronic devices appear most suitable for large-scale integration and potential applications. We suggest to use low-capacitance Josephson junctions, exploiting the coherence of tunneling in the superconducting state combined with the possibility to control individual charges by Coulomb blockade effects (cond-mat/9706016,cond-mat/9808067). These systems constitute quantum bits, with logical states differing by one Cooper-pair charge. Single- and two-bit operations can be performed by applying a sequence of gate voltages. The phase coherence time is sufficiently long to allow a series of these steps. In addition to the manipulation of qubits the resulting quantum state has to be read out. This can be accomplished by coupling a single-electron transistor capacitively to the qubit (cond-mat/9801125). To describe this quantum measurement process we study the time evolution of the density matrix of the coupled system. Only when a transport voltage is turned on, the transistor destroys the phase coherence of the qubit; in this case within a short time. The measurement is accomplished after a longer time scale, when the signal resolves the different quantum states. At still longer times the measurement process itself destroys the information about the initial state. We present a suitable set of system parameters, which can be realized by present-day technology.

cond-mat.mes-hall↗