We provide insight into the qubit measurement process involving a switching type of detector. We study the switching-induced decoherence during escape events. We present a simple method to obtain analytical results for the qubit dephasing and bit-flip errors, which can be easily adapted to various systems. Within this frame we investigate potential of switching detectors for a fast but only weakly invasive type of detection. We show that the mechanism that leads to strong dephasing, and thus fast measurement, inverts potential bit flip errors due to an intrinsic approximate time reversal symmetry.
Decoherence of a flux qubit due to inelastic scattering of thermal phonons by the qubit is studied. The computed decoherence rates contain no unknown constants and are expressed entirely in terms of measurable parameters of the qubit. The answer depends strongly on the size of the qubit as compared to the wavelength of phonons of frequency corresponding to the tunnel splitting of the qubit. Thermal phonons set the upper limit on the operating temperature of a small qubit at around 10-20 K. For large qubits acoustic decoherence due to one phonon processes should be taken into account at any tem…
On the way to solid-state quantum computing, overcoming decoherence is the central issue. In this contribution, we discuss the modeling of decoherence of a superonducting flux qubit coupled to dissipative electronic circuitry. We discuss its impact on single qubit decoherence rates and on the performance of two-qubit gates. These results can be used for designing decoherence-optimal setups.
We study theoretically how decoherence affects superposition states composed of entangled states in inductively coupled two superconducting flux-qubits. We discover that the quantum fluctuation of an observable in a coupled flux-qubit system plays a crucial role in decoherence when the expectation value of the observable is zero. This examplifies that decoherence can be also induced through a quantum mechanically higher-order effect. We also find that there exists a decoherence free subspace for the environment coupled via a charge degree of freedom of the qubit system.
This work deals with two pressing issues in the design and operation of Josephson qubits -- loss of coherence and measurement. (Longer abstract follows in the work.)
The charge-phase Josephson qubit based on a superconducting single charge transistor inserted in a low-inductance superconducting loop is considered. The loop is inductively coupled to a radio-frequency driven tank circuit enabling the readout of the qubit states by measuring the effective Josephson inductance of the transistor. The effect of qubit dephasing and relaxation due to electric and magnetic control lines as well as the measuring system is evaluated. Recommendations for operation of the qubit in magic points producing minimum decoherence are given.
The transmon superconducting qubit is being intensely investigated as a promising approach for the physical implementation of quantum information processing, and high quality factors of order $10^6$ have been achieved both in two- and three-dimensional architectures. These high quality factors enable detailed investigations of decoherence mechanisms. An intrinsic decoherence process originates from the coupling between the qubit degree of freedom and the quasiparticles that tunnel across Josephson junctions. In a transmon, tunneling of a single quasiparticle is associated with a change in pari…
In this lectures, we have described some essential features of loss of coherence by a qubit coupled to the environment. We have first presented well known semiclassical arguments that relate both decoherence and relaxation to the environmental noise. Then we have shown that models with pure decoherence (but no relaxation in qubit states) can be exactly solvable. As an example, we have treated in detail the model of fluctuating background charges which is believed to describe one of the most important channels for decoherence for the charge Josephson junction qubit. We have shown that the decoh…
We analyze the spontaneous switching between the two Néel states of Fe chains on Cu$_2$N/Cu(100), experimentally studied by Loth et al. [Science 335, 196 (2012)]. We show that, in the experimental low-temperature regime (T ~ 1K), decoherence induced by substrate electrons deeply modifies the dynamics of the chain magnetization. The Rabi oscillations associated to quantum tunneling of the isolated chain are replaced by an irreversible decay of considerably longer characteristic time. The computed switching rate is small, rapidly decreasing with chain length, with a 1/T behavior and in good agre…
We examine the decoherence of an asymmetric two-qubit system that is coupled via a tunable interaction term to a common bath or two individual baths of harmonic oscillators. The dissipative dynamics are evaluated using the Bloch-Redfield formalism. It is shown that the behaviour of the decoherence effects is affected mostly by different symmetries between the qubit operator which is coupled to the environment and temperature, whereas the differences between the two bath configurations are very small. Moreover, it is elaborated that small imperfections of the qubit parameters do not lead to a d…
A flux qubit can have a relatively long decoherence time at the degeneracy point, but away from this point the decoherence time is greatly reduced by dephasing. This limits the practical applications of flux qubits. Here we propose a new qubit design modified from the commonly used flux qubit by introducing an additional capacitor shunted in parallel to the smaller Josephson junction (JJ) in the loop. Our results show that the effects of noise can be considerably suppressed, particularly away from the degeneracy point, by both reducing the coupling energy of the JJ and increasing the shunt cap…
We have developed quantitative description of quantum coherent oscillations in the system of two coupled qubits in the presence of weak decoherence that in general can be correlated between the two qubits. It is shown that in the experimentally realized scheme of excitation of the oscillations, their waveform is not very sensitive to the magnitude of decoherence correlations. Modification of this scheme into potentially useful probe of the degree of decoherence correlations at the two qubits is suggested.
We review progress at UCSB on understanding the physics of decoherence in superconducting qubits. Although many decoherence mechanisms were studied and fixed in the last 5 years, the most important ones are two-level state defects in amorphous dielectrics, non-equilibrium quasiparticles generated from stray infrared light, and radiation to slotline modes. With improved design, the performance of integrated circuit transmons using the Xmon design are now close to world record performance: these devices have the advantage of retaining coherence when scaled up to 9 qubits.
We investigate effects of the particle-hole asymmetry on the properties of Majorana qubtis. Particle-hole asymmetric pertrubation shifts Majorana zero mode from zero-energy. This type of asymmetry can act as a source of decoherence in Majorana qubits. We find that particle-hole asymmetric pertrubation causes phase-shifts and bit-flips decoherence processes in Majorana qubits. However, these sources of decoherence are negligible in uniform system with spatially separated Majorana zero modes.
In this paper, we study the quantum decoherence induced by accumulation of electron tunnelings during the quantum measurement of a charge qubit. The charge qubit is a single electron confined in coupled quantum dots. The measurement of the qubit states is performed using a quantum point contact. A set of master equations for qubit states is derived within a nonequilibrium perturbation to the equilibrium reservoir due to the electron accumulation between the source and drain of the quantum point contact. The quantum decoherence of the qubit states arose from the electron accumulation during the…
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 discuss how to make use of high-Tc d-wave Josephson junctions in the construction of a phase qubit. We especially focus on the effect of the quasiparticle dissipation and the zero energy bound state on the macroscopic quantum tunneling which corresponds to the final measurement process of the d-wave phase qubit.
We report experiments on superconducting flux qubits in a circuit quantum electrodynamics (cQED) setup. Two qubits, independently biased and controlled, are coupled to a coplanar waveguide resonator. Dispersive qubit state readout reaches a maximum contrast of $72\,\%$. We find intrinsic energy relaxation times at the symmetry point of $7\,μ\text{s}$ and $20\,μ\text{s}$ and levels of flux noise of $2.6\,μΦ_0/\sqrt{\text{Hz}}$ and $2.7\,μΦ_0/\sqrt{\text{Hz}}$ at 1 Hz for the two qubits. We discuss the origin of decoherence in the measured devices. These results demonstrate the potential of cQED…
We analyze the robustness of decoherence-free (DF) subspace and subsystem in charge qubits, when difference from the collective decoherence measurement condition is large in the long time period, which is applicable for solid-state qubits using as a quantum memory. We solve master equations of up to four charge qubits and a detector as a quantum point contact (QPC). We show that robustness of DF states is strongly affected by local non-uniformities. We also discuss the possible two-qubit logical states by exactly solving the master equations.
Based on a network graph analysis of the underlying circuit, a quantum theory of arbitrary superconducting charge qubits is derived. Describing the dissipative elements of the circuit with a Caldeira-Leggett model, we calculate the decoherence and leakage rates of a charge qubit. The analysis includes decoherence due to a dissipative circuit element such as a voltage source or the quasiparticle resistances of the Josephson junctions in the circuit. The theory presented here is dual to the quantum circuit theory for superconducting flux qubits. In contrast to spin-boson models, the full Hilbert…
Rapid progress in semiconductor spin qubits has enabled experimental demonstrations of a two-qubit logic gate. Understanding spin decoherence in a two-qubit logic gate is necessary for optimal qubit operation. We study spin decoherence due to $1/f$ charge noise for two electrons in a double quantum dot used for a two-qubit controlled-phase gate. In contrast to the usual belief, spin decoherence can be dominated by the tunneling noise from $1/f$ charge noise instead of the detuning noise. Tunneling noise can dominate because the effect of tunneling noise on the spin qubit is first order in the …
We have investigated decoherence in Josephson-junction flux qubits. Based on the measurements of decoherence at various bias conditions, we discriminate contributions of different noise sources. In particular, we present a Gaussian decay function of the echo signal as evidence of dephasing due to $1/f$ flux noise whose spectral density is evaluated to be about $(10^{-6} Φ_0)^2$/Hz at 1 Hz. We also demonstrate that at an optimal bias condition where the noise sources are well decoupled the coherence observed in the echo measurement is mainly limited by energy relaxation of the qubit.
Quantum dot-based spin qubits are resilient towards charge noise and are affected by magnetic noise only. However, environmental interaction leads to decoherence in these qubit systems. The external control parameters are directly related to the magnitude of decoherence. This in turn limits the range of values of those parameters for which operations can be done with high fidelity. In this work, using a model of quantum dot spin qubit system, we investigate the impact of varying ac magnetic fields on suppression of decoherence. We report an increment in the usable range of static magnetic fiel…
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…
We study a pair of capacitively coupled singlet-triplet spin qubits. We characterize the two-qubit decoherence through two complementary measures, the decay time of coupled-qubit oscillations and the fidelity of entangled state preparation. We provide a quantitative map of their dependence on charge noise and field noise, and we highlight the magnetic field gradient across each singlet-triplet qubit as an effective tool to suppress decoherence due to charge noise.
Qubit realizations based on Majorana bound states have been considered promising candidates for quantum information processing which is inherently inert to decoherence. We put the underlying general arguments leading to this conjecture to the test from an open quantum system perspective. It turns out that, from a fundamental point of view, the Majorana qubit is as susceptible to decoherence as any local paradigm of a qubit.
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…
We study decoherence of a quantum dot charge qubit due to coupling to piezoelectric acoustic phonons in the Born-Markov approximation. After including appropriate form factors, we find that phonon decoherence rates are one to two orders of magnitude weaker than was previously predicted. We calculate the dependence of the Q-factor on lattice temperature, quantum dot size, and interdot coupling. Our results suggest that mechanisms other than phonon decoherence play a more significant role in current experimental setups.
The control of discrete quantum states in solids and their use for quantum information processing is complicated by the lack of a detailed understanding of the mechanisms responsible for qubit decoherences. For spin qubits in semiconductor quantum dots, phenomenological models of decoherence currently recognize two Basic stages; fast ensemble dephasing due to the coherent precession of spin qubits around nearly static but randomly distributed hyperfine fields and a much slower process of irreversible relaxation of spin qubit polarization due to dynamics of the nuclear spin bath induced by comp…
We study the decoherence effect of charge noise on a single flip-flop qubit and two dipole-coupled qubits. We find that a single flip-flop qubit is highly resistant to charge noise at its sweet spots. However, due to the proximity of the charge excited states to the flip-flop logical states, the presence of charge noise greatly reduces the fidelity of two-qubit operations. We identify leakage from the qubit Hilbert space as the main culprit for the reduced gate fidelity. We also explore different bias conditions to mitigate this decoherence channel.
By coupling with a qubit, we demonstrate that qubit decoherence can unambiguously detect the occurrence of ground-state degeneracy in many-body systems. We first demonstrate universality using the two-band model. Consequently, several exemplifications, focused on topological condensed matter systems in one, two, and three dimensions, are presented to validate our proposal. The key point is that qubit decoherence varies significantly when energy bands touch each other at the Fermi surface. In addition, it can partially reflect the degeneracy inside the band. This feature implies that qubit deco…
We analyze the quantum process tomography (QPT) in the presence of decoherence, focusing on distinguishing local and non-local decoherence mechanisms for a two-partite system from experimental QPT data. In particular, we consider the $\sqrt{\rm iSWAP}$ gate realized with superconducting phase qubits and calculate the QPT matrix $χ$ in the presence of several local and non-local decoherence processes. We determine specific patterns of these decoherence processes, which can be used for a fast identification of the main decoherence mechanisms from an experimental $χ$-matrix.
Interaction of solid state qubits with environmental degrees of freedom strongly affects the qubit dynamics, and leads to decoherence. In quantum information processing with solid state qubits, decoherence significantly limits the performances of such devices. Therefore, it is necessary to fully understand the mechanisms that lead to decoherence. In this review we discuss how decoherence affects two of the most successful realizations of solid state qubits, namely, spin-qubits and superconducting qubits. In the former, the qubit is encoded in the spin 1/2 of the electron, and it is implemented…
In this report, we examine the decoherence of a spin qubits system coupled to counted spin chain with a $1/r^2$ interaction by using influence functional. We also examine the time evolution of density matrix numerically when environment is Gaussian noise.
It has often been assumed that electrically floating qubits, such as flux qubits, are immune to decoherence due to capacitive coupling. We show that capacitive coupling to bias leads can be a dominant source of dissipation, and therefore of decoherence, for such floating qubits. Classical electrostatic arguments are sufficient to get a good estimate of this source of relaxation for standard superconducting qubit designs. We show that relaxation times can be improved by designing floating qubits so they couple symmetrically to the bias leads. Observed coherence times of flux qubits with varying…
We discuss the origin of decoherence in Josephson junction qubits. We find that two level systems in the surrounding insulator cannot be the dominant source of noise in small qubits. We argue that electron traps in the Josephson barrier with large Coulomb repulsion would give noise that agrees both in magnitude and in temperature dependence with experimental data.
Recent experiments by Hayashi et al. [Phys. Rev. Lett. 91, 226804 (2003)] demonstrate coherent oscillations of a charge quantum bit (qubit) in laterally defined quantum dots. We study the intrinsic electron-phonon decoherence and gate performance for the next step: a system of two coupled charge qubits. The effective decoherence model contains properties of local as well as collective decoherence. Decoherence channels can be classified by their multipole moments, which leads to different low-energy spectra. It is shown that due to the super-Ohmic spectrum, the gate quality is limited by the si…
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.
We study the dynamics of impurity bound electrons interacting with a bath of conduction band electrons in a semiconductor. Only the exchange interaction is considered. We derive master equations for the density matrices of single and two qubit systems under the usual Born and Markov approximations. The bath mediated RKKY interaction in the two qubit case arises naturally. It leads to an energy shift significant only when the ratio ($R_{T}$) of the inter-qubit distance to the thermal deBroglie wavelength of the bath electrons is small. This bath mediated interaction also has a profound impact o…
We discuss decoherence due to electromagnetic fluctuations in charge qubits formed by two lateral quantum dots. We use an effective circuit model to evaluate correlations of voltage fluctuations in the qubit setup. These correlations allows us to estimate energy (T1) and phase (T2) relaxation times of the the qubit system. Our theoretical estimate of the quality factor due to dephasing by electromagnetic fluctuations yields values much higher than those found in recent experiments, indicating that other sources of decoherence play a dominant role.
In spin-based architectures of quantum devices, the hyperfine interaction between the electron spin qubit and the nuclear spin environment remains one of the main sources of decoherence. This paper provides a short review of the current advances in the theoretical description of the qubit decoherence dynamics. Next, we study the qubit-environment entanglement using negativity as its measure. For an initial maximally mixed state of the environment, we study negativity dynamics as a function of environment size, changing the numbers of environmental nuclei and the total spin of the nuclei. Furth…
We study qubit decoherence under generalized dispersive readout, i.e., we investigate a qubit coupled to a resonantly driven dissipative harmonic oscillator. We provide a complete picture by allowing for arbitrarily large qubit-oscillator detuning and by considering also a coupling to the square of the oscillator coordinate, which is relevant for flux qubits. Analytical results for the decoherence time are obtained by a transformation of the qubit-oscillator Hamiltonian to the dispersive frame and a subsequent master equation treatment beyond the Markov limit. We predict a crossover from Marko…
It is known that it is possible to encode a logical qubit over many physical qubits such that it is immune to the effects of collective decoherence, and it is possible to perform universal quantum computation using these `decoherence-free' qubits. However, current proposed methods of performing gates on these encoded qubits could be difficult to implement, or could take too much time to perform. Here we investigate whether exploiting ring-exchange interactions, which may be naturally present, can simplify the implementation of these gates in any way. Using a ring exchange interaction, we have …
We study decoherence of a field-driven qubit in the presence of environmental noises. For a general qubit, we find that driving, whether on-resonance or off-resonance, alters the qubit decoherence rates (including dissipation and pure dephasing), allowing both blue and red sideband contributions from the reservoir. Depending on the noise spectral density, driving field detuning and driving field phase shift, the qubit decoherence rates could be either accelerated or reduced. We apply our general theory to the system of an electron spin qubit that is confined in a quantum dot and driven by an i…
The quantum nature of a microscopic system can only be revealed when it is sufficiently decoupled from surroundings. Interactions with the environment induce relaxation and decoherence that turn the quantum state into a classical mixture. Here, we study the timescales of these processes for a qubit encoded in the collective state of a set of magnetic atoms deposited on a metallic surface. For that, we provide a generalization of the commonly used definitions of $T_{1}$ and $T_{2}$ characterizing relaxation and decoherence rates. We calculate these quantities for several atomic structures, incl…
Decoherence of a solid state based qubit can be caused by coupling to microscopic degrees of freedom in the solid. We lay out a simple theory and use it to estimate decoherence for a recently proposed superconducting persistent current design. All considered sources of decoherence are found to be quite weak, leading to a high quality factor for this qubit.
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…
We describe a method by which the decoherence time of a solid state qubit may be measured. The qubit is coded in the orbital degree of freedom of a single electron bound to a pair of donor impurities in a semiconductor host. The qubit is manipulated by adiabatically varying an external electric field. We show that, by measuring the total probability of a successful qubit rotation as a function of the control field parameters, the decoherence rate may be determined. We estimate various system parameters, including the decoherence rates due to electromagnetic fluctuations and acoustic phonons. W…
We consider an electrostatic qubit located near a Bose-Einstein condensate (BEC) of noninteracting bosons in a double-well potential, which is used for qubit measurements. Tracing out the BEC variables we obtain a simple analytical expression for the qubit's density-matrix. The qubit's evolution exhibits a slow ($\propto1/\sqrt{t}$) damping of the qubit's coherence term, which however turns to be a Gaussian one in the case of static qubit. This stays in contrast to the exponential damping produced by most classical detectors. The decoherence is, in general, incomplete and strongly depends on t…
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 …
We compare approaches to evaluation of decoherence at low temperatures in two-state quantum systems weakly coupled to the environment. By analyzing an exactly solvable model, we demonstrate that a non-Markovian approximation scheme yields good quality estimates of the reduced density matrix for time scales appropriate for evaluation of quantum computing designs.
We discuss decoherence in charge qubits formed by multiple lateral quantum dots in the framework of the spin-boson model and the Born-Markov approximation. We consider the intrinsic decoherence caused by the coupling to bulk phonon modes. Two distinct quantum dot configurations are studied: (i) Three quantum dots in a ring geometry with one excess electron in total and (ii) arrays of quantum dots where the computational basis states form multipole charge configurations. For the three-dot qubit, we demonstrate the possibility of performing one- and two-qubit operations by solely tuning gate vol…
Many quantum dot qubits operate in regimes where the energy splittings between qubit states are large and phonons can be the dominant source of decoherence. The recently proposed charge quadrupole qubit, based on one electron in a triple quantum dot, employs a highly symmetric charge distribution to suppress the influence of charge noise. To study the effects of phonons on the charge quadrupole qubit, we consider Larmor and Ramsey pulse sequences to identify favorable operating parameters. We show that it is possible to implement typical gates with $>99.99\%$ fidelity in the presence of phonon…
We investigate the decoherence process for a quantum register composed of N qubits coupled to an environment. We consider an environment composed of one common phonon bath and several electronic baths. This environment is relevant to the implementation of a charge based solid-state quantum computer. We explicitly compute the time evolution of all off-diagonal terms of the register's reduced density matrix. We find that in realistic configurations, "superdecoherence" and "decoherence free subspaces" do not exist for an N-qubit system. This means that all off-diagonal terms decay like exp(-q(t)N…
We analyze decoherence of an electron in a double-dot due to the interaction with acoustic phonons. For large tunneling rates between the quantum dots, the main contribution to decoherence comes from the phonon emission relaxation processes, while for small tunneling rates, the virtual-phonon, dephasing processes dominate. Our results show that in common semiconductors, such as Si and GaAs, the latter mechanism determines the upper limit for the double-dot charge qubit performance measure.
We investigate hyperfine-induced decoherence in a triangular spin-cluster for different qubit encodings. Electrically controllable eigenstates of spin chirality (C_z) show decoherence times that approach milliseconds, two orders of magnitude longer than those estimated for the eigenstates of the total spin projection (S_z) and of the partial spin sum (S_{12}). The robustness of chirality is due to its decoupling from both the total- and individual-spin components in the cluster. This results in a suppression of the effective interaction between C_z and the nuclear spin bath.
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 d…
