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arXiv:1705.07873 · Physical Review Letters

Demonstration of Protection of a Superconducting Qubit from Energy Decay

Yen‐Hsiang Lin, Long B. Nguyen, Nicholas Grabon, Jonathan San Miguel, Natalia Pankratova, Vladimir Manucharyan

Published Apr 13, 2018• 110 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevlett.120.150503

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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.
Encoding a qubit in logical quantum states with wave functions characterized by disjoint support and robust energies can offer simultaneous protection against relaxation and pure dephasing. One of the most promising candidates for such a fully protected superconducting qubit is the 0-π circuit [Brooks et al., Phys. Rev. A 87, 052306 (2013)]. Here we realize the proposed circuit topology in an experimentally obtainable parameter regime, where the ground-state degeneracy is lifted but the qubit is still largely noise protected. More precisely, the logical states of this qubit feature disjoint support and are exponentially protected against relaxation and exponentially (first order) protected against dephasing due to charge (flux) noise. We name the resultant device the "soft 0-π qubit."Multitone spectroscopy measurements reveal the energy-level structure of the system, which can be precisely described by a simple two-mode Hamiltonian. Using a Raman-type protocol, we exploit a higher-lying charge-insensitive energy level of the device to realize coherent population transfer and logical operations. The measured relaxation (T1 = 1.6 ms) and dephasing (TR = 9 μs, T2E = 25μs) times demonstrate that the soft 0-π circuit not only broadens the family of superconducting qubits but also constitutes an important step toward quantum computing with intrinsically protected superconducting qubits.
This thesis reports recent achievements toward scalable quantum computing with fluxonium, a superconducting artificial atom with rich energy spectrum and selection rules similar to those found in natural atoms. We show how such spectral properties can be harnessed to protect the qubit from energy relaxation and dephasing. At half-integer flux quantum bias, we show that fluxonium’s |0〉→ |1〉qubit transition has high coherence by design, with T1, T2≈500 μs in one device, the highest reported in superconducting circuits so far. Yet, the qubit exhibits the same level of addressability found in more conventional superconducting qubits (Tgate<50 ns). In addition, a controlled-Z gate can be implemented by sending a short2π-pulse at a frequency near the |1〉→|2〉transition of the target qubit. Preliminary results suggest that this gate can be used to entangle two fluxonium qubits with high fidelity. We also discuss experimental techniques employed to characterize the qubits, and present a perspective on future fluxonium-based quantum technologies.
Interfacing long-lived qubits with propagating photons is a fundamental challenge in quantum technology. Cavity and circuit quantum electrodynamics (cQED) architectures rely on an off-resonant cavity, which blocks the qubit emission and enables a quantum non-demolition (QND) dispersive readout. However, no such buffer mode is necessary for controlling a large class of three-level systems that combine a metastable qubit transition with a bright cycling transition, using the electron shelving effect. Here we demonstrate shelving of a circuit atom, fluxonium, placed inside a microwave waveguide. With no cavity modes in the setup, the qubit coherence time exceeds 50 μs, and the cycling transition's radiative lifetime is under 100 ns. By detecting a homodyne fluorescence signal from the cycling transition, we implement a QND readout of the qubit and account for readout errors using a minimal optical pumping model. Our result establishes a resource-efficient (cavityless) alternative to cQED for controlling superconducting qubits.
Superconducting qubits offer an unprecedentedly high degree of flexibility in terms of circuit encoding and parameter choices. However, in designing the qubit parameters, one typically faces the conflicting goals of long coherence times and simple control capabilities. Both are determined by the wavefunction overlap of the qubit basis states and the corresponding matrix elements. Here, we address this problem by introducing a qubit architecture with real-time tunable bit-flip protection. In the first, the “heavy” regime, the energy relaxation time can be on the order of hours for fluxons located in two near-degenerate ground states, as recently demonstrated in Ref. [Hassani ., (2023)]. The second, “light” regime, facilitates high-fidelity control on nanosecond timescales without the need for microwave signals. We propose two different tuning mechanisms of the qubit potential and show that base-band flux-pulses of around 10 ns are sufficient to realize a universal set of high-fidelity single- and two-qubit gates. This realizes a hardware-efficient and strongly noise-biased qubit platform with analogies to cat qubits with the potential for efficient quantum error correction. We expect that the introduced concept of fast and real-time wavefunction control can also be applied to other hardware-protected qubit designs.
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.
To control and measure the state of a quantum system, it must necessarily be coupled to external degrees of freedom. This inevitably leads to spontaneous emission via the Purcell effect, photon-induced dephasing from measurement backaction, and errors caused by unwanted interactions with nearby quantum systems. To tackle this fundamental challenge, we make use of the design flexibility of superconducting quantum circuits to form a multimode element—an artificial molecule—with symmetry-protected modes. The proposed circuit consists of three superconducting islands coupled to a central island via Josephson junctions. It exhibits two essential nonlinear modes, one of which is flux insensitive and used as the protected qubit mode. The second mode is flux tunable and serves via a cross-Kerr-type coupling as a mediator to control the dispersive coupling of the qubit mode to the readout resonator. We demonstrate the Purcell protection of the qubit mode by measuring relaxation times that are independent of the mediated dispersive coupling. We show that the coherence of the qubit is not limited by photon-induced dephasing when detuning the mediator mode from the readout resonator and thereby reducing the dispersive coupling. The resulting highly protected qubit, which we refer to as P-mon, with tunable interactions may serve as a basic building block of a scalable quantum processor architecture, in which qubit decoherence is strongly suppressed. Published by the American Physical Society 2024