Arbitrary controlled-phase gate on fluxonium qubits using differential ac-Stark shifts
Haonan Xiong, Quentin Ficheux, Aaron Somoroff, Long B. Nguyen, Ebru Dogan, Dario Rosenstock, Chen Wang, Konstantin N. Nesterov, Maxim G. Vavilov, Vladimir E. Manucharyan
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 superconducting qubits, 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 $\textrm{ZZ}$-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 $\textrm{ZZ}$-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 demonstrate a controlled-Z gate between capacitively coupled fluxonium qubits with transition frequencies $72.3~\textrm{MHz}$ and $136.3~\textrm{MHz}$. The gate is activated by a $61.6~\textrm{ns}$ long pulse at the frequency between non-computational transitions $|10\rangle - |20\rangle$ and $|11\rangle - |21\rangle$, during which the qubits complete only $4$ and $8$ Larmor periods, respectively. The measured gate error of $(8\pm1)\times 10^{-3}$ is limited by decoherence in the non-computational subspace, which will likely improve in the next generation devices. Although our qubits are ab…
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-frequency of the $|00\rangle - |11\rangle$ 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 $\sqrt{\rm SWAP}$-like and controlled-phase gates. The gate error c…
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 pulses at 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 computation…
The superconducting fluxonium qubit has a great potential for high-fidelity quantum gates with its long coherence times and strong anharmonicity at the half flux quantum sweet spot. However, current implementations of two-qubit gates compromise fluxonium's coherence properties by requiring either a temporary population of the non-computational states or tuning the magnetic flux off the sweet spot. Here we realize a fast all-microwave cross-resonance gate between two capacitively-coupled fluxoniums with the qubit dynamics well confined to the computational space. We demonstrate a direct CNOT ga…
The superconducting fluxonium circuit is an artificial atom with a strongly anharmonic spectrum: when biased at a half flux quantum, the lowest qubit transition is an order of magnitude smaller in frequency than those to higher levels. Similar to conventional atomic systems, such a frequency separation between the computational and noncomputational subspaces allows independent optimizations of the qubit coherence and two-qubit interactions. Here we describe a controlled-Z gate for two fluxoniums connected either capacitively or inductively, with qubit transitions fixed near 500 MHz. The gate i…
Circuit quantum electrodynamics, where photons are coherently coupled to artificial atoms built with superconducting circuits, has enabled the investigation and control of macroscopic quantum-mechanical phenomena in superconductors. Recently, hybrid circuits incorporating semiconducting nanowires and other electrostatically-gateable elements have provided new insights into mesoscopic superconductivity. Extending the capabilities of hybrid flux-based circuits to work in magnetic fields would be especially useful both as a probe of spin-polarized Andreev bound states and as a possible platform f…
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 loop away 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 $\sqrt{i\mathrm{swap}}$-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…
Cross-Resonant Gates in Hybrid Fluxonium-Transmon Systems
University of Wisconsin-Madison（威斯康星大学麦迪逊分校）；SEEQC, Inc.（SEEQC公司）；University of Massachusetts-Amherst（马萨诸塞大学阿默斯特分校）；Ecole Polytechnique Federale de Lausanne（洛桑联邦理工学院）
Superconducting fluxonium qubits provide a promising alternative to transmons on the path toward large-scale superconductor-based quantum computing due to their better coherence and larger anharmonicity. A major challenge for multi-qubit fluxonium devices is the experimental demonstration of a scalable crosstalk-free multi-qubit architecture with high fidelity single-qubit and two-qubit gates, single-shot readout and state initialization. Here, we present a two-qubit fluxonium-based quantum processor with a tunable coupler element following our theoretical proposal [DOI: 10.1063/5.0064800]. We…
The superconducting fluxonium circuit is an RF-SQUID-type flux qubit that uses a large inductance built from an array of Josephson junctions or a high kinetic inductance material. This inductance suppresses charge sensitivity exponentially and flux sensitivity quadratically. In contrast to the transmon qubit, the anharmonicity of fluxonium can be large and positive, allowing for better separation between the low energy qubit manifold of the circuit and higher-lying excited states. Here, we propose a tunable coupling scheme for implementing two-qubit gates on fixed-frequency fluxonium qubits, b…
Interaction-Resilient Scalable Fluxonium Architecture with All-Microwave Gates
Institute of Science and Technology Austria（奥地利科学技术研究所）；National University of Science and Technology ‘‘MISIS’’（国立科技大学 MISIS）；Russian Quantum Center（俄罗斯量子中心）
Optimizing LZSM protocol for high-fidelity gates in open-system fluxonium
Centro Atómico Bariloche（巴里洛切原子中心）；Instituto Balseiro (Universidad Nacional de Cuyo)（巴尔塞罗研究所（门多萨国立大学））；Grupo de Circuitos Cuánticos Bariloche, Div. Dispositivos y Sensores, Centro Atómico Bariloche-CNEA（巴里洛切量子电路组，设备与传感器部，巴里洛切原子中心-国家原子能委员会）；Instituto de Nanociencia y Nanotecnología (INN), CONICET-CNEA（纳米科学与技术研究所（INN），阿根廷国家科学和技术研究委员会-国家原子能委员会）
Long coherence times, large anharmonicity and robust charge-noise insensitivity render fluxonium qubits an interesting alternative to transmons. Recent experiments have demonstrated record coherence times for low-frequency fluxonia. Here, we propose a galvanic-coupling scheme with flux-tunable $\textit{XX}$ coupling. To implement a high-fidelity entangling $\sqrt{i\mathrm{SWAP}}$ gate, we modulate the strength of this coupling and devise variable-time identity gates to synchronize required single-qubit operations. Both types of gates are implemented using strong ac flux drives, lasting for onl…
Fast entangling gates on fluxoniums via parametric modulation of plasmon interaction
Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area（粤港澳大湾区量子科学中心）；Nanjing University of Posts and Telecommunications（南京邮电大学）；Shanxi University（山西大学）；South China Normal University（华南师范大学）
The technological development of hardware heading toward universal fault-tolerant quantum computation requires a large-scale processing unit with high performance. While fluxonium qubits are promising with high coherence and large anharmonicity, their scalability has not been systematically explored. In this work, we propose a superconducting quantum information processor based on compact high-coherence fluxoniums with suppressed crosstalk, reduced design complexity, improved operational efficiency, high-fidelity gates, and resistance to parameter fluctuations. In this architecture, the qubits…
Correlation-Assisted Odd-Parity Encoded Gates in Coupled Fluxonium Qubits under Non-Markovian TLS Noise
School of Physics, Hangzhou Dianzi University（杭州电子科技大学物理学院）；State Key Laboratory of Quantum Optics Technologies and Devices, Shanxi University（山西大学量子光学技术与器件国家重点实验室）；Zhejiang Key Laboratory of Quantum State Control and Optical Field Manipulation, Hangzhou Dianzi University（杭州电子科技大学量子态调控与光场操纵浙江省重点实验室）
We present a tradeoff between leakage and pure dephasing errors for the fluxonium circuit. We show that in the insulating regime, i.e., when the persistent current flowing across the circuit is suppressed, the pure dephasing rate decreases exponentially as the impedance of the circuit is increased. In contrast to this exponential decrease, the qubit remains sufficiently anharmonic so that gates times can still be short, allowing for significant reduction in the computational error rates.
Observation of coherent flux-charge interaction in a gate-tunable fluxonium
University of Colorado Boulder（科罗拉多大学博尔德分校）；Université de Sherbrooke（舍布鲁克大学）；Niels Bohr Institute, University of Copenhagen（哥本哈根大学尼尔斯·玻尔研究所）；Technical University of Munich（慕尼黑工业大学）；Bayerische Akademie der Wissenschaften（巴伐利亚科学院）
We report superconducting fluxonium qubits with coherence times largely limited by energy relaxation and reproducibly satisfying T2 > 100 microseconds (T2 > 300 microseconds in one device). Moreover, given the state of the art values of the surface loss tangent and the 1/f flux noise amplitude, coherence can be further improved beyond 1 millisecond. Our results violate a common viewpoint that the number of Josephson junctions in a superconducting circuit -- over 100 here -- must be minimized for best qubit coherence. We outline how the unique to fluxonium combination of long coherence time and…
Superconducting qubits provide a promising path toward building large-scale quantum computers. The simple and robust transmon qubit has been the leading platform, achieving multiple milestones. However, fault-tolerant quantum computing calls for qubit operations at error rates significantly lower than those exhibited in the state of the art. Consequently, alternative superconducting qubits with better error protection have attracted increasing interest. Among them, fluxonium is a particularly promising candidate, featuring large anharmonicity and long coherence times. Here, we engineer a fluxo…
Fast CZ gate in hybrid fluxonium-transmon systems with tunable couplers
Nanjing University of Posts and Telecommunications（南京邮电大学）；Nanjing University（南京大学）；Shanxi University（山西大学）；Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area（粤港澳大湾区量子科学中心）
Native CCZ Gate with Fluxonium Qubits and a Microwave-Driven Coupler
National University of Science and Technology “MISIS”（国立科技大学 MISIS）；International Center for Quantum Optics and Quantum Technologies, Assn（国际量子光学与量子技术协会）；Moscow Center for Advanced Studies（莫斯科高等研究中心）
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 coherence time reaching $T_2^*= 1.48 \pm 0.13 \mathrm{~ms}$, 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 quasipa…
In circuit QED, protocols for quantum gates and readout of superconducting qubits often rely on the dispersive regime, reached when the qubit-photon detuning Δ is large compared to their mutual coupling strength. For qubits including the Cooper-pair box and transmon, selection rules dramatically restrict the contributions to dispersive level shifts χ. By contrast, without selection rules many virtual transitions contribute to χ and can produce sizable dispersive shifts even at large detuning. We present theory for a generic multi-level qudit capacitively coupled to one or multiple harmonic mod…
The \textit{heavy-fluxonium} circuit is a promising building block for superconducting quantum processors due to its long relaxation and dephasing time at the half-flux frustration point. However, the suppressed charge matrix elements and low transition frequency have made it challenging to perform fast single-qubit gates using standard protocols. We report on new protocols for reset, fast coherent control, and readout, that allow high-quality operation of the qubit with a 14 MHz transition frequency, an order of magnitude lower in energy than the ambient thermal energy scale. We utilize highe…
We developed a versatile integrated control and readout instrument for experiments with superconducting quantum bits (qubits), based on a field-programmable gate array (FPGA) platform. Using this platform, we perform measurement-based, closed-loop feedback operations with $428 \, \mathrm{ns}$ platform latency. The feedback capability is instrumental in realizing active reset initialization of the qubit into the ground state in a time much shorter than its energy relaxation time $T_1$. We show experimental results demonstrating reset of a fluxonium qubit with $99.4\,\%$ fidelity, using a readou…
Characterization and Comparison of Energy Relaxation in Fluxonium Qubits
Lincoln Laboratory, Massachusetts Institute of Technology（麻省理工学院林肯实验室）；Research Laboratory of Electronics, Massachusetts Institute of Technology（麻省理工学院电子研究实验室）；Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology（麻省理工学院电气工程和计算机科学系）；Google Quantum AI（谷歌量子AI）
