Qubit Relaxation Research Articles

Valley-enhanced fast relaxation of gate-controlled donor qubits in silicon

Gate control of donor electrons near interfaces is a generic ingredient of donor-based quantum computing. Here, we address the question: how is the phonon-assisted qubit relaxation time T1 affected as the electron is shuttled between the donor and the interface? We focus on the example of the ‘flip-flop qubit’ (Tosi et al arXiv:1509.08538v1), defined as a combination of the nuclear and electronic states of a phosphorus donor in silicon, promising fast electrical control and long dephasing times when the electron is halfway between the donor and the interface. We theoretically describe orbital relaxation, flip-flop relaxation, and electron spin relaxation. We estimate that the flip-flop qubit relaxation time can be of the order of 100 μs, 8 orders of magnitude shorter than the value for an on-donor electron in bulk silicon, and a few orders of magnitude shorter (longer) than the predicted inhomogeneous dephasing time (gate times). All three relaxation processes are boosted by (i) the nontrivial valley structure of the electron–phonon interaction, and (ii) the different valley compositions of the involved electronic states.

Increasing energy relaxation time of superconducting qubits with nonmagnetic infrared filter and shield**Project supported by the National Natural Science Foundation of China (Grant Nos. 91321310, 11274156, 11474152, 11474153, 61521001, and 11504165) and the State Key Program for Basic Research of China (Grant Nos. 2011CB922104 and 2011CBA00205).

One of the primary origins of the energy relaxation in superconducting qubits is the quasiparticle loss. The quasiparticles can be excited remarkably by infrared radiation. In order to minimize the density of quasiparticle and increase the qubit relaxation time, we design and fabricate the infrared filter and shield for superconducting qubits. In comparison with previous filters and shields, a nonmagnetic dielectric is used as the infrared absorbing material, greatly suppressing the background magnetic fluctuations. The filters can be made to impedance-match with other microwave devices. Using the as-fabricated infrared filter and shield, we increased the relaxation time of a transmon qubit from 519 ns to 1125 ns.

Controllable high-fidelity quantum state transfer and entanglement generation in circuit QED.

We propose a scheme to realize controllable quantum state transfer and entanglement generation among transmon qubits in the typical circuit QED setup based on adiabatic passage. Through designing the time-dependent driven pulses applied on the transmon qubits, we find that fast quantum sate transfer can be achieved between arbitrary two qubits and quantum entanglement among the qubits also can also be engineered. Furthermore, we numerically analyzed the influence of the decoherence on our scheme with the current experimental accessible systematical parameters. The result shows that our scheme is very robust against both the cavity decay and qubit relaxation, the fidelities of the state transfer and entanglement preparation process could be very high. In addition, our scheme is also shown to be insensitive to the inhomogeneous of qubit-resonator coupling strengths.

Three-stage decoherence dynamics of an electron spin qubit in an optically active quantum dot

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 complex many-body interaction effects. We unambiguosly demonstrate that such a view on decoherence is greatly oversimplified; the relaxation of a spin qubit state is determined by three rather than two basic stages. The additional stage corresponds to the effect of coherent dephasing processes that occur in the nuclear spin bath that manifests itself by a relatively fast but incomplete non-monotonous relaxation of the central spin polarization at intermediate timescales. This observation changes our understanding of the electron spin qubit decoherence mechanisms in solid state systems.

Quantum theory of a bandpass Purcell filter for qubit readout

The readout fidelity of superconducting transmon and Xmon qubits is partially limited by the qubit energy relaxation through the resonator into the transmission line, which is also known as the Purcell effect. One way to suppress this energy relaxation is to employ a filter which impedes microwave propagation at the qubit frequency. We present semiclassical and quantum analyses for the bandpass Purcell filter realized by E.\ Jeffrey \textit{et al}.\ [Phys.\ Rev.\ Lett.\ 112, 190504 (2014)]. For typical experimental parameters, the bandpass filter suppresses the qubit relaxation rate by up to two orders of magnitude while maintaining the same measurement rate. We also show that in the presence of a microwave drive the qubit relaxation rate further decreases with increasing drive strength.

Dephasing and dissipation in qubit thermodynamics.

We analyze the stochastic evolution and dephasing of a qubit within the quantum jump approach. It allows one to treat individual realizations of inelastic processes, and in this way it provides solutions, for instance, to problems in quantum thermodynamics and distributions in statistical mechanics. We demonstrate that dephasing and relaxation of the qubit render the Jarzynski and Crooks fluctuation relations (FRs) of nonequilibrium thermodynamics intact. On the contrary, the standard two-measurement protocol, taking into account only the fluctuations of the internal energy U, leads to deviations in FRs under the same conditions. We relate the average 〈e(-βU)〉 (where β is the inverse temperature) with the qubit's relaxation and dephasing rates in the weak dissipation limit and discuss this relationship for different mechanisms of decoherence.

Measurement of quality factor and losses in superconducting microwave resonator integrated with NbN/AlN/NbN qubit circuit

Dielectric loss from two-level systems (TLSs) formed by local defects have shown a significant impact on the qubit coherence time. These defects can originate in the insulation material for superconducting wires isolation or in the Josephson junction tunnel barrier material. Due to the complexity of the qubit circuit fabrication process, identifying the contribution from each decoherence source is challenging. In an effort to address this issue, we have developed superconducting qubit that consists of full epitaxially-grown NbN/AlN/NbN Josephson junctions in NbN coplanar waveguide (CPW) resonator circuit. The dielectric loss introduced from TLFs in tunnel junction barrier has been largely reduced due to the unique epitaxial feature of the tunnel junction. The quality factor Qi of the CPW resonator was measured and the dielectric loss tanδ is 3×10−4. The relaxation time inferred from the measured resonator quality factor was comparable to the qubit relaxation time.

Spatially resolving valley quantum interference of a donor in silicon

Electron and nuclear spins of donor ensembles in isotopically pure silicon experience a vacuum-like environment, giving them extraordinary coherence. However, in contrast to a real vacuum, electrons in silicon occupy quantum superpositions of valleys in momentum space. Addressable single-qubit and two-qubit operations in silicon require that qubits are placed near interfaces, modifying the valley degrees of freedom associated with these quantum superpositions and strongly influencing qubit relaxation and exchange processes. Yet to date, spectroscopic measurements have only probed wavefunctions indirectly, preventing direct experimental access to valley population, donor position and environment. Here we directly probe the probability density of single quantum states of individual subsurface donors, in real space and reciprocal space, using scanning tunnelling spectroscopy. We directly observe quantum mechanical valley interference patterns associated with linear superpositions of valleys in the donor ground state. The valley population is found to be within 5% of a bulk donor when 2.85 ± 0.45 nm from the interface, indicating that valley-perturbation-induced enhancement of spin relaxation will be negligible for depths greater than 3 nm. The observed valley interference will render two-qubit exchange gates sensitive to atomic-scale variations in positions of subsurface donors. Moreover, these results will also be of interest for emerging schemes proposing to encode information directly in valley polarization.

Purcell effect with microwave drive: Suppression of qubit relaxation rate

We analyze the Purcell relaxation rate of a superconducting qubit coupled to a resonator, which is coupled to a transmission line and pumped by an external microwave drive. Considering the typical regime of the qubit measurement, we focus on the case when the qubit frequency is significantly detuned from the resonator frequency. Surprisingly, the Purcell rate decreases when the strength of the microwave drive is increased. This suppression becomes significant in the nonlinear regime. In the presence of the microwave drive, the loss of photons to the transmission line also causes excitation of the qubit; however, the excitation rate is typically much smaller than the relaxation rate. Our analysis also applies to a more general case of a two-level quantum system coupled to a cavity.

Phonon-mediated decay of singlet-triplet qubits in double quantum dots

We study theoretically the phonon-induced relaxation ($T_1$) and decoherence times ($T_2$) of singlet-triplet qubits in lateral GaAs double quantum dots (DQDs). When the DQD is biased, Pauli exclusion enables strong dephasing via two-phonon processes. This mechanism requires neither hyperfine nor spin-orbit interaction and yields $T_2 \ll T_1$, in contrast to previous calculations of phonon-limited lifetimes. When the DQD is unbiased, we find $T_2 \simeq 2 T_1$ and much longer lifetimes than in the biased DQD. For typical setups, the decoherence and relaxation rates due to one-phonon processes are proportional to the temperature $T$, whereas the rates due to two-phonon processes reveal a transition from $T^2$ to higher powers as $T$ is decreased. Remarkably, both $T_1$ and $T_2$ exhibit a maximum when the external magnetic field is applied along a certain axis within the plane of the two-dimensional electron gas. We compare our results with recent experiments and analyze the dependence of $T_1$ and $T_2$ on system properties such as the detuning, the spin-orbit parameters, the hyperfine coupling, and the orientation of the DQD and the applied magnetic field with respect to the main crystallographic axes.

Non-Markovian dynamics and noise characteristics in continuous measurement of a solid-state charge qubit

We investigate the non-Markovian characteristics in continuous measurement of a charge qubit by a quantum point contact. The backflow of information from the reservoir to the system in the non-Markovian domain gives rise to strikingly different qubit relaxation and dephasing in comparison with the Markovian case. The intriguing non-Markovian dynamics is found to have a direct impact on the output noise feature of the detector. Unambiguously, we observe that the non-Markovian memory effect results in an enhancement of the signal-to-noise ratio, which can even exceed the upper limit of “4,” leading thus to the violation of the Korotkov-Averin bound in quantum measurement. Our study thus may open new possibilities to improve detector's measurement efficiency in a direct and transparent way.

Spin qubit relaxation in a moving quantum dot

Long-range quantum communication for spin qubits is an important open problem. Here we study decoherence of an electron spin qubit that is being transported in a moving quantum dot. We focus on spin decoherence due to spin-orbit interaction and a random electric potential. We find that at the lowest order, the motion induces longitudinal spin relaxation, with a rate linear in the dot velocity. Our calculated spin relaxation time ranges from sub $\mu$s in GaAs to above ms in Si, making this relaxation a significant decoherence channel. Our results also give clear indications on how to reduce the decoherence effect of electron motion.

Millisecond charge-parity fluctuations and induced decoherence in a superconducting transmon qubit.

The tunnelling of quasiparticles across Josephson junctions in superconducting quantum circuits is an intrinsic decoherence mechanism for qubit degrees of freedom. Understanding the limits imposed by quasiparticle tunnelling on qubit relaxation and dephasing is of theoretical and experimental interest, particularly as improved understanding of extrinsic mechanisms has allowed crossing the 100 microsecond mark in transmon-type charge qubits. Here, by integrating recent developments in high-fidelity qubit readout and feedback control in circuit quantum electrodynamics, we transform a state-of-the-art transmon into its own real-time charge-parity detector. We directly measure the tunnelling of quasiparticles across the single junction and isolate the contribution of this tunnelling to qubit relaxation and dephasing, without reliance on theory. The millisecond timescales measured demonstrate that quasiparticle tunnelling does not presently bottleneck transmon qubit coherence, leaving room for yet another order of magnitude increase.

Cavity-Mediated Entanglement Generation Via Landau-Zener Interferometry

We demonstrate quantum control and entanglement generation using a Landau-Zener beam splitter formed by coupling two transmon qubits to a superconducting cavity. Single passage through the cavity-mediated qubit-qubit avoided crossing provides a direct test of the Landau-Zener transition formula. Consecutive sweeps result in Landau-Zener-Stückelberg interference patterns, with a visibility that can be sensitively tuned by adjusting the level velocity through both the nonadiabatic and adiabatic regimes. Two-qubit state tomography indicates that a Bell state can be generated via a single passage, with a fidelity of 78% limited by qubit relaxation.

Qubit relaxation from evanescent-wave Johnson noise

In many quantum computer architectures, the qubits are in close proximity to metallic device elements. Metals have a high density of photon modes, and the fields spill out of the bulk metal because of the evanescent-wave component. Thus thermal and quantum electromagnetic Johnson-type noise from metallic device elements can decohere nearby qubits. In this Rapid Communication we use quantum electrodynamics to compute the strength of this evanescent-wave Johnson noise as a function of distance $z$ from a metallic half space. Previous treatments have shown unphysical divergences at $z=0$. We remedy this by using a proper nonlocal dielectric function. Decoherence rates of local qubits are proportional to the magnitude of electric or magnetic correlation functions evaluated at the qubit position. We present formulas for the decoherence rates. These formulas serve as an important constraint on future device architectures. Comparison with single-electron spin relaxation measurements shows that evanescent-wave Johnson noise may constitute the dominant relaxation mechanism in experiments performed at low magnetic field.

Dissipation and ultrastrong coupling in circuit QED

Cavity and circuit QED study light-matter interaction at its most fundamental level. Yet, this interaction is most often neglected when considering the coupling of this system with an environment. In this paper, we show how this simplification, which leads to the standard quantum optics master equation, is at the root of unphysical effects. Including qubit relaxation and dephasing, and cavity relaxation, we derive a master equation that takes into account the qubit-resonator coupling. Special attention is given to the ultrastrong coupling regime, where the failure of the quantum optical master equation is manifest. In this situation, our model predicts an asymmetry in the vacuum Rabi splitting that could be used to probe dephasing noise at unexplored frequencies. We also show how fluctuations in the qubit frequency can cause sideband transitions, squeezing, and Casimir-like photon generation.

Generation of superposition states and charge-qubit relaxation probing in a circuit

We demonstrate how a superposition of coherent states can be generated for a microwave field inside a coplanar transmission line coupled to a single superconducting charge qubit, with the addition of a single classical magnetic pulse for chirping of the qubit transition frequency. We show how the qubit dephasing induces decoherence on the field superposition state, and how it can be probed by the qubit charge detection. The character of the charge qubit relaxation process itself is imprinted in the field state decoherence profile.

Ideal quantum nondemolition measurement of a flux qubit at variable bias

We propose a scheme to realize a quantum non-demolition (QND) measurement of a superconducting flux qubit by a Josephson bifurcation amplifier. Our scheme can implement a perfect QND measurement for a qubit subject to a variable magnetic bias. Measurement back-action induced qubit relaxation can be suppressed and hence the QND fidelity is expected to be high over a wide range of bias conditions.

Quantum behavior of a flux qubit coupled to a resonator

A detailed theory for a system of a superconducting qubit coupled to a transmission line resonator is presented. We describe the system by solving analytically and numerically the master equation for the density matrix, which includes a dissipative Lindblad term. We calculate the transmission coefficient, which provides a way to probe the dressed states of a qubit. The theoretical results are related to experiments with intermediate coupling between a qubit and a resonator when the coupling energy is of the same order as the qubit relaxation rate.

Fast reset and suppressing spontaneous emission of a superconducting qubit

Spontaneous emission through a coupled cavity can be a significant decay channel for qubits in circuit quantum electrodynamics. We present a circuit design that effectively eliminates spontaneous emission due to the Purcell effect while maintaining strong coupling to a low-Q cavity. Excellent agreement over a wide range in frequency is found between measured qubit relaxation times and the predictions of a circuit model. Using fast (nanosecond time-scale) flux biasing of the qubit, we demonstrate in situ control of qubit lifetime over a factor of 50. We realize qubit reset with 99.9% fidelity in 120 ns.