We benchmark the decoherence of superconducting qubits to examine the temporal stability of energy-relaxation and dephasing. By collecting statistics during measurements spanning multiple days, we find the mean parameters $\overline{T_{1}}$ = 49 $μ$s and $\overline{T_{2}^{*}}$ = 95 $μ$s, however, both of these quantities fluctuate explaining the need for frequent re-calibration in qubit setups. Our main finding is that fluctuations in qubit relaxation are local to the qubit and are caused by instabilities of near-resonant two-level-systems (TLS). Through statistical analysis, we determine switching rates of these TLS and observe the coherent coupling between an individual TLS and a transmon qubit. Finally, we find evidence that the qubit's frequency stability is limited by capacitance noise. Importantly, this produces a 0.8 ms limit on the pure dephasing which we also observe. Collectively, these findings raise the need for performing qubit metrology to examine the reproducibility of qubit parameters, where these fluctuations could affect qubit gate fidelity.
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.
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…
We present a multi-level quantum theory of decoherence for a general circuit realization of a superconducting qubit. Using electrical network graph theory, we derive a Hamiltonian for the circuit. The dissipative circuit elements (external impedances, shunt resistors) are described using the Caldeira-Leggett model. The master equation for the superconducting phases in the Born-Markov approximation is derived and brought into the Bloch-Redfield form in order to describe multi-level dissipative quantum dynamics of the circuit. The model takes into account leakage effects, i.e. transitions from t…
We demonstrate coherent dynamics of quantized magnetic fluxes in a superconducting loop with a weak link - a nanobridge patterned from the same thin NbN film as the loop. The bridge is a short rounded shape constriction, close to 10 nm long and 20 - 30 nm wide, having minimal width at its center. Quantum state control and coherent oscillations in the driven time evolution of the tunnel-junctionless system are achieved. Decoherence and energy relaxation in the system are studied using a combination of microwave spectroscopy and direct time-domain techniques. The effective flux noise behavior su…
It is usually argued that the presence of gapless quasiparticle excitations at the nodes of the d-wave superconducting gap should strongly decohere the quantum states of a d-wave qubit, making quantum effects practically unobservable. Using a self-consistent linear response non-equilibrium quasiclassical formalism, we show that this is not necessarily true. We find quasiparticle conductance of a d-wave grain boundary junction to be strongly phase dependent. Midgap states as well as nodal quasiparticles contribute to the conductance and therefore decoherence. Quantum behavior is estimated to be…
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.
Decoherence in quantum bit circuits is presently a major limitation to their use for quantum computing purposes. We present experiments, inspired from NMR, that characterise decoherence in a particular superconducting quantum bit circuit, the quantronium. We introduce a general framework for the analysis of decoherence, based on the spectral densities of the noise sources coupled to the qubit. Analysis of our measurements within this framework indicates a simple model for the noise sources acting on the qubit. We discuss various methods to fight decoherence.
To implement a set of universal quantum logic gates based on non-Abelian geometric phases, it is a conventional wisdom that quantum systems beyond two levels are required, which is extremely difficult to fulfil for superconducting qubits, appearing to be a main reason why only single qubit gates was implemented in a recent experiment [A. A. Abdumalikov Jr \emph{et al}., Nature 496, 482 (2013)]. Here we propose to realize non-adiabatic holonomic quantum computation in decoherence-free subspace on circuit QED, where one can use only the two levels in transmon qubits, a usual interaction, and a m…
Quasiparticle excitations adversely affect the performance of superconducting devices in a wide range of applications. They limit the sensitivity of photon detectors in astronomy, the accuracy of current sources in metrology, the cooling power of micro-refrigerators, and could break the topological protection of Majorana qubits. In superconducting circuits for quantum information processing, tunneling of quasiparticles across Josephson junctions constitutes a decoherence mechanism. As relaxation and pure dephasing times of transmon-type charge qubits now reach 100 microseconds, understanding w…
The decoherence rate of a quantum dot coupled to a fluctuating environment described by a normal-metal superconductor junction is considered. The density-density correlator at low frequencies constitutes the kernel which enters the calculation of the phase coherence time. The density fluctuations are connected to the finite frequency current-current correlations in the point contact via the continuity equation. Below and above the gap, at zero temperature the density correlator contains spatial oscillations at half of the Fermi wave length on the normal side. As the bias crosses the supercondu…
We present an experimental realization of the transmon qubit, an improved superconducting charge qubit derived from the Cooper pair box. We experimentally verify the predicted exponential suppression of sensitivity to 1/f charge noise [J. Koch et al., Phys. Rev. A 76, 042319 (2007)]. This removes the leading source of dephasing in charge qubits, resulting in homogenously broadened transitions with relaxation and dephasing times in the microsecond range. Our systematic characterization of the qubit spectrum, anharmonicity, and charge dispersion shows excellent agreement with theory, rendering t…
A particular superconducting quantum interference device (SQUID)qubit, indicated as double SQUID qubit, can be manipulated by rapidly modifying its potential with the application of fast flux pulses. In this system we observe coherent oscillations exhibiting non-exponential decay, indicating a non trivial decoherence mechanism. Moreover, by tuning the qubit in different conditions (different oscillation frequencies) by changing the pulse height, we observe a crossover between two distinct decoherence regimes and the existence of an "optimal" point where the qubit is only weakly sensitive to in…
Many superconducting qubits are highly sensitive to dielectric loss, making the fabrication of coherent quantum circuits challenging. To elucidate this issue, we characterize the interfaces and surfaces of superconducting coplanar waveguide resonators and study the associated microwave loss. We show that contamination induced by traditional qubit lift-off processing is particularly detrimental to quality factors without proper substrate cleaning, while roughness plays at most a small role. Aggressive surface treatment is shown to damage the crystalline substrate and degrade resonator quality. …
We show that the relaxation and decoherence rates 1/T_1 and 1/T_2 of a qubit coupled to several noise sources are in general not additive, i.e., that the total rates are not the sums of the rates due to each individual noise source. To demonstrate this, we calculate the relaxation and pure dephasing rates 1/T_1 and 1/T_ϕof a superconducting (SC) flux qubit in the Born-Markov approximation in the presence of several circuit impedances Z_i using network graph theory and determine their deviation from additivity (the mixing term). We find that there is no mixing term in 1/T_ϕand that the mixing t…
Critical current fluctuations with a 1/ f spectral density (f is frequency) are potentially a limiting source of intrinsic decoherence in superconducting quantum bits (qubits) based on Josephson tunnel junctions. Prior measurements of this noise were made at nonzero voltages whereas qubits are operated in the zero voltage state. We report measurements of 1/ f noise in a dc superconducting quantum interference device first, coupled to a resonant tank circuit and operated in a dispersive mode at zero voltage, and, second, operated conventionally with a current bias in the voltage regime. Both me…
A superconducting ring has different sectors of states corresponding to different values of the trapped magnetic flux; this multitude of states can be used for quantum information storage. If a current supporting a nonzero flux is set up in the ring, fluctuations of electromagnetic field will be able to ``detect'' that current and thus cause a loss of quantum coherence. We estimate the decoherence exponent for a ring of a round type-II wire and find that it contains a macroscopic suppression factor $(δ/ R_{1})^{2}$, where $R_{1}$ is the radius of the wire, and $δ$ is the London penetration dep…
We find that stray infrared light from the 4 K stage in a cryostat can cause significant loss in superconducting resonators and qubits. For devices shielded in only a metal box, we measured resonators with quality factors Q = 10^5 and qubits with energy relaxation times T_1=120 ns, consistent with a stray light-induced quasiparticle density of 170-230 μm^{-3}. By adding a second black shield at the sample temperature, we found about an order of magnitude improvement in performance and no sensitivity to the 4 K radiation. We also tested various shielding methods, implying a lower limit of Q = 1…
We consider the use of a pi-junction for flux qubits to realize degenerate quantum levels without external magnetic field. On the basis of the Caldeira-Leggett model, we derive an effective spin-Boson model, and study decoherece of this type of qubits. We estimate the dephasing time by using parameters from recent experiments of SIFS junctions, and show that high critical current and large subgap resistance are required for the pi-junction to realize a long coherent time.
We investigate the Fano-type spectroscopic lineshapes of the T-shape double quantum dot coupled between the conducting and superconducting electrodes and analyze their stability on a decoherence. Because of the proximity effect the quantum interference patterns appear simultaneously at +/- epsilon_2, where epsilon_2 is an energy of the side-attached quantum dot. We find that decoherence gradually suppresses both such interferometric structures. We also show that at low temperatures another tiny Fano-type structure can be induced upon forming the Kondo state on the side-coupled quantum dot due …
We introduce simple qubit-encodings and logic gates which eliminate the need for certain difficult single-qubit operations in superconducting phase-qubits, while preserving universality. The simplest encoding uses two physical qubits per logical qubit. Two architectures for its implementation are proposed: one employing N physical qubits out of which N/2 are ancillas fixed in the |1> state, the other employing N/2+1 physical qubits, one of which is a bus qubit connected to all others. Details of a minimal set of universal encoded logic operations are given, together with recoupling schemes, th…
Superconducting circuits fabricated using the widely used shadow evaporation technique can contain unintended junctions which change their quantum dynamics. We discuss a superconducting flux qubit design that exploits the symmetries of a circuit to protect the qubit from unwanted coupling to the noisy environment, in which the unintended junctions can spoil the quantum coherence. We present a theoretical model based on a recently developed circuit theory for superconducting qubits and calculate relaxation and decoherence times that can be compared with existing experiments. Furthermore, the co…
We present a superconducting qubit for the circuit quantum electrodynamics architecture that has a tunable coupling strength g. We show that this coupling strength can be tuned from zero to values that are comparable with other superconducting qubits. At g = 0 the qubit is in a decoherence free subspace with respect to spontaneous emission induced by the Purcell effect. Furthermore we show that in the decoherence free subspace the state of the qubit can still be measured by either a dispersive shift on the resonance frequency of the resonator or by a cycling-type measurement.
Quantum states inevitably decay with time into a probabilistic mixture of classical states, due to their interaction with the environment and measurement instrumentation. We present the first measurement of the decoherence dynamics of complex photon states in a condensed-matter system. By controllably preparing a number of distinct, quantum-superposed photon states in a superconducting microwave resonator, we show that the subsequent decay dynamics can be quantitatively described by taking into account only two distinct decay channels, energy relaxation and dephasing. Our ability to prepare sp…
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 consider realistic, multi-parameter error models and investigate the performance of the surface code for three possible fault-tolerant superconducting quantum computer architectures. We map amplitude and phase damping to a diagonal Pauli "depolarization" channel via the Pauli twirl approximation, and obtain the logical error rate as a function of the qubit T1, T2 and state preparation, gate, and readout errors. A numerical Monte Carlo simulation is performed to obtain the logical error rates and a leading-order analytic formula is derived to estimate their behavior below threshold. Our resu…
The performance of superconducting qubits is orders of magnitude below what is expected from theoretical estimates based on the loss tangents of the constituent bulk materials. This has been attributed to the presence of uncontrolled surface oxides formed during fabrication which can introduce defects and impurities that create decoherence channels. Here, we develop an ab initio Shiba theory to investigate the microscopic origin of magnetic-induced decoherence in niobium thin film superconductors and the formation of native oxides. Our ab initio calculations encompass the roles of structural d…
In superconducting qubits, the interaction of the qubit degree of freedom with quasiparticles defines a fundamental limitation for the qubit coherence. We develop a theory of the pure dephasing rate Γ_ϕ caused by quasiparticles tunneling through a Josephson junction and of the inhomogeneous broadening due to changes in the occupations of Andreev states in the junction. To estimate Γ_ϕ, we derive a master equation for the qubit dynamics. The tunneling rate of free quasiparticles is enhanced by their large density of states at energies close to the superconducting gap. Nevertheless, we find that…
We present measurements of single-qubit gate errors for a superconducting qubit. Results from quantum process tomography and randomized benchmarking are compared with gate errors obtained from a double pi pulse experiment. Randomized benchmarking reveals a minimum average gate error of 1.1+/-0.3% and a simple exponential dependence of fidelity on the number of gates. It shows that the limits on gate fidelity are primarily imposed by qubit decoherence, in agreement with theory.
A phenomenon of a periodic staircase of macroscopic jumps in the admitted magnetic field has been observed, as the magnitude of an externally applied magnetic field is smoothly increased or decreased upon a superconducting (SC) loop of type II niobium-titanium wire which is coated with a non-superconducting layer of copper. Large temperature spikes were observed to occur simultaneously with the jumps, suggesting brief transitions to the normal state, caused by en masse motions of Abrikosov vortices. An experiment that exploits this phenomenon to explore the global decoherence of a large superc…
Teleportation of a quantum state may be used for distributing entanglement between distant qubits in quantum communication and for quantum computation. Here we demonstrate the implementation of a teleportation protocol, up to the single-shot measurement step, with superconducting qubits coupled to a microwave resonator. Using full quantum state tomography and evaluating an entanglement witness, we show that the protocol generates a genuine tripartite entangled state of all three-qubits. Calculating the projection of the measured density matrix onto the basis states of two qubits allows us to r…
A fundamental challenge for quantum information processing is reducing the impact of environmentally-induced errors. Quantum error detection (QED) provides one approach to handling such errors, in which errors are rejected when they are detected. Here we demonstrate a QED protocol based on the idea of quantum un-collapsing, using this protocol to suppress energy relaxation due to the environment in a three-qubit superconducting circuit. We encode quantum information in a target qubit, and use the other two qubits to detect and reject errors caused by energy relaxation. This protocol improves t…
It is frequently observed that even at very low temperatures the number of quasiparticles in superconducting materials is higher than predicted by standard BCS-theory. These quasiparticles can interact with two-level systems, such as superconducting qubits or two-level systems (TLS) in the amorphous oxide layer of a Josephson junction. This interaction leads to decay and decoherence of the TLS, with specific results, such as the time dependence, depending on the distribution of quasiparticles and the form of the interaction. We study the resulting decay laws for different experimentally releva…
We explore theoretically electromagnetically-induced transparency (EIT) in a superconducting quantum circuit (SQC). The system is a persistent-current flux qubit biased in a $Λ$ configuration. Previously [Phys. Rev. Lett. 93, 087003 (2004)], we showed that an ideally-prepared EIT system provides a sensitive means to probe decoherence. Here, we extend this work by exploring the effects of imperfect dark-state preparation and specific decoherence mechanisms (population loss via tunneling, pure dephasing, and incoherent population exchange). We find an initial, rapid population loss from the $Λ$ …
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 implementation of a Lambda scheme in superconducting artificial atoms could allow detec- tion of stimulated Raman adiabatic passage (STIRAP) and other quantum manipulations in the microwave regime. However symmetries which on one hand protect the system against decoherence, yield selection rules which may cancel coupling to the pump external drive. The tradeoff between efficient coupling and decoherence due to broad-band colored Noise (BBCN), which is often the main source of decoherence is addressed, in the class of nanodevices based on the Cooper pair box (CPB) design. We study transfer …
We study decoherence effects in qubits coupled to environments that exhibit resonant frequencies in their spectral function. We model the coupling of the qubit to its environment via the Caldeira-Leggett formulation of quantum dissipation/coherence, and study the simplest example of decoherence effects in circuits with resonances such as a dc SQUID phase qubit in the presence of an isolation circuit, which is designed to enhance the coherence time. We emphasize that the spectral density of the environment is strongly dependent on the circuit design, and can be engineered to produce longer deco…
Entangled multi-qubit states may be generated through a dispersive collective QND measurement of superconducting qubits coupled to a microwave transmission line resonator. Using the quantum trajectory approach, we analyze the stochastic measurement traces that would be observed in experiments. We illustrate the synthesis of three-qubit W- and GHZ-states, and we analyze how the fidelity and the entanglement evolve in time during the measurement. We discuss the influence of decoherence and relaxation, as well as of imperfect control over experimental parameters. We show that the desired states c…
Solid-state qubits have the potential for the large-scale integration and for the flexibility of layout for quantum computing. However, their short decoherence time due to the coupling to the environment remains an important problem to be overcome. We propose a new superconducting qubit which incorporates a spin-electronic device: the qubit consists of a superconducting ring with a ferromagnetic pi junction which has a metallic contact and a normal Josephson junction with an insulating barrier. Thus, a quantum coherent two-level state is formed without an external magnetic field. This feature …
We analyze the effect of local decoherence of two qubits on their entanglement and the Bell inequality violation. Decoherence is described by Kraus operators, which take into account dephasing and energy relaxation at an arbitrary temperature. We show that in the experiments with superconducting phase qubits the survival time for entanglement should be much longer than for the Bell inequality violation.
We show that fundamental conservation laws mandate parameter-free mechanisms of decoherence of quantum oscillations of the superconducting current between opposite directions in a SQUID -- emission of phonons and photons at the oscillation frequency. The corresponding rates are computed and compared with experimental findings. The decohering effects of external mechanical and magnetic noise are investigated.
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…
We combine the ideas of qubit encoding and dispersive dynamics to enable robust and easy quantum information processing (QIP) on paired superconducting charge boxes sharing a common bias lead. We establish a decoherence free subspace on these and introduce universal gates by dispersive interaction with a LC resonator and inductive couplings between the encoded qubits. These gates preserve the code space and only require the established local symmetry and the control of the voltage bias.
Macroscopic quantum tunneling (MQT) is a fundamental phenomenon of quantum mechanics related to the actively debated topic of quantum-to-classical transition. The ability to realize MQT affects implementation of qubit-based quantum computing schemes and their protection against decoherence. Decoherence in qubits can be reduced by means of topological protection, e.g. by exploiting various parity effects. In particular, paired phase slips can provide such protection for superconducting qubits. Here, we report on the direct observation of quantum paired phase slips in thin-wire superconducting l…
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 conditions for violation of the Bell inequality in the Clauser-Horne-Shimony-Holt form, focusing on the Josephson phase qubits. We start the analysis with maximum violation in the ideal case, and then take into account the effects of the local measurement errors and decoherence. A special attention is paid to configurations of the qubit measurement directions in the pseudospin space lying within either horizontal or vertical planes; these configurations are optimal in certain cases. Besides local measurement errors and decoherence, we also discuss the effect of measurement crosstalk…
Solid state qubits realized in superconducting circuits are potentially extremely scalable. However, strong decoherence may be transferred to the qubits by various elements of the circuits that couple individual qubits, particularly when coupling is implemented over long distances. We propose here an encoding that provides full protection against errors originating from these coupling elements, for a chain of superconducting qubits with a nearest neighbor anisotropic XY-interaction. The encoding is also seen to provide partial protection against errors deriving from general electronic noise.
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…
Superconducting quantum computing is experiencing a tremendous growth. Although major milestones have already been achieved, useful quantum-computing applications are hindered by a variety of decoherence phenomena. Decoherence due to two-level systems (TLSs) hosted by amorphous dielectric materials is ubiquitous in planar superconducting devices. We use high-quality quasilumped element resonators as quantum sensors to investigate TLS-induced loss and noise. We perform two-tone experiments with a probe and pump electric field; the pump is applied at different power levels and detunings. We meas…
We have studied decoherence in a system where two Josephson-junction flux qubits share a part of their superconducting loops and are inductively coupled. By tuning the flux bias condition, we control the sensitivities of the energy levels to flux noises in each qubit. The dephasing rate of the first excited state is enhanced or suppressed depending on the amplitudes and the signs of the sensitivities. We have quantified the $1/f$ flux noises and their correlations and found that the dominant contribution is by local fluctuations.
We have investigated dielectric losses in amorphous SiO thin films under operating conditions of superconducting qubits (mK temperatures and low microwave powers). For this purpose, we have developed a broadband measurement setup employing multiplexed lumped element resonators using a broadband power combiner and a low-noise amplifier. The measured temperature and power dependences of the dielectric losses are in good agreement with those predicted for atomic two-level tunneling systems (TLS). By measuring the losses at different frequencies, we found that the TLS density of states is energy d…
We present a new experimental protocol for performing universal gates in a register of superconducting qubits coupled by fixed on-chip linear reactances. The qubits have fixed, detuned Larmor frequencies and can remain, during the entire gate operation, biased at their optimal working point where decoherence due to fluctuations in control parameters is suppressed to first order. Two-qubit gates are performed by simultaneously irradiating two qubits at their respective Larmor frequencies with appropriate amplitude and phase, while one-qubit gates are performed by the usual single-qubit irradiat…
We propose a scheme in which the quantum coherence of a nanomechanical resonator can be probed using a superconducting qubit. We consider a mechanical resonator coupled capacitively to a Cooper-pair box and assume that the superconducting qubit is tuned to the degeneracy point so that its coherence time is maximised and the electro-mechanical coupling can be approximated by a dispersive Hamiltonian. When the qubit is prepared in a superposition of states this drives the mechanical resonator progressively into a superposition which in turn leads to apparent decoherence of the qubit. Applying a …
