We analyze the cross-resonance effect for fluxonium circuits and investigate a two-qubit gate scheme based on selective darkening of a transition. In this approach, two microwave pulsesat the frequency of the target qubit are applied simultaneously with a proper ratio between their amplitudes to achieve a controlled-NOT operation. We study in detail coherent gate dynamics and calculate gate error. With nonunitary effects accounted for, we demonstrate that gate error below 10−4 is possible for realistic hardware parameters. This number is facilitated by long coherence times of computational transitions and strong anharmonicity of fluxoniums, which easily prevents excitation to higher excited states during the gate microwave drive.
We analyze a high-fidelity two-qubit gate using fast flux pulses on superconducting fluxonium qubits. The gate is realized by temporarily detuning magnetic flux through fluxonium loopaway from the half flux quantum sweet spot. We simulate dynamics of two capacitively coupled fluxoniums during the flux pulses and optimize the pulse parameters to obtain a highly accurate iswap‾‾‾‾‾‾√-like entangling gate. We also evaluate the effect of the flux noise and qubit relaxation on the gate fidelity. Our results demonstrate that the gate error remains below 10−4 for currently achievable magnitude of the flux noise and qubit relaxation time.
Increasing the degree of control over physical qubits is a crucial component of quantum computing research. We report a superconducting qubit of fluxonium type with the Ramsey coherencetime reaching T∗2=1.48±0.13 ms, which exceeds the state of the art value by an order of magnitude. As a result, the average single-qubit gate fidelity grew above 0.9999, surpassing, to our knowledge, any other solid-state quantum system. Furthermore, by measuring energy relaxation of the parity-forbidden transition to second excited state, we exclude the effect of out-of-equilibrium quasiparticles on coherence in our circuit. Combined with recent demonstrations of two-qubit gates on fluxoniums, our result paves the way for the next generation of quantum processors.
Large scale quantum computing motivates the invention of two-qubit gate schemes that not only maximize the gate fidelity but also draw minimal resources. In the case of superconductingqubits, the weak anharmonicity of transmons imposes profound constraints on the gate design, leading to increased complexity of devices and control protocols. Here we demonstrate a resource-efficient control over the interaction of strongly-anharmonic fluxonium qubits. Namely, applying an off-resonant drive to non-computational transitions in a pair of capacitively-coupled fluxoniums induces a ZZ-interaction due to unequal ac-Stark shifts of the computational levels. With a continuous choice of frequency and amplitude, the drive can either cancel the static ZZ-term or increase it by an order of magnitude to enable a controlled-phase (CP) gate with an arbitrary programmed phase shift. The cross-entropy benchmarking of these non-Clifford operations yields a sub 1% error, limited solely by incoherent processes. Our result demonstrates the advantages of strongly-anharmonic circuits over transmons in designing the next generation of quantum processors.
We propose a family of microwave-activated entangling gates on two capacitively coupled fluxonium qubits. A microwave pulse applied to either qubit at a frequency near the half-frequencyof the |00⟩−|11⟩ transition induces two-photon Rabi oscillations with a negligible leakage outside the computational subspace, owing to the strong anharmonicity of fluxoniums. By adjusting the drive frequency, amplitude, and duration, we obtain the gate family that is locally equivalent to the fermionic-simulation gates such as SWAP−−−−−−√-like and controlled-phase gates. The gate error can be tuned below 10−4 for a pulse duration under 100 ns without excessive circuit parameter matching. Given that the fluxonium coherence time can exceed 1 ms, our gate scheme is promising for large-scale quantum processors.
We demonstrate a controlled-Z gate between capacitively coupled fluxonium qubits with transition frequencies 72.3 MHz and 136.3 MHz. The gate is activated by a 61.6 ns long pulse atthe frequency between non-computational transitions |10⟩−|20⟩ and |11⟩−|21⟩, during which the qubits complete only 4 and 8 Larmor periods, respectively. The measured gate error of (8±1)×10−3 is limited by decoherence in the non-computational subspace, which will likely improve in the next generation devices. Although our qubits are about fifty times slower than transmons, the two-qubit gate is faster than microwave-activated gates on transmons, and the gate error is on par with the lowest reported. Architectural advantages of low-frequency fluxoniums include long qubit coherence time, weak hybridization in the computational subspace, suppressed residual ZZ-coupling rate (here 46 kHz), and absence of either excessive parameter matching or complex pulse shaping requirements.
Instantons, spacetime-localized quantum field tunneling events, are ubiquitous in correlated condensed matter and high energy systems. However, their direct observation through collisionswith conventional particles has not been considered possible. We show how recent advance in circuit quantum electrodynamics, specifically, the realization of galvanic coupling of a transmon qubit to a high-impedance transmission line, allows the observation of inelastic collisions of single microwave photons with instantons (phase slips). We develop the formalism for calculating the photon-instanton cross section, which should be useful in other quantum field theoretical contexts. In particular, we show that the inelastic scattering probability can significantly exceed the effect of conventional Josephson quartic anharmonicity, and reach order unity values.
Light does not typically scatter light, as witnessed by the linearity of Maxwell’s equations. We constructed a superconducting circuit, in which microwave photons have well-definedenergy and momentum, but their lifetime is finite due to decay into lower energy photons. The inelastic photon-photon interaction originates from quantum phase-slip fluctuation in a single Josephson junction and has no analogs in quantum optics. Instead, the surprisingly high decay rate is explained by mapping the system to a Luttinger liquid containing an impurity. Our result connects circuit quantum electrodynamics to the topic of boundary quantum field theories in two dimensions, influential to both high-energy and condensed matter physics. The photon lifetime data is a rare example of a verified and useful quantum many-body simulation.
Interfacing stationary qubits with propagating photons is a fundamental problem in quantum technology. Cavity quantum electrodynamics (CQED) invokes a mediator degree of freedom inthe form of a far-detuned cavity mode, the adaptation of which to superconducting circuits (cQED) proved remarkably fruitful. The cavity both blocks the qubit emission and it enables a dispersive readout of the qubit state. Yet, a more direct (cavityless) interface is possible with atomic clocks, in which an orbital cycling transition can scatter photons depending on the state of a hyperfine or quadrupole qubit transition. Originally termed „electron shelving“, such a conditional fluorescence phenomenon is the cornerstone of many quantum information platforms, including trapped ions, solid state defects, and semiconductor quantum dots. Here we apply the shelving idea to circuit atoms and demonstrate a conditional fluorescence readout of fluxonium qubit placed inside a matched one-dimensional waveguide. Cycling the non-computational transition between ground and third excited states produces a microwave photon every 91 ns conditioned on the qubit ground state, while the qubit coherence time exceeds 50 us. The readout has a built-in quantum non-demolition property, allowing over 100 fluorescence cycles in agreement with a four-level optical pumping model. Our result introduces a resource-efficient alternative to cQED. It also adds a state-of-the-art quantum memory to the growing toolbox of waveguide QED.
The non-dissipative non-linearity of a Josephson junction converts macroscopic superconducting circuits into artificial atoms, enabling some of the best controlled quantum bits (qubits)today. Three fundamental types of superconducting qubits are known, each reflecting a distinct behavior of quantum fluctuations in a Cooper pair condensate: single charge tunneling (charge qubit), single flux tunneling (flux qubit), and phase oscillations (phase qubit). Yet, the dual nature of charge and flux suggests that circuit atoms must come in pairs. Here we introduce the missing one, named „blochnium“. It exploits a coherent insulating response of a single Josephson junction that emerges from the extension of phase fluctuations beyond the 2π-interval. Evidence for such effect was found in an out-of-equilibrium dc-transport through junctions connected to high-impedance leads, although a full consensus is absent to date. We shunt a weak junction with an exceptionally high-value inductance — the key technological innovation behind our experiment — and measure the rf-excitation spectrum as a function of external magnetic flux through the resulting loop. The junction’s insulating character manifests by the vanishing flux-sensitivity of the qubit transition between the ground and the first excited states, which nevertheless rapidly recovers for transitions to higher energy states. The spectrum agrees with a duality mapping of blochnium onto transmon, which replaces the external flux by the offset charge and introduces a new collective quasicharge variable in place of the superconducting phase. Our result unlocks the door to an unexplored regime of macroscopic quantum dynamics in ultrahigh-impedance circuits, which may have applications to quantum computing and quantum metrology of direct current.