Coherent suppression of electromagnetic dissipation due to superconducting quasiparticles

Efficient Initialization of Fluxonium Qubits based on Auxiliary Energy Levels

Fast and high-fidelity qubit initialization is crucial for low-frequency qubits such as fluxonium, and in applications of many quantum algorithms and quantum error correction codes. In a circuit quantum electrodynamics system, the initialization is typically achieved by transferring the state between the qubit and a short-lived cavity through microwave driving, also known as the sideband cooling process in atomic system. Constrained by the selection rules from the parity symmetry of the wave functions, the sideband transitions are only enabled by multiphoton processes which require multitone or strong driving. Leveraging the flux tunability of fluxonium, we circumvent this limitation by breaking flux symmetry to enable an interaction between a noncomputational qubit transition and the cavity excitation. With single-tone sideband driving, we realize qubit initialization with a fidelity exceeding 99% within a duration of 300 ns, robust against the variation of control parameters. Furthermore, we show that our initialization scheme has a built-in benefit in simultaneously removing the second-excited state population of the qubit, and can be easily incorporated into a large-scale fluxonium processor.

Coexistence of Nonequilibrium Density and Equilibrium Energy Distribution of Quasiparticles in a Superconducting Qubit

The density of quasiparticles typically observed in superconducting qubits exceeds the value expected in equilibrium by many orders of magnitude. Can this out-of-equilibrium quasiparticle density still possess an energy distribution in equilibrium with the phonon bath? Here, we answer this question affirmatively by measuring the thermal activation of charge-parity switching in a transmon qubit with a difference in superconducting gap on the two sides of the Josephson junction. We then demonstrate how the gap asymmetry of the device can be exploited to manipulate its parity.

Heat Bath in a Quantum Circuit

We discuss the concept and realization of a heat bath in solid state quantum systems. We demonstrate that, unlike a true resistor, a finite one-dimensional Josephson junction array or analogously a transmission line with non-vanishing frequency spacing, commonly considered as a reservoir of a quantum circuit, does not strictly qualify as a Caldeira-Leggett type dissipative environment. We then consider a set of quantum two-level systems as a bath, which can be realized as a collection of qubits. We show that only a dense and wide distribution of energies of the two-level systems can secure long Poincare recurrence times characteristic of a proper heat bath. An alternative for this bath is a collection of harmonic oscillators, for instance, in the form of superconducting resonators.

Mechanically induced correlated errors on superconducting qubits with relaxation times exceeding 0.4 ms

Superconducting qubits are among the most advanced candidates for achieving fault-tolerant quantum computing. Despite recent significant advancements in the qubit lifetimes, the origin of the loss mechanism for state-of-the-art qubits is still subject to investigation. Furthermore, the successful implementation of quantum error correction requires negligible correlated errors between qubits. Here, we realize long-lived superconducting transmon qubits that exhibit fluctuating lifetimes, averaging 0.2 ms and exceeding 0.4 ms - corresponding to quality factors above 5 million and 10 million, respectively. We then investigate their dominant error mechanism. By introducing novel time-resolved error measurements that are synchronized with the operation of the pulse tube cooler in a dilution refrigerator, we find that mechanical vibrations from the pulse tube induce nonequilibrium dynamics in highly coherent qubits, leading to their correlated bit-flip errors. Our findings not only deepen our understanding of the qubit error mechanisms but also provide valuable insights into potential error-mitigation strategies for achieving fault tolerance by decoupling superconducting qubits from their mechanical environments.

Native Approach to Controlled-Z Gates in Inductively Coupled Fluxonium Qubits

The fluxonium qubits have emerged as a promising platform for gate-based quantum information processing. However, their extraordinary protection against charge fluctuations comes at a cost: when coupled capacitively, the qubit-qubit interactions are restricted to XX interactions. Consequently, effective ZZ or XZ interactions are only constructed either by temporarily populating higher-energy states, or by exploiting perturbative effects under microwave driving. Instead, we propose and demonstrate an inductive coupling scheme, which offers a wide selection of native qubit-qubit interactions for fluxonium. In particular, we leverage a built-in, flux-controlled ZZ interaction to perform qubit entanglement. To combat the increased flux-noise-induced dephasing away from the flux-insensitive position, we use a continuous version of the dynamical decoupling scheme to perform noise filtering. Combining these, we demonstrate a 20 ns controlled-z gate with a mean fidelity of 99.53%. More than confirming the efficacy of our gate scheme, this high-fidelity result also reveals a promising but rarely explored parameter space uniquely suitable for gate operations between fluxonium qubits.

In-Plane Anisotropy of Electrical Transport in Y0.85Tb0.15Ba2Cu3O7-x Films

We fabricated high-quality c-axis-oriented epitaxial YBa2Cu3O7-x films with 15% of the yttrium atoms replaced by terbium (YTBCO) and studied their electrical properties. The Tb substitution reduced the charge carrier density, resulting in increased resistivity and decreased critical current density compared to pure YBa2Cu3O7-x films. The electrical properties of the YTBCO films showed an in-plane anisotropy in both the superconducting and normal states that, together with the XRD data, provided evidence for, at least, a partially twin-free film. Unexpectedly, the resistive transition of the bridges also demonstrated the in-plane anisotropy that could be explained within the framework of Tinkham's model of resistive transition and the Berezinskii-Kosterlitz-Thouless (BKT) model, depending on the sample parameters. Measurements of the differential resistance in the temperature range of the resistive transition confirmed the occurrence of the BKT transition in the YTBCO bridges. Therefore, we consider the YTBCO films to be a promising platform for both the fabrication of devices with high kinetic inductance and fundamental research on the BKT transition in cuprate superconductors.

Superconducting Qubit Based on Twisted Cuprate Van der Waals Heterostructures

Van-der-Waals assembly enables the fabrication of novel Josephson junctions featuring an atomically sharp interface between two exfoliated and relatively twisted Bi_{2}Sr_{2}CaCu_{2}O_{8+x} (Bi2212) flakes. In a range of twist angles around 45°, the junction provides a regime where the interlayer two-Cooper pair tunneling dominates the current-phase relation. Here we propose employing this novel junction to realize a capacitively shunted qubit that we call flowermon. The d-wave nature of the order parameter endows the flowermon with inherent protection against charge-noise-induced relaxation and quasiparticle-induced dissipation. This inherently protected qubit paves the way to a new class of high-coherence hybrid superconducting quantum devices based on unconventional superconductors.

Nonequilibrium Fractional Josephson Effect

Josephson tunnel junctions exhibit a supercurrent typically proportional to the sine of the superconducting phase difference ϕ. In general, a term proportional to cos(ϕ) is also present, alongside microscopic electronic retardation effects. We show that voltage pulses sharply varying in time prompt a significant impact of the cos(ϕ) term. Its interplay with the sin(ϕ) term results in a nonequilibrium fractional Josephson effect (NFJE) ∼sin(ϕ/2) in the presence of bound states close to zero frequency. Our microscopic analysis reveals that the interference of nonequilibrium virtual quasiparticle excitations is responsible for this phenomenon. We also analyze this phenomenon for topological Josephson junctions with Majorana bound states. Remarkably, the NFJE is independent of the ground state fermion parity unlike its equilibrium counterpart.

Dynamical Polarization of the Fermion Parity in a Nanowire Josephson Junction

Josephson junctions in InAs nanowires proximitized with an Al shell can host gate-tunable Andreev bound states. Depending on the bound state occupation, the fermion parity of the junction can be even or odd. Coherent control of Andreev bound states has recently been achieved within each parity sector, but it is impeded by incoherent parity switches due to excess quasiparticles in the superconducting environment. Here, we show that we can polarize the fermion parity dynamically using microwave pulses by embedding the junction in a superconducting LC resonator. We demonstrate polarization up to 94%±1% (89%±1%) for the even (odd) parity as verified by single shot parity readout. Finally, we apply this scheme to probe the flux-dependent transition spectrum of the even or odd parity sector selectively, without any postprocessing or heralding.

Proposal for Trapped-Ion Quantum Memristor

A quantum memristor combines the memristive dynamics with the quantum behavior of the system. We analyze the idea of a quantum memristor based on ultracold ions trapped in a Paul trap. Corresponding input and output memristor signals are the ion electronic levels populations. We show that under certain conditions the output/input dependence is a hysteresis curve similar to classical memristive devices. This behavior becomes possible due to the partial decoherence provided by the feedback loop, which action depends on previous state of the system (memory). The feedback loop also introduces nonlinearity in the system. Ion-based quantum memristor possesses several advantages comparing to other platforms-photonic and superconducting circuits-due to the presence of a large number of electronic levels with different lifetimes as well as strong Coulomb coupling between ions in the trap. The implementation of the proposed ion-based quantum memristor will be a significant contribution to the novel direction of "quantum neural networks".

Inductively shunted transmons exhibit noise insensitive plasmon states and a fluxon decay exceeding 3 hours

Currently available quantum processors are dominated by noise, which severely limits their applicability and motivates the search for new physical qubit encodings. In this work, we introduce the inductively shunted transmon, a weakly flux-tunable superconducting qubit that offers charge offset protection for all levels and a 20-fold reduction in flux dispersion compared to the state-of-the-art resulting in a constant coherence over a full flux quantum. The parabolic confinement provided by the inductive shunt as well as the linearity of the geometric superinductor facilitates a high-power readout that resolves quantum jumps with a fidelity and QND-ness of >90% and without the need for a Josephson parametric amplifier. Moreover, the device reveals quantum tunneling physics between the two prepared fluxon ground states with a measured average decay time of up to 3.5 h. In the future, fast time-domain control of the transition matrix elements could offer a new path forward to also achieve full qubit control in the decay-protected fluxon basis.

Millisecond Coherence in a Superconducting Qubit

Improving control over physical qubits is a crucial component of quantum computing research. Here we report a superconducting fluxonium qubit with uncorrected coherence time T_{2}^{*}=1.48±0.13  ms, exceeding the state of the art for transmons by an order of magnitude. The average gate fidelity was benchmarked at 0.99991(1). Notably, even in the millisecond range, the coherence time is limited by material absorption and could be further improved with a more rigorous fabrication. Our demonstration may be useful for suppressing errors in the next generation quantum processors.

Engineering superconducting qubits to reduce quasiparticles and charge noise

Identifying, quantifying, and suppressing decoherence mechanisms in qubits are important steps towards the goal of engineering a quantum computer or simulator. Superconducting circuits offer flexibility in qubit design; however, their performance is adversely affected by quasiparticles (broken Cooper pairs). Developing a quasiparticle mitigation strategy compatible with scalable, high-coherence devices is therefore highly desirable. Here we experimentally demonstrate how to control quasiparticle generation by downsizing the qubit, capping it with a metallic cover, and equipping it with suitable quasiparticle traps. Using a flip-chip design, we shape the electromagnetic environment of the qubit above the superconducting gap, inhibiting quasiparticle poisoning. Our findings support the hypothesis that quasiparticle generation is dominated by the breaking of Cooper pairs at the junction, as a result of photon absorption by the antenna-like qubit structure. We achieve record low charge-parity switching rate (<1 Hz). Our aluminium devices also display improved stability with respect to discrete charging events.

Ultrahigh Kinetic Inductance Superconducting Materials from Spinodal Decomposition

Disordered superconducting nitrides with kinetic inductance have long been considered to be leading material candidates for high-inductance quantum-circuit applications. Despite continuing efforts toward reducing material dimensions to increase the kinetic inductance and the corresponding circuit impedance, achieving further improvements without compromising material quality has become a fundamental challenge. To this end, a method to drastically increase the kinetic inductance of superconducting materials via spinodal decomposition while maintaining a low microwave loss is proposed. Epitaxial Ti_0.48 Al_0.52 N is used as a model system and the utilization of spinodal decomposition to trigger the insulator-to-superconductor transition with a drastically enhanced material disorder is demonstrated. The measured kinetic inductance increases by two to three orders of magnitude compared with the best disordered superconducting nitrides reported to date. This work paves the way for substantially enhancing and deterministically controlling the inductance for advanced superconducting quantum circuits.

Materials challenges and opportunities for quantum computing hardware

Quantum computing hardware technologies have advanced during the past two decades, with the goal of building systems that can solve problems that are intractable on classical computers. The ability to realize large-scale systems depends on major advances in materials science, materials engineering, and new fabrication techniques. We identify key materials challenges that currently limit progress in five quantum computing hardware platforms, propose how to tackle these problems, and discuss some new areas for exploration. Addressing these materials challenges will require scientists and engineers to work together to create new, interdisciplinary approaches beyond the current boundaries of the quantum computing field.

Bias-preserving gates with stabilized cat qubits

The code capacity threshold for error correction using biased-noise qubits is known to be higher than with qubits without such structured noise. However, realistic circuit-level noise severely restricts these improvements. This is because gate operations, such as a controlled-NOT (CX) gate, which do not commute with the dominant error, unbias the noise channel. Here, we overcome the challenge of implementing a bias-preserving CX gate using biased-noise stabilized cat qubits in driven nonlinear oscillators. This continuous-variable gate relies on nontrivial phase space topology of the cat states. Furthermore, by following a scheme for concatenated error correction, we show that the availability of bias-preserving CX gates with moderately sized cats improves a rigorous lower bound on the fault-tolerant threshold by a factor of two and decreases the overhead in logical Clifford operations by a factor of five. Our results open a path toward high-threshold, low-overhead, fault-tolerant codes tailored to biased-noise cat qubits.

Active Quasiparticle Suppression in a Non-Equilibrium Superconductor

Quasiparticle (qp) poisoning is a major issue that impairs the operation of various superconducting devices. Even though these devices are often operated at temperatures well below the critical point where the number density of excitations is expected to be exponentially suppressed, their bare operation and stray microwave radiation excite the non-equilibrium qp's. Here we use voltage-biased superconducting junctions to demonstrate and quantify qp extraction in the turnstile operation of a superconductor-insulator-normal metal-insulator-superconductor single-electron transistor. In this operation regime, excitations are injected into the superconducting leads at a rate proportional to the driving frequency. We reach a reduction of density by an order of magnitude even for the highest injection rate of 2.4 × 108 qp's per second when extraction is turned on.

Multi-qubit phase gate on multiple resonators mediated by a superconducting bus

We propose a one-step scheme for implementing multi-qubit phase gates on microwave photons in multiple resonators mediated by a superconducting bus in circuit quantum electrodynamics (QED) system. In the scheme, multiple single-mode resonators carry quantum information with their vacuum and single-photon Fock states, and a multi-level artificial atom acts as a quantum bus which induces the indirect interaction among resonators. The method of pulse engineering is used to shape the coupling strength between resonators and the bus so as to improve the fidelity and robustness of the scheme. We also discuss the influence of finite coherence time for the bus and resonators on gate fidelity respectively. Finally, we consider the suppression of unwanted transitions and propose the method of optimized detuning compensation for offsetting unwanted transitions, showing the feasibility of the scheme within the current experiment technology.

Photon-Assisted Charge-Parity Jumps in a Superconducting Qubit

We evaluate the rates of energy and phase relaxation of a superconducting qubit caused by stray photons with energy exceeding the threshold for breaking a Cooper pair. All channels of relaxation within this mechanism are associated with the change in the charge parity of the qubit, enabling the separation of the photon-assisted processes from other contributions to the relaxation rates. Among the signatures of the new mechanism is the same order of rates of the transitions in which a qubit loses or gains energy, which is in agreement with recent experiments. Our theory offers the possibility to characterize the electromagnetic environment of superconducting devices at the single-photon level for frequencies above the superconducting gap.

Granular aluminium as a superconducting material for high-impedance quantum circuits

Superconducting quantum information processing machines are predominantly based on microwave circuits with relatively low characteristic impedance, about 100 Ω, and small anharmonicity, which can limit their coherence and logic gate fidelity^1,2. A promising alternative is circuits based on so-called superinductors^3-6, with characteristic impedances exceeding the resistance quantum R_Q = 6.4 kΩ. However, previous implementations of superinductors, consisting of mesoscopic Josephson junction arrays^7,8, can introduce unintended nonlinearity or parasitic resonant modes in the qubit vicinity, degrading its coherence. Here, we present a fluxonium qubit design based on a granular aluminium superinductor strip^9-11. We show that granular aluminium can form an effective junction array with high kinetic inductance and be in situ integrated with standard aluminium circuit processing. The measured qubit coherence time [Formula: see text] illustrates the potential of granular aluminium for applications ranging from protected qubit designs to quantum-limited amplifiers and detectors.

Nanowire Superinductance Fluxonium Qubit

We characterize a fluxonium qubit consisting of a Josephson junction inductively shunted with a NbTiN nanowire superinductance. We explain the measured energy spectrum by means of a multimode theory accounting for the distributed nature of the superinductance and the effect of the circuit nonlinearity to all orders in the Josephson potential. Using multiphoton Raman spectroscopy, we address multiple fluxonium transitions, observe multilevel Autler-Townes splitting and measure an excited state lifetime of T_{1}=20  μs. By measuring T_{1} at different magnetic flux values, we find a crossover in the lifetime limiting mechanism from capacitive to inductive losses.

Circuit QED: single-step realization of a multiqubit controlled phase gate with one microwave photonic qubit simultaneously controlling n - 1 microwave photonic qubits

We present a novel method to realize a multi-target-qubit controlled phase gate with one microwave photonic qubit simultaneously controlling n - 1 target microwave photonic qubits. This gate is implemented with n microwave cavities coupled to a superconducting flux qutrit. Each cavity hosts a microwave photonic qubit, whose two logic states are represented by the vacuum state and the single photon state of a single cavity mode, respectively. During the gate operation, the qutrit remains in the ground state and thus decoherence from the qutrit is greatly suppressed. This proposal requires only a single-step operation and thus the gate implementation is quite simple. The gate operation time is independent of the number of the qubits. In addition, this proposal does not need applying classical pulse or any measurement. Numerical simulations demonstrate that high-fidelity realization of a controlled phase gate with one microwave photonic qubit simultaneously controlling two target microwave photonic qubits is feasible with current circuit QED technology. The proposal is quite general and can be applied to implement the proposed gate in a wide range of physical systems, such as multiple microwave or optical cavities coupled to a natural or artificial Λ-type three-level atom.

Hot Nonequilibrium Quasiparticles in Transmon Qubits

Nonequilibrium quasiparticle excitations degrade the performance of a variety of superconducting circuits. Understanding the energy distribution of these quasiparticles will yield insight into their generation mechanisms, the limitations they impose on superconducting devices, and how to efficiently mitigate quasiparticle-induced qubit decoherence. To probe this energy distribution, we systematically correlate qubit relaxation and excitation with charge-parity switches in an offset-charge-sensitive transmon qubit, and find that quasiparticle-induced excitation events are the dominant mechanism behind the residual excited-state population in our samples. By itself, the observed quasiparticle distribution would limit T_{1} to ≈200  μs, which indicates that quasiparticle loss in our devices is on equal footing with all other loss mechanisms. Furthermore, the measured rate of quasiparticle-induced excitation events is greater than that of relaxation events, which signifies that the quasiparticles are more energetic than would be predicted from a thermal distribution describing their apparent density.

Loss Mechanisms and Quasiparticle Dynamics in Superconducting Microwave Resonators Made of Thin-Film Granular Aluminum

Superconducting high kinetic inductance elements constitute a valuable resource for quantum circuit design and millimeter-wave detection. Granular aluminum (grAl) in the superconducting regime is a particularly interesting material since it has already shown a kinetic inductance in the range of nH/□ and its deposition is compatible with conventional Al/AlOx/Al Josephson junction fabrication. We characterize microwave resonators fabricated from grAl with a room temperature resistivity of 4×10^{3}  μΩ cm, which is a factor of 3 below the superconductor to insulator transition, showing a kinetic inductance fraction close to unity. The measured internal quality factors are on the order of Q_{i}=10^{5} in the single photon regime, and we demonstrate that nonequilibrium quasiparticles (QPs) constitute the dominant loss mechanism. We extract QP relaxation times in the range of 1 s and we observe QP bursts every ∼20  s. The current level of coherence of grAl resonators makes them attractive for integration in quantum devices, while it also evidences the need to reduce the density of nonequilibrium QPs.

Steady-State Coherences by Composite System-Bath Interactions

We identify sufficient conditions on the structure of the interaction Hamiltonian between a two-level quantum system and a thermal bath that, without any external drive or coherent measurement, guarantee the generation of steady-state coherences (SSC). The SSC obtained this way, remarkably, turn out to be independent of the initial state of the system, which could therefore be taken as initially incoherent. We characterize in detail this phenomenon, first analytically in the weak coupling regime for two paradigmatic models, and then numerically in more complex systems without any assumption on the coupling strength. In all of these cases, we find that SSC become increasingly significant as the bath is cooled down. These results can be directly verified in many experimental platforms.

Hybrid rf SQUID qubit based on high kinetic inductance

We report development and microwave characterization of rf SQUID (Superconducting QUantum Interference Device) qubits, consisting of an aluminium-based Josephson junction embedded in a superconducting loop patterned from a thin film of TiN with high kinetic inductance. Here we demonstrate that the systems can offer small physical size, high anharmonicity, and small scatter of device parameters. The work constitutes a non-tunable prototype realization of an rf SQUID qubit built on the kinetic inductance of a superconducting nanowire, proposed in Phys. Rev. Lett. 104, 027002 (2010). The hybrid devices can be utilized as tools to shed further light onto the origin of film dissipation and decoherence in phase-slip nanowire qubits, patterned entirely from disordered superconducting films.

Demonstration of Protection of a Superconducting Qubit from Energy Decay

Long-lived transitions occur naturally in atomic systems due to the abundance of selection rules inhibiting spontaneous emission. By contrast, transitions of superconducting artificial atoms typically have large dipoles, and hence their lifetimes are determined by the dissipative environment of a macroscopic electrical circuit. We designed a multilevel fluxonium artificial atom such that the qubit's transition dipole can be exponentially suppressed by flux tuning, while it continues to dispersively interact with a cavity mode by virtual transitions to the noncomputational states. Remarkably, energy decay time T_{1} grew by 2 orders of magnitude, proportionally to the inverse square of the transition dipole, and exceeded the benchmark value of T_{1}>2  ms (quality factor Q_{1}>4×10^{7}) without showing signs of saturation. The dephasing time was limited by the first-order coupling to flux noise to about 4  μs. Our circuit validated the general principle of hardware-level protection against bit-flip errors and can be upgraded to the 0-π circuit [P. Brooks, A. Kitaev, and J. Preskill, Phys. Rev. A 87, 052306 (2013)PLRAAN1050-294710.1103/PhysRevA.87.052306], adding protection against dephasing and certain gate errors.

One-step implementation of a hybrid Fredkin gate with quantum memories and single superconducting qubit in circuit QED and its applications

In a recent remarkable experiment [Sci. Adv. 2, e1501531 (2016)], a 3-qubit quantum Fredkin (i.e., controlled-SWAP) gate was demonstrated by using linear optics. Here we propose a simple experimental scheme by utilizing the dispersive interaction in superconducting quantum circuit to implement a hybrid Fredkin gate with a superconducting flux qubit as the control qubit and two separated quantum memories as the target qudits. The quantum memories considered here are prepared by the superconducting coplanar waveguide resonators or nitrogen-vacancy center ensembles. In particular, it is shown that this Fredkin gate can be realized using a single-step operation and more importantly, each target qudit can be in an arbitrary state with arbitrary degrees of freedom. Furthermore, we show that this experimental scheme has many potential applications in quantum computation and quantum information processing such as generating arbitrary entangled states (discrete-variable states or continuous-variable states) of the two memories, measuring the fidelity and the entanglement between the two memories. With state-of-the-art circuit QED technology, the numerical simulation is performed to demonstrate that two-memory NOON states, entangled coherent states, and entangled cat states can be efficiently synthesized.

Towards phase-coherent caloritronics in superconducting circuits

The emerging field of phase-coherent caloritronics (from the Latin word calor, heat) is based on the possibility of controlling heat currents by using the phase difference of the superconducting order parameter. The goal is to design and implement thermal devices that can control energy transfer with a degree of accuracy approaching that reached for charge transport by contemporary electronic components. This can be done by making use of the macroscopic quantum coherence intrinsic to superconducting condensates, which manifests itself through the Josephson effect and the proximity effect. Here, we review recent experimental results obtained in the realization of heat interferometers and thermal rectifiers, and discuss a few proposals for exotic nonlinear phase-coherent caloritronic devices, such as thermal transistors, solid-state memories, phase-coherent heat splitters, microwave refrigerators, thermal engines and heat valves. Besides being attractive from the fundamental physics point of view, these systems are expected to have a vast impact on many cryogenic microcircuits requiring energy management, and possibly lay the first stone for the foundation of electronic thermal logic.

Quantum information processing with superconducting circuits: a review

During the last ten years, superconducting circuits have passed from being interesting physical devices to becoming contenders for near-future useful and scalable quantum information processing (QIP). Advanced quantum simulation experiments have been shown with up to nine qubits, while a demonstration of quantum supremacy with fifty qubits is anticipated in just a few years. Quantum supremacy means that the quantum system can no longer be simulated by the most powerful classical supercomputers. Integrated classical-quantum computing systems are already emerging that can be used for software development and experimentation, even via web interfaces. Therefore, the time is ripe for describing some of the recent development of superconducting devices, systems and applications. As such, the discussion of superconducting qubits and circuits is limited to devices that are proven useful for current or near future applications. Consequently, the centre of interest is the practical applications of QIP, such as computation and simulation in Physics and Chemistry.

Degeneracy-Preserving Quantum Nondemolition Measurement of Parity-Type Observables for Cat Qubits

A central requirement for any quantum error correction scheme is the ability to perform quantum nondemolition measurements of an error syndrome, corresponding to a special symmetry property of the encoding scheme. It is in particular important that such a measurement does not introduce extra error mechanisms, not included in the error model of the correction scheme. In this Letter, we ensure such a robustness by designing an interaction with a measurement device that preserves the degeneracy of the measured observable. More precisely, we propose a scheme to perform continuous and quantum nondemolition measurement of photon-number parity in a microwave cavity. This corresponds to the error syndrome in a class of error correcting codes called the cat codes, which have recently proven to be efficient and versatile for quantum information processing. In our design, we exploit the strongly nonlinear Hamiltonian of a high-impedance Josephson circuit, coupling a high-Q cavity storage cavity mode to a low-Q readout one. By driving the readout resonator at its resonance, the phase of the reflected or transmitted signal carries directly exploitable information on parity-type observables for encoded cat qubits of the high-Q mode.

0-π phase-controllable thermal Josephson junction

Two superconductors coupled by a weak link support an equilibrium Josephson electrical current that depends on the phase difference ϕ between the superconducting condensates. Yet, when a temperature gradient is imposed across the junction, the Josephson effect manifests itself through a coherent component of the heat current that flows opposite to the thermal gradient for |ϕ| < π/2 (refs 2-4). The direction of both the Josephson charge and heat currents can be inverted by adding a π shift to ϕ. In the static electrical case, this effect has been obtained in a few systems, for example via a ferromagnetic coupling or a non-equilibrium distribution in the weak link. These structures opened new possibilities for superconducting quantum logic and ultralow-power superconducting computers. Here, we report the first experimental realization of a thermal Josephson junction whose phase bias can be controlled from 0 to π. This is obtained thanks to a superconducting quantum interferometer that allows full control of the direction of the coherent energy transfer through the junction. This possibility, in conjunction with the completely superconducting nature of our system, provides temperature modulations with an unprecedented amplitude of ∼100 mK and transfer coefficients exceeding 1 K per flux quantum at 25 mK. Then, this quantum structure represents a fundamental step towards the realization of caloritronic logic components such as thermal transistors, switches and memory devices. These elements, combined with heat interferometers and diodes, would complete the thermal conversion of the most important phase-coherent electronic devices and benefit cryogenic microcircuits requiring energy management, such as quantum computing architectures and radiation sensors.

Transport Signatures of Quasiparticle Poisoning in a Majorana Island

We investigate effects of quasiparticle poisoning in a Majorana island with strong tunnel coupling to normal-metal leads. In addition to the main Coulomb blockade diamonds, "shadow" diamonds appear, shifted by 1e in gate voltage, consistent with transport through an excited (poisoned) state of the island. Comparison to a simple model yields an estimate of parity lifetime for the strongly coupled island (∼1  μs) and sets a bound for a weakly coupled island (>10  μs). Fluctuations in the gate-voltage spacing of Coulomb peaks at high field, reflecting Majorana hybridization, are enhanced by the reduced lever arm at strong coupling. When converted from gate voltage to energy units, fluctuations are consistent with previous measurements.

Quantum Memristors with Superconducting Circuits

Memristors are resistive elements retaining information of their past dynamics. They have garnered substantial interest due to their potential for representing a paradigm change in electronics, information processing and unconventional computing. Given the advent of quantum technologies, a design for a quantum memristor with superconducting circuits may be envisaged. Along these lines, we introduce such a quantum device whose memristive behavior arises from quasiparticle-induced tunneling when supercurrents are cancelled. For realistic parameters, we find that the relevant hysteretic behavior may be observed using current state-of-the-art measurements of the phase-driven tunneling current. Finally, we develop suitable methods to quantify memory retention in the system.

Thermal conductance of Nb thin films at sub-kelvin temperatures

We determine the thermal conductance of thin niobium (Nb) wires on a silica substrate in the temperature range of 0.1–0.6 K using electron thermometry based on normal metal-insulator-superconductor tunnel junctions. We find that at 0.6 K, the thermal conductance of Nb is two orders of magnitude lower than that of Al in the superconducting state, and two orders of magnitude below the Wiedemann-Franz conductance calculated with the normal state resistance of the wire. The measured thermal conductance exceeds the prediction of the Bardeen-Cooper-Schrieffer theory, and demonstrates a power law dependence on temperature as T^4.5, instead of an exponential one. At the same time, we monitor the temperature profile of the substrate along the Nb wire to observe possible overheating of the phonon bath. We show that Nb can be successfully used for thermal insulation in a nanoscale circuit while simultaneously providing an electrical connection.

Observation of Classical-Quantum Crossover of 1/f Flux Noise and Its Paramagnetic Temperature Dependence

By analyzing the dissipative dynamics of a tunable gap flux qubit, we extract both sides of its two-sided environmental flux noise spectral density over a range of frequencies around 2k_{B}T/h≈1  GHz, allowing for the observation of a classical-quantum crossover. Below the crossover point, the symmetric noise component follows a 1/f power law that matches the magnitude of the 1/f noise near 1 Hz. The antisymmetric component displays a 1/T dependence below 100 mK, providing dynamical evidence for a paramagnetic environment. Extrapolating the two-sided spectrum predicts the linewidth and reorganization energy of incoherent resonant tunneling between flux qubit wells.

Loops and Strings in a Superconducting Lattice Gauge Simulator

We propose an architecture for an analog quantum simulator of electromagnetism in 2+1 dimensions, based on an array of superconducting fluxonium devices. The encoding is in the integer (spin-1) representation of the quantum link model formulation of compact U(1) lattice gauge theory. We show how to engineer Gauss' law via an ancilla mediated gadget construction, and how to tune between the strongly coupled and intermediately coupled regimes. The witnesses to the existence of the predicted confining phase of the model are provided by nonlocal order parameters from Wilson loops and disorder parameters from 't Hooft strings. We show how to construct such operators in this model and how to measure them nondestructively via dispersive coupling of the fluxonium islands to a microwave cavity mode. Numerical evidence is found for the existence of the confined phase in the ground state of the simulation Hamiltonian on a ladder geometry.

Suppressing relaxation in superconducting qubits by quasiparticle pumping

Dynamical error suppression techniques are commonly used to improve coherence in quantum systems. They reduce dephasing errors by applying control pulses designed to reverse erroneous coherent evolution driven by environmental noise. However, such methods cannot correct for irreversible processes such as energy relaxation. We investigate a complementary, stochastic approach to reducing errors: Instead of deterministically reversing the unwanted qubit evolution, we use control pulses to shape the noise environment dynamically. In the context of superconducting qubits, we implement a pumping sequence to reduce the number of unpaired electrons (quasiparticles) in close proximity to the device. A 70% reduction in the quasiparticle density results in a threefold enhancement in qubit relaxation times and a comparable reduction in coherence variability.

The flux qubit revisited to enhance coherence and reproducibility

The scalable application of quantum information science will stand on reproducible and controllable high-coherence quantum bits (qubits). Here, we revisit the design and fabrication of the superconducting flux qubit, achieving a planar device with broad-frequency tunability, strong anharmonicity, high reproducibility and relaxation times in excess of 40 μs at its flux-insensitive point. Qubit relaxation times T1 across 22 qubits are consistently matched with a single model involving resonator loss, ohmic charge noise and 1/f-flux noise, a noise source previously considered primarily in the context of dephasing. We furthermore demonstrate that qubit dephasing at the flux-insensitive point is dominated by residual thermal-photons in the readout resonator. The resulting photon shot noise is mitigated using a dynamical decoupling protocol, resulting in T2≈85 μs, approximately the 2T1 limit. In addition to realizing an improved flux qubit, our results uniquely identify photon shot noise as limiting T2 in contemporary qubits based on transverse qubit-resonator interaction.

Robust quantum control using smooth pulses and topological winding

The greatest challenge in achieving the high level of control needed for future technologies based on coherent quantum systems is the decoherence induced by the environment. Here, we present an analytical approach that yields explicit constraints on the driving field which are necessary and sufficient to ensure that the leading-order noise-induced errors in a qubit's evolution cancel exactly. We derive constraints for two of the most common types of noise that arise in qubits: slow fluctuations of the qubit energy splitting and fluctuations in the driving field itself. By theoretically recasting a phase in the qubit's wavefunction as a topological winding number, we can satisfy the noise-cancelation conditions by adjusting driving field parameters without altering the target state or quantum evolution. We demonstrate our method by constructing robust quantum gates for two types of spin qubit: phosphorous donors in silicon and nitrogen-vacancy centers in diamond.

Non-Poissonian quantum jumps of a fluxonium qubit due to quasiparticle excitations

As the energy relaxation time of superconducting qubits steadily improves, nonequilibrium quasiparticle excitations above the superconducting gap emerge as an increasingly relevant limit for qubit coherence. We measure fluctuations in the number of quasiparticle excitations by continuously monitoring the spontaneous quantum jumps between the states of a fluxonium qubit, in conditions where relaxation is dominated by quasiparticle loss. Resolution on the scale of a single quasiparticle is obtained by performing quantum nondemolition projective measurements within a time interval much shorter than T₁, using a quantum-limited amplifier (Josephson parametric converter). The quantum jump statistics switches between the expected Poisson distribution and a non-Poissonian one, indicating large relative fluctuations in the quasiparticle population, on time scales varying from seconds to hours. This dynamics can be modified controllably by injecting quasiparticles or by seeding quasiparticle-trapping vortices by cooling down in a magnetic field.

Flux qubits with long coherence times for hybrid quantum circuits

We present measurements of superconducting flux qubits embedded in a three dimensional copper cavity. The qubits are fabricated on a sapphire substrate and are measured by coupling them inductively to an on-chip superconducting resonator located in the middle of the cavity. At their flux-insensitive point, all measured qubits reach an intrinsic energy relaxation time in the 6-20  μs range and a pure dephasing time comprised between 3 and 10  μs. This significant improvement over previous works opens the way to the coherent coupling of a flux qubit to individual spins.