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arXiv:2008.00593 · Physical Review Applied

Characterization of Multilevel Dynamics and Decoherence in a High-Anharmonicity Capacitively Shunted Flux Circuit

Muhammet Ali Yurtalan, Jiahao Shi, Graydon J. K. Flatt, Adrian Lupaşcu

Published Nov 30, 2021• 12 citations
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Abstract

We present the design and characterization of a three-Josephson-junction superconducting loop circuit with three large shunt capacitors. Used as a qubit, the circuit shows long energy-relaxation times, of the order of $40\phantom{\rule{0.2em}{0ex}}\ensuremath{\mu}\mathrm{s}$ and a spin-echo dephasing time of $9.4\phantom{\rule{0.2em}{0ex}}\ensuremath{\mu}\mathrm{s}$. The circuit has high anharmonicity, of $2\ensuremath{\pi}\ifmmode\times\else\texttimes\fi{}3.69\phantom{\rule{0.2em}{0ex}}\mathrm{GHz}$. We extract the multilevel relaxation and dephasing rates of the circuit used as a qutrit and discuss the possible sources for the decoherence. The high anharmonicity allows for fast qubit control with nanosecond-range gate durations and a measured average gate fidelity of 99.92%, characterized by randomized benchmarking. These results demonstrate interesting potential use for fast nanosecond-time-scale two-qubit gates and multilevel quantum logic.

DOI
10.1103/physrevapplied.16.054051

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We present the design and characterization of a three-Josephson-junction superconducting loop circuit with three large shunt capacitors. Used as a qubit, the circuit shows long energy-relaxation times, of the order of 40\ensuremathμs40\phantom{\rule{0.2em}{0ex}}\ensuremath{\mu}\mathrm{s}40\ensuremathμs and a spin-echo dephasing time of 9.4\ensuremathμs9.4\phantom{\rule{0.2em}{0ex}}\ensuremath{\mu}\mathrm{s}9.4\ensuremathμs. The circuit has high anharmonicity, of 2\ensuremathπ\ifmmode×\else\texttimes\fi3.69GHz2\ensuremath{\pi}\ifmmode\times\else\texttimes\fi{}3.69\phantom{\rule{0.2em}{0ex}}\mathrm{GHz}2\ensuremathπ\ifmmode×\else\texttimes\fi3.69GHz. We extract the multilevel relaxation and dephasing rates of the circuit used as a qutrit and discuss the possible sources for the decoherence. The high anharmonicity allows for fast qubit control with nanosecond-range gate durations and a measured average gate fidelity of 99.92%, characterized by randomized benchmarking. These results demonstrate interesting potential use for fast nanosecond-time-scale two-qubit gates and multilevel quantum logic.
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Superconducting devices have emerged as leading candidates for building practical quantum computers, owing to their scalability, designability, and ease of control. Development of superconducting devices has been accompanied by increases in coherence times from nanoseconds to tens of microseconds, and a multitude of new types of superconducting qubits. In turn, these improvements in coherence, and study of superconducting qubits has produced models for these devices accurate and trustworthy enough to enable design decisions to be determined prior to device fabrication. Recent work by the superconducting quantum devices (SQD) group has produced a variant of the capacitively-shunted flux qubit that features fast control over the lowest three levels, allowing the device to be used as a qutrit. This thesis presents a model and characterization results for this device. \n \nThis thesis also presents experimental results characterizing control fidelity for a qutrit using randomized benchmarking (RB). Quantum process tomography and application of repeated gate sequences are also used to support the randomized benchmarking results. The method of synthesizing the gates in the qutrit Clifford group can decompose any gate into two-state rotations. The fidelity of 99.0 +/- 0.2% obtained by randomized benchmarking establishes the device as a useful qutrit, and outlines interesting directions in using higher levels to improve qubit-based quantum computers, and in using higher levels to pack more states into fewer devices in quantum computers. Analysis of experimental results indicates errors are dominated by ac-Stark and Bloch-Siegert shifts during qutrit control. \n \nThis thesis then presents two new devices meant to study the impact of changing design parameters on the suitability of flux qubits for multilevel control. The first device test individual qubits, with the goal of further improving the coherence time, and improving qutrit control. The second device couples two devices together, so that two-qubit gates can be studied. The available design parameters and their impact on qubit properties are discussed, and design variations are selected for the single and two-qubit devices. The result is a set of devices ready for manufacture and experimental characterization.
We demonstrate high-fidelity single-qubit gates on a C-shunt flux qubit that simultaneously combines a large anharmonicity (A/2π=848 MHz\mathcal{A}/2π=848~\mathrm{MHz}A/2π=848 MHz) with long relaxation time (T1=23 μsT_1 = 23~μ\text{s}T1​=23 μs). The large anharmonicity significantly suppresses leakage to higher energy levels, enabling fast and precise microwave control. Using DRAG pulses and randomized benchmarking, the qubit achieves gate fidelities exceeding 99.9\%, highlighting the capability of C-shunt flux qubits for robust and high-performance quantum operations. These results establish them as a promising platform for scalable quantum information processing.
We demonstrate high-fidelity single-qubit gates on a C-shunt flux qubit that simultaneously combines a large anharmonicity (A/2π=848 MHz) with long relaxation time (T1=23 μs). The large anharmonicity significantly suppresses leakage to higher energy levels, enabling fast and precise microwave control. Using derivative removal by adiabatic gate pulses and randomized benchmarking, the qubit achieves gate fidelities exceeding 99.9%, highlighting the capability of C-shunt flux qubits for robust and high-performance quantum operations. These results establish them as a promising platform for scalable quantum information processing.
We proposed and theoretically investigated the self-shunted superconducting flux qubits (SSFQs) with relatively large Josephson junctions with the diameter over1  μm\text{1}\; \mu \text{m}1μm. Because of the large self-capacitance of several 10 fF in the junctions, the large shunt capacitor with dimensions of several 100$ \mu \text{m}oftheconventionalcapacitivelyshuntedfluxquantumbits(qubits)canbeeliminated,resultinginsignificantreductionofthefootprint.WesystematicallycalculatedtheSSFQperformances,suchastheanharmonicity,andinvestigatedtheirdependencesonthecircuitparameters.Asaresult,itwasshownthattheSSFQshavethelargeanharmonicityof400–2000MHzforthereasonableparameters,suchasthelargejunctionareaofaround1of the conventional capacitively shunted flux quantum bits (qubits) can be eliminated, resulting in significant reduction of the footprint. We systematically calculated the SSFQ performances, such as the anharmonicity, and investigated their dependences on the circuit parameters. As a result, it was shown that the SSFQs have the large anharmonicity of 400–2000 MHz for the reasonable parameters, such as the large junction area of around 1oftheconventionalcapacitivelyshuntedfluxquantumbits(qubits)canbeeliminated,resultinginsignificantreductionofthefootprint.WesystematicallycalculatedtheSSFQperformances,suchastheanharmonicity,andinvestigatedtheirdependencesonthecircuitparameters.Asaresult,itwasshownthattheSSFQshavethelargeanharmonicityof400–2000MHzforthereasonableparameters,suchasthelargejunctionareaofaround1 \mu \text{m}^{2}andthesmallcriticalcurrentdensityofaround10and the small critical current density of around 10andthesmallcriticalcurrentdensityofaround10\text{A/cm}^{2}$. Furthermore, we derived and estimated the relative relaxation time of the SSFQs due to the charge and flux noises. As a result, we found that the high anharmonicity over 800 MHz could be achieved without degrading the relaxation time from that of the high-coherence flux qubits. The SSFQs offer the new choice of the highly scalable qubits, which achieve both the small footprint and high anharmonicity.
Superconducting flux qubits are promising candidates for the physical realization of a scalable quantum processor. Indeed, these circuits may have both a small decoherence rate and a large anharmonicity. These properties enable the application of fast quantum gates with high fidelity and reduce scaling limitations due to frequency crowding. The major difficulty of flux qubits' design consists of controlling precisely their transition energy - the so-called qubit gap - while keeping long and reproducible relaxation times. Solving this problem is challenging and requires extremely good control of e-beam lithography, oxidation parameters of the junctions and sample surface. Here we present measurements of a large batch of flux qubits and demonstrate a high level of reproducibility and control of qubit gaps, relaxation times and pure echo dephasing times. These results open the way for potential applications in the fields of quantum hybrid circuits and quantum computation.