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arXiv:2312.04321

Universal flux-based control of a πππ-SQUID

J. Wilson Staples, Thomas B. Smith, Andrew C. Doherty

Published Dec 7, 2023• 0 citations
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Abstract

We describe a protocol for the universal control of non-ideal $π$-periodic superconducting qubits. Our proposal relies on a $π$-SQUID: a superconducting loop formed by two $π$-periodic circuit elements, with an external magnetic flux threading the circuit. The system exhibits an extensive sweet spot around half-flux where residual $2π$-periodic Cooper pair tunneling is highly suppressed. We demonstrate that universal single-qubit operations can be realised by tuning the flux adiabatically and diabatically within this broad sweet spot. We also assess how residual $2π$-periodicity in $π$-SQUIDs impacts holonomic phase gates.

DOI
10.48550/arxiv.2312.04321

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We describe a protocol for the universal control of non-ideal πππ-periodic superconducting qubits. Our proposal relies on a πππ-SQUID: a superconducting loop formed by two πππ-periodic circuit elements, with an external magnetic flux threading the circuit. The system exhibits an extensive sweet spot around half-flux where residual 2π2π2π-periodic Cooper pair tunneling is highly suppressed. We demonstrate that universal single-qubit operations can be realised by tuning the flux adiabatically and diabatically within this broad sweet spot. We also assess how residual 2π2π2π-periodicity in πππ-SQUIDs impacts holonomic phase gates.
Scaling up superconducting quantum processors with optimized performance requires a sufficient flexibility in the choice of operating points for single and two qubit gates to maximize their fidelity and cope with imperfections. Flux control is an efficient technique to manipulate the parameters of tunable qubits, in particular to activate entangling gates. At flux sensitive points of operation, the ubiquitous presence of 1/f flux noise however gives rise to dephasing by inducing fluctuations of the qubit frequency. We show how two-tone modulation of the flux bias, a bichromatic modulation, gives rise to a continuum of dynamical sweet spots where dephasing due to slow flux noise is suppressed to first order for a wide range of time-averaged qubit frequencies. The qubits can be operated at these dynamical sweet spots to realize protected entangling gates and to avoid collisions with two-level-system defects.
A bistable superconducting quantum interference device (SQUID) exclusively comprising Josephson junctions (JJs) is proposed. The design integrates two 2Φ2 \Phi2Φ-JJs within the loop structure, while the state of the SQUID is monitored through a conventional 2π2 \pi2π-periodic JJ\mathbf{J J}JJ (0\mathbf{0}0-JJ). This configuration eliminates the need for geometric inductors, leveraging the nonlinear phase dynamics for bistability. Extensive simulations confirm robust bistable operation under controlled external flux bias, positioning the proposed SQUID as an area-efficient building block for superconducting memory cells, sensors for various applications, and SFQ-compatible logic elements.
Tunable Josephson harmonics open new avenues for qubit design. We demonstrate a superconducting circuit element consisting of a tunnel junction in series with a SQUID loop, yielding a Josephson potential whose harmonic content is strongly tunable by magnetic flux. Through spectroscopy of the first four qubit transitions, together with an effective single-mode model renormalized by the internal mode, we resolve a second harmonic with an amplitude up to ∼10%\sim10\%∼10% of the fundamental. We identify a flux sweet spot where the dispersive shift vanishes, achieved by balancing the dispersive couplings to the internal and qubit modes. This highly tunable element provides a route toward protected qubits and customizable nonlinear microwave devices.
Current superconducting quantum processors require strategies for coping with material defects and imperfect parameter targeting in order to scale up while maintaining high performance.To that end, in situ control of qubit frequencies with magnetic flux can be used to avoid spurious resonances.However, increased dephasing due to 1/f flux noise limits performance at all of these operating points except for noise-protected sweet spots, which are sparse under dc flux bias and monochromatic flux modulation.Here we experimentally demonstrate that two-tone flux modulation can be used to create a continuum of dynamical sweet spots, greatly expanding the range of qubit frequencies achievable while first-order insensitive to slow flux noise.To illustrate some advantages of this flexibility, we use bichromatic flux control to reduce the error rates and gate times of parametric entangling operations between transmons.Independent of the gate scheme, the ability to use flux control to freely select qubit frequencies while maintaining qubit coherence represents an important step forward in the robustness and scalability of near-term superconducting qubit devices.
Superconducting quantum circuits derive their nonlinearity from the Josephson energy-phase relation. Besides the fundamental cos⁡φ\cosφcosφ term, this relation can also contain higher Fourier harmonics cos⁡(kφ)\cos(kφ)cos(kφ) corresponding to correlated tunneling of kkk Cooper pairs. The parity of the dominant tunneling process, i.e.~whether an odd or even number of Cooper pairs tunnel, results in qualitatively different properties, and controlling this opens up a wide range of applications in superconducting technology. However, access to even-dominated regimes has remained challenging and has so far relied on complex multi-junction or all-hybrid architectures. Here, we demonstrate a simple "harmonic parity qubit" (HPQ); an element that combines two aluminum-oxide tunnel junctions in parallel to a gate-tunable InAs/Al nanowire junction forming a SQUID, and use spectroscopy versus flux to reconstruct its energy-phase relation at 85 gate voltage points. At half flux quantum, the odd harmonics of the Josephson potential can be suppressed by up to two orders of magnitude relative to the even harmonics, producing a double-well potential dominated by even harmonics with minima near ±π/2\pmπ/2±π/2. The ability to control harmonic parity enables supercurrent carried by pairs of Cooper pairs and provides a new building block for Fourier engineering in superconducting circuits.
Crosstalk refers to unwanted qubit addressing. This is particularly detrimental when scaling up quantum information systems because unintended interactions limit their overall performance. For superconducting qubits, tunable couplings and frequency tunability achieved through externally applied magnetic fluxes enable high-fidelity entangling gates; however, they also introduce crosstalk through unintended flux coupling. In this work, we investigate the impact of time-dependent external magnetic fluxes in quantized circuits on superconducting qubit couplings. We find that non-trivial cross-voltage driving emerges between capacitively linked qubits when the magnetic flux threading the SQUID loop of a qubit varies in time, in a manner analogous to Faraday's law of induction. Crucially, we show that this effect enables fast single qubit control through the coupler element in standard tunable-coupler architectures, potentially eliminating the need for individual microwave XYXYXY control lines.