We investigate the decoherence of a qubit coupled to either a quantum two-level system (TLS) again coupled to an environment, or a classical fluctuator modeled by random telegraph noise. In order to do this we construct a model for the quantum TLS where we can adjust the temperature of its environment, and the decoherence rate independently. The model has a well-defined classical limit at any temperature and this corresponds to the appropriate random telegraph process, which is symmetric at high temperatures and becomes asymmetric at low temperatures. We find that the difference in the qubit decoherence rates predicted by the two models depends on the ratio between the qubit-TLS coupling and the decoherence rate in the pointer basis of the TLS. This is then the relevant parameter which determines whether the TLS has to be treated quantum mechanically or can be replaced by a classical telegraph process. We also compare the mutual information between the qubit and the TLS in the classical and quantum cases.
We study dynamical decoupling of a qubit from non gaussian quantum noise due to discrete sources, as bistable fluctuators and 1/f noise. We obtain analytic and numerical results for generic operating point. For very large pulse frequency, where dynamic decoupling compensates decoherence, we found universal behavior. At intermediate frequencies noise can be compensated or enhanced, depending on the nature of the fluctuators and on the operating point. Our technique can be applied to a larger class of non-gaussian environments.
We describe the transport properties of a point contact under the influence of a classical two-level fluctuator. We employ a transfer matrix formalism allowing us to calculate arbitrary correlation functions of the stochastic process by mapping them on matrix products. The result is used to obtain the generating function of the full counting statistics of a classical point contact subject to a classical fluctuator, including extensions to a pair of two-level fluctuators as well as to a quantum point contact. We show that the noise in the quantum point contact is a sum of the (quantum) partitio…
Some papers represent the environment of a mesosopic system (e.g. a qubit in a quantum computer or a quantum junction) by a neighboring fluctuator, which generates a fluctuating electric field -- a telegraph noise (TN) -- on the electrons in the system. An example is a two-level system, that randomly fluctuates between two states with Boltzmann weights determined by an effective temperature. To consider whether this description is physically reasonable, we study it in the simplest example of a quantum dot which is coupled to two electronic reservoirs and to a single fluctuator. Averaging over …
The effects of a nearby two-level charge fluctuator on a double-dot two-spin qubit are studied theoretically. Assuming no direct tunneling between the charge fluctuator and the qubit quantum dots, the Coulomb couplings between the qubit orbital states and the fluctuator are calculated within the Hund-Mulliken framework to quadrupole-quadrupole order in a multipole expansion. We identify and quantify the coupling term that entangles the qubit to the fluctuator and analyze qubit decoherence effects that result from the decay of the fluctuator to its reservoir. Our results show that the charge en…
The effects of a collection of classical two-level charge fluctuators on the coherence of a dynamically-decoupled qubit are studied. Distinct dynamics are found at different qubit working positions. Exact analytical formulae are derived at pure dephasing and approximate solutions are found at the general working position, for weakly- and strongly-coupled fluctuators. Analysis of these solutions, combined with numerical simulations of the multiple random telegraph processes, reveal the scaling of the noise with the number of fluctuators and the number of control pulses, as well as dependence on…
We study decoherence due to random telegraph and 1/f noise in Josephson qubits. We illustrate differences between gaussian and non gaussian effects at different working points and for different protocols. Features of the intrinsically non-gaussian and non-Markovian low-frequency noise may explain the rich physics observed in the spectroscopy and the dynamics of charge based devices.
We report on long-term measurements of a highly coherent, non-tunable superconducting transmon qubit, revealing low-frequency burst noise in coherence times and qubit transition frequency. We achieve this through a simultaneous measurement of the qubit's relaxation and dephasing rate as well as its resonance frequency. The analysis of correlations between these parameters yields information about the microscopic origin of the intrinsic decoherence mechanisms in Josephson qubits. Our results are consistent with a small number of microscopic two-level systems located at the edges of the supercon…
Thermal-fluctuator driven decoherence of an oscillator resonantly coupled to a two-level system
School of Physics and Astronomy and Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham（诺丁汉大学物理与天文学院及量子非平衡系统数学与理论物理中心）
We investigate the decoherence effect of telegraph noise on a single qubit, usually provoked by bistable fluctuators. To diminish the dephasing and relaxation impact an effective refocusing scheme (so-called Bang-Bang pulses) is proposed. Detailed numerical as well as analytical random walk analysis allows in particular to evaluate the applicability of non-perfect Bang-Bang pulses.
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.
Based on the stochastic theory developed by Kubo and Anderson, we present an exact result of the decoherence function of a qubit in telegraph-like noises under dynamical decoupling control. We prove that for telegraph-like noises, the decoherence can be suppressed at most to the third order of the time and the periodic Carr-Purcell-Merboom-Gill sequences are the most efficient scheme in protecting the qubit coherence in the short-time limit.
The efficiency of the future devices for quantum information processing is limited mostly by the finite decoherence rates of the qubits. Recently a substantial progress was achieved in enhancing the time, which a solid-state qubit demonstrates a coherent dynamics. This progress is based mostly on a successful isolation of the qubits from external decoherence sources. Under these conditions the material-inherent sources of noise start to play a crucial role. In most cases the noise that quantum device demonstrate has 1/f spectrum. This suggests that the environment that destroys the phase coher…
With the growing efforts in isolating solid-state qubits from external decoherence sources, the origins of noise inherent to the material start to play a relevant role. One representative example are charged impurities in the device material or substrate, which typically produce telegraph noise and can hence be modelled as bistable fluctuators. In order to demonstrate the possibility of the active suppression of the disturbance from a {\em single} fluctuator, we theoretically implement an elementary bang-bang control protocol. We numerically simulate the random walk of the qubit state on the B…
We study decoherence in a qubit with the distance between the two levels affected by random flips of bistable fluctuators. For the case of a single fluctuator we evaluate explicitly an exact expression for the phase-memory decay in the echo experiment with a resonant ac excitation. The echo signal as a function of time shows a sequence of plateaus. The position and the height of the plateaus can be used to extract the fluctuator switching rate γand its coupling strength v. At small times the logarithm of the echo signal is proportional to t^3. The plateaus disappear when the decoherence is ind…
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 theoreti…
The major contribution to decoherence of a double quantum dot or a Josephson junction charge qubit comes from the electrostatic coupling to fluctuating background charges hybridized with the conduction electrons in the reservoir. However, estimations according to previously developed theories show that finding a sufficient number of effective fluctuators in a realistic experimental layout is quite improbable. We show that this paradox is resolved by allowing for a short-range Coulomb interaction of the fluctuators with the electrons in the reservoir. This dramatically enhances both the number …
By performing experiments with thin-film resonators of NbSi, we elucidate a decoherence mechanism at work in disordered superconductors. This decoherence is caused by charged Two Level Systems (TLS) which couple to the conduction electrons in the BCS ground state; it does not involve any out-of-equilibrium quasiparticles, vortices, etc. Standard theories of mesoscopic disordered conductors enable making predictions regarding this mechanism, notably that decoherence should increase as the superconductor cross section decreases. Given the omnipresence of charged TLS in solid-state systems, this …
We investigate the time-evolution of a charge qubit subject to quantum telegraph noise produced by a single electronic defect level. We obtain results for the time-evolution of the coherence that are strikingly different from the usual case of a harmonic oscillator bath (Gaussian noise). When the coupling strength crosses a certain temperature-dependent threshold, we observe coherence oscillations in the strong-coupling regime. Moreover, we present the time-evolution of the echo signal in a spin-echo experiment. Our analysis relies on a numerical evaluation of the exact solution for the densit…
We study the dissipative dynamics of a qubit that is afflicted by classical random telegraph noise and it is subject to dynamical decoupling. We derive exact formulas for the qubit dynamics at arbitrary working points in the limit of infinitely strong control pulses (bang-bang control) and we investigate in great detail the efficiency of the dynamical decoupling techniques both for Gaussian and non-Gaussian (slow) noise at qubit pure dephasing and at optimal point. We demonstrate that control sequences can be successfully implemented as diagnostic tools to infer spectral proprieties of a few f…
In this study, we examine decoherence of qubits system coupled independently by using influence functional. We especially concentrated on the effect of qubit flip process. We examine the zero-dimensional qubit and one-dimensional qubits system coupled with multi-band one-dimensional system. The qubit flip process leads to oscillation and self-excitation. We also obtained the time evolution of von Neumann entropy.The pure dephasing channel indicates entropy. These results show quantum brown motion. We present the numerical calculation of the entropy for random telegraph noise. This indicates th…
A qubit (containing two quantum states, 1 and 2), is coupled to a control register (state 3), which is subject to telegraph noise. We study the time evolution of the density matrix $ρ$ of an electron which starts in some coherent state on the qubit. At infinite time, $ρ$ usually approaches the fully decoherent state, with $ρ^{}_{nm}=δ^{}_{nm}/3$. However, when the Hamiltonian is symmetric under $1\leftrightarrow 2$, the element $ρ^{}_{12}$ approaches a non-zero real value, implying a partial coherence of the asymptotic state. The asymptotic density matrix depends only on ${\rm Re}[ρ^{}_{12}(t=…
We study a pair of quantum dot exciton qubits interacting with a number of fluctuating charges that can induce a Stark shift of both exciton transition energies. We do this by solving the optical master equation using a numerical transfer matrix method. We find that the collective influence of the charge environment on the dots can be detected by measuring the correlation between the photons emitted when each dot is driven independently. Qubits in a common charge environment display photon bunching, if both dots are driven on resonance or if the driving laser detunings have the same sense for …
We consider quantum decoherence in solid-state systems by studying the transverse dynamics of a single qubit interacting with a fermionic bath and driven by external pulses. Our interest is in investigating the extent to which the lost coherence can be restored by the application of external pulses to the qubit. We show that the qubit evolution under various pulse sequences can be mapped onto Keldysh path integrals. This approach allows a simple diagrammatic treatment of different bath excitation processes contributing to qubit decoherence. We apply this theory to the evolution of the qubit co…
We analyze theoretically the decoherence of two interacting electrons in a double self-assembled quantum dot due to a random telegraph noise. For this purpose we have examined the pure dephasing rate by evaluating the decoherence factor. This latter has been shown to be different from that calculated within the Gaussian approximation in the strong coupling regime. In order to determine the influence of the random telegraph noise on the entanglement of the system states, the concurrence, the populations and the entropy are evaluated as well. Our results show that telegraph noise can severely im…
Using a qubit to probe non-Gaussian noise environments is theoretically studied in the context of classical random telegraph processes. Protocols for control pulses are developed to effectively scan higher noise correlations, offering valuable information on the charge environment of the qubit. Specifically, the noise power spectrum and trispectrum are reconstructed simultaneously for a wide range of qubit-fluctuator coupling strengths, demonstrating the method's robustness. These protocols are readily testable in various qubit systems with well-developed quantum control, including quantum dot…
In a scenario where data-storage qubits are kept in isolation as far as possible, with minimal measurements and controls, noise mitigation can still be done using additional noise probes, with corrections applied only when needed. Motivated by the case of solid-state qubits, we consider dephasing noise arising from a two-state fluctuator, described by random telegraph process, and a noise probe which is also a qubit, a so-called spectator qubit (SQ). We construct the theoretical model assuming projective measurements on the SQ, and derive the performance of different measurement and control st…
Spectator qubits (SQs) are a tool to mitigate noise in hard-to-access data qubits. The SQ, designed to be much more sensitive to the noise, is measured frequently, and the accumulated results used rarely to correct the data qubits. For the hardware-relevant example of dephasing from random telegraph noise, we introduce a Bayesian method employing complex linear maps which leads to a plausibly optimal adaptive measurement and control protocol. The suppression of the decoherence rate is quadratic in the SQ sensitivity, establishing that the SQ paradigm works arbitrarily well in the right regime.
The qubit (or a system of two quantum dots) has become a standard paradigm for studying quantum information processes. Our focus is Decoherence due to interaction of the qubit with its environment, leading to noise. We consider quantum noise generated by a dissipative quantum bath. A detailed comparative study with the results for a classical noise source such as generated by a telegraph process, enables us to set limits on the applicability of this process vis a vis its quantum counterpart, as well as lend handle on the parameters that can be tuned for analyzing decoherence. Both Ohmic and no…
We present experiments on the dynamics of a two-state parametric fluctuator in a superconducting flux qubit. In spectroscopic measurements, the fluctuator manifests itself as a doublet line. When the qubit is excited in resonance with one of the two doublet lines, the correlation of readout results exhibits an exponential time decay which provides a measure of the fluctuator transition rate. The rate increases with temperature in the interval 40 to 158 mK. Based on the magnitude of the transition rate and the doublet line splitting we conclude that the fluctuation is induced by quasiparticle t…
We propose and study a model of dephasing due to an environment of bistable fluctuators. We apply our analysis to decoherence of Josephson Qubits, induced by background charges present in the substrate, which are also responsible for the 1/f noise. The discrete nature of the environment leads to a number of new features which are mostly pronounced for slowly moving charges. Far away from degeneracy this model for the dephasing is solved exactly.
Entangled qubit pairs can serve as a quantum memory or as a resource for quantum communication. The utility of such pairs is measured by how long they take to disentangle or decohere. To answer the question of whether qubit-qubit interactions can prolong entanglement, we calculate the dissipative dynamics of a pair of qubits coupled via the exchange interaction in the presence of random telegraph noise and $1/f$ noise. We show that for maximally entangled (Bell) states, the exchange interaction generally suppresses decoherence and disentanglement. This suppression is more apparent for random t…
We report on low-temperature noise measurements of a single electron transistor (SET) immersed in superfluid $^4$He. The device acts as a charge sensitive electrometer able to detect the fluctuations of charged defects in close proximity to the SET. In particular, we measure telegraph switching of the electric current through the device originating from a strongly coupled individual two-level fluctuator. By embedding the device in a superfluid helium immersion cell we are able to systematically control the thermalizing environment surrounding the SET and investigate the effect of the superflui…
The dynamics of a spin in the presence of a deterministic and a fluctuating magnetic field is solved for analytically to obtain the averaged value of the spin as a function of time for various kinds of fluctuations (noise). Specifically, analytic results are obtained for the time dependence of the expectation value of the spin, averaged over fluctuations, for Gaussian white noise and Guassian colored noise, as well as non-Gaussian telegraph noise. Fluctuations cause the decay of the average spin vector (decoherence). For noise with finite temporal correlation time, a deterministic component of…
Telegraph noise, which originates from the switching of charge between meta-stable trapping sites, becomes increasingly important as device sizes approach the nano-scale. For charge-based quantum computing, this noise may lead to decoherence and loss of read out fidelity. Here we use a radio frequency single electron transistor (rf-SET) to probe the telegraph noise present in a typical semiconductor-based quantum computer architecture. We frequently observe micro-second telegraph noise, which is a strong function of the local electrostatic potential defined by surface gate biases. We present a…
We review our recent contributions to two topics that have become of interest in the field of open, dissipative quantum systems: non-Gaussian noise and decoherence in fermionic systems. Decoherence by non-Gaussian noise, i.e. by an environment that cannot be approximated as a bath of harmonic oscillators, is important in nanostructures (e.g. qubits) where there might be strong coupling to a small number of fluctuators. We first revisit the pedagogical example of dephasing by classical telegraph noise. Then we address two models where the quantum nature of the noise becomes essential: "quantum …
With the growing efforts in isolating solid-state qubits from external decoherence sources, the material-inherent sources of noise start to play crucial role. One representative example is electron traps in the device material or substrate. Electrons can tunnel or hop between a charged and an empty trap, or between a trap and a gate electrode. A single trap typically produces telegraph noise and can hence be modeled as a bistable fluctuator. Since the distribution of hopping rates is exponentially broad, many traps produce flicker-noise with spectrum close to 1/f. Here we develop a theory of d…
The time evolution of a qubit, consisting of two single-level quantum dots, is studied in the presence of telegraph noise. The dots are connected by two tunneling paths, with an Aharonov-Bohm flux enclosed between them. Under special symmetry conditions, which can be achieved by tuning gate voltages, there develops partial decoherence: at long times, the off-diagonal element of the reduced density matrix (in the basis of the two dot states) approaches a non-zero value, generating a circulating current around the loop. The flux dependence of this current contains full information on the initial…
A three-site mesoscopic ring provides an ideal setting for an exact calculation of the bond current when the ring is threaded by an Aharonov-Bohm flux. The bond current is a measurable outcome of the coherent properties of the quantum phase. However the coherence is impeded by noise when the ring is put in contact with an environment. This coherence-to-incoherence transition is analyzed in detail here for both classical (Gaussian and telegraphic) and quantum noise and a comparative assessment is made when the quantum noise is governed by a spin-boson Hamiltonian of dissipative quantum mechanic…
We theoretically investigate the influence of designed pulse sequences in restoring quantum coherence lost due to background noise in superconducting qubits. We consider both 1/f noise and Random Telegraph Noise, and show that the qubit coherence time can be substantially enhanced by carefully engineered pulse sequences. Conversely, the time dependence of qubit coherence under external pulse sequences could be used as a spectroscopic tool for extracting the noise mechanisms in superconducting qubits, i.e. by using Uhrig's pulse sequence one can obtain information about moments of the spectral …
Recent experiments on Josephson junction qubits have suggested the existence in the tunnel barrier of bistable two level fluctuators that are responsible for decoherence and 1/f critical current noise. In this article we treat these two-level systems as fictitious spins and investigate their influence quantum mechanically with both analytical and numerical means. We find that the Rabi oscillations of the qubit exhibit multiple stages of decay. New approaches are established to characterize different decoherence times and to allow for easier feature extraction from experimental data. The Rabi o…
A high degree of quantum coherence is a crucial requirement for the implementation of quantum logic devices. Solid state nanodevices seem particularly promising from the point of view of integrability and flexibility in the design. However decoherence is a serious limitation, due to the presence of many types low energy excitations in the ``internal'' environment and of ``external'' sources due to the control circuitery. Here we study both kind of dephasing in a special implementation, the charge Josephson qubit, however many of our results are applicable to a large class of solid state qubits…
We use a quasi Hamiltonian formalism to describe the dissipative dynamics of a circuit QED qubit that is affected by several fluctuating two level systems with a 1/f noise power spectrum. The qubit-resonator interactions are described by the Jaynes Cummings model. We argue that the presence of pure dephasing noise in such a qubit-resonator system will also induce an energy relaxation mechanism via a fluctuating dipole coupling term. This random modulation of the coupling is seen to lead to rich physical behavior. For non-Markovian noise, the coupling can either worsen or alleviate decoherence …
We have detected coherent quantum oscillations between Josephson phase qubits and microscopic critical-current fluctuators by implementing a new state readout technique that is an order of magnitude faster than previous methods. The period of the oscillations is consistent with the spectroscopic splittings observed in the qubit's resonant frequency. The results point to a possible mechanism for decoherence and reduced measurement fidelity in superconducting qubits and demonstrate the means to measure two-qubit interactions in the time domain.
We consider non-interacting multi-qubit systems as controllable probes of an environment of defects/impurities modelled as a composite spin-boson environment. The spin-boson environment consists of a small number of quantum-coherent two-level fluctuators (TLFs) damped by independent bosonic baths. A master equation of the Lindblad form is derived for the probe-plus-TLF system. We discuss how correlation measurements in the probe system encode information about the environment structure and could be exploited to efficiently discriminate between different experimental preparation techniques, wit…
Probing charge noise in bilayer graphene quantum dots by Landau-Zener-Stückelberg-Majorana spectroscopy
RWTH Aachen University（亚琛工业大学）；JARA-FIT；nd Institute of Physics, RWTH Aachen University（亚琛工业大学第二物理研究所）；Peter Grünberg Institute (PGI-9), Forschungszentrum Jülich（于利希研究中心彼得·格林伯格研究所（PGI-9））；Forschungszentrum Jülich（于利希研究中心）；CST - Compound Semiconductor Technology, RWTH Aachen University（亚琛工业大学化合物半导体技术）；University of Vienna, Faculty of Physics（维也纳大学物理系）；National Institute for Materials Science（国立材料研究所）
The energy landscape of a single electron in a triple quantum dot can be tuned such that the energy separation between ground and excited states becomes a flat function of the relevant gate voltages. These so-called sweet spots are beneficial for charge coherence, since the decoherence effects caused by small fluctuations of gate voltages or surrounding charge fluctuators are minimized. We propose a new operation point for a triple quantum dot charge qubit, a so-called $CQ_3$-qubit, having a third order sweet spot. We show strong coupling of the qubit to single photons in a frequency tunable h…
The efficiency of the future devices for quantum information processing will be limited mostly by the finite decoherence rates of the individual qubits and quantum gates. Recently, substantial progress was achieved in enhancing the time within which a solid-state qubit demonstrates coherent dynamics. This progress is based mostly on a successful isolation of the qubits from external decoherence sources obtained by clever engineering. Under these conditions, the material-inherent sources of noise start to play a crucial role. In most cases, quantum devices are affected by noise decreasing with …
The spin of an electron or a nucleus in a semiconductor [1] naturally implements the unit of quantum information -- the qubit -- while providing a technological link to the established electronics industry [2]. The solid-state environment, however, may provide deleterious interactions between the qubit and the nuclear spins of surrounding atoms [3], or charge and spin fluctuators in defects, oxides and interfaces [4]. For group IV materials such as silicon, enrichment of the spin-zero 28-Si isotope drastically reduces spin-bath decoherence [5]. Experiments on bulk spin ensembles in 28-Si cryst…
We address the interaction of single- and two-qubit systems with external fluctuating transverse fields and analyze in details the dynamical decoherence induced by Gaussian and non-Gaussian noise, e.g. random telegraph noise (RTN). Upon exploiting the exact RTN solution of the time-dependent Von Neumann equation, we analyze in details the behavior of quantum correlations and prove the non-Markovianity of the dynamical map in the full parameter range, i.e. for either fast or slow noise. The dynamics induced by Gaussian noise is studied numerically and compared to the RTN solution, showing the e…
Spin qubits in Silicon quantum dots can have long coherence times, yet their manipulation relies on the exchange interaction, through which charge noise can induce decoherence. Charge traps near the interface of a Si heterostructure lead to fluctuations in the quantum-dot confinement and barrier potentials, which cause gating errors and two-spin dephasing. We quantify these effects in Si double quantum dots using a realistic model of noise. Specifically, we consider both random telegraph noise from a few traps (good for dots grown on submicron wafers) and 1/f noise from many traps (good for la…
