Session B47: Superconducting Tunable Couplers & Gates I

Designing quantum gates for superconducting qubits with tunable couplers

Selecting the architecture of a superconducting quantum processor requires making many design choices, sometimes trying to meet conflicting demands. In this talk, I will discuss the architecture we have developed for our processors in the Wallenberg Centre for Quantum Technology. I will show how we use tunable couplers between fixed-frequency transmon qubits to realize various two- and three-qubit gates based on parametric modulation of the couplers [1,2,3], and how the frequencies of the qubits are chosen to avoid crosstalk between such gates in a square lattice containing several tens, or more, qubits [4]. I will also discuss how we can both mitigate and use ZZ coupling between the qubits in this setup [5], as well as quantify the impact of decoherence for all gates in a simple way [6,7].

[1] Kosen et al., Quantum Sci. Technol. 7, 035018 (2022)

[2] Gu et al., PRX Quantum 2, 040348 (2021)

[3] Warren et al., npj Quantum Inf. 9, 44 (2023)

[4] Osman et al., Phys. Rev. Res. 5, 043001 (2023)

[5] Pettersson Fors et al., in preparation

[6] Abad et al., Phys. Rev. Lett. 129, 150504 (2022)

[7] Abad et al., arXiv:2302.13885   

Large On:Off ratio two-qubit coupler in circuit QED

Tunable two-qubit couplers are important elements of the circuit QED architecture for quantum information processing as they enable, on demand, qubit-qubit entanglement generation. Their performance is typically assessed in the “on-regime” where the focus lies on the fidelity of gate operations and their execution time. Yet, even during idle times, couplers can introduce undesired interactions which detrimentally affect other qubit operations. In order to mitigate these deleterious effects, a large on-off ratio coupler was introduced by Leroux et al  [1]. Fundamentally, this coupler allows for the exponential suppression of all two-qubit interactions during the off state, effectively mitigating undesired effects. In this work, we propose and fully characterize a simplified implementation of a large on:off ratio coupler. Our approach simplifies the original proposal [1] since no higher-order wave mixing is needed, while keeping its advantages, namely the exponential suppression of residual interactions.   

Tunable coupler to fully decouple superconducting qubits

Enhancing the capabilities of superconducting quantum hardware, requires higher gate fidelities and lower crosstalk, particularly in larger scale devices, in which qubits are coupled to multiple neighbors. Progress towards both of these objectives would highly benefit from the ability to fully control all interactions between pairs of qubits. Here we propose a new coupler model that allows to fully decouple dispersively detuned Transmon qubits from each other, i.e. ZZ-crosstalk is completely suppressed while maintaining a maximal localization of the qubits' computational basis states. We further reason that, for a dispersively detuned Transmon system, this can only be the case if the anharmonicity of the coupler is positive at the idling point. A simulation of a 40 ns CZ-gate for a lumped element model suggests that achievable process infidelity can be pushed below the limit imposed by state-of-the-art coherence times of Transmon qubits. On the other hand, idle gates between qubits are no longer limited by parasitic interactions. We show that our scheme can be applied to large integrated qubit grids, where it allows to fully isolate a pair of qubits, that undergoes a gate operation, from the rest of the chip while simultaneously pushing the fidelity of gates to the limit set by the coherence time of the individual qubits.   

Crosstalk analysis of the double-transmon coupler toward its scalability

Recently, a new type of tunable coupler called the double-transmon coupler (DTC) has been proposed [1,2,3]. It consists of two fixed-frequency transmons coupled via a loop including an additional Josephson junction. It has been numerically demonstrated that this coupler enables fast, high-fidelity two-qubit gate operations in a two-qubit system[1,2]. However, its scalability has remained unclear so far. That is, it is unclear whether the DTC can maintain its high performance even for systems with qubits more than two, where additional parasitic couplings, such as couplings between couplers and between non-adjacent qubits, exist, unlike two-qubit systems. In this study, we numerically evaluate the performance of a system with three qubits coupled via two DTCs. Our results demonstrate that the DTC can almost eliminate ZZ couplings between arbitrary two qubits and also the ZZZ coupling among the three qubits. Moreover, our simulations have shown that high-performance single-qubit and two-qubit gates, namely, a π/2 pulse and a CZ gate,can be implemented successfully. These results indicate the high scalability of the DTC. We will also provide simulation results for the single-transmon coupler (STC) [1,2,4] and discuss the differences between the DTC and the STC.

[1] H. Goto, Phys. Rev. Appl. 18, 034038 (2022).

[2] K. Kubo and H. Goto, Appl. Phys. Lett. 122, 064001 (2023).

[3] D. L. Campbell et al., Phys. Rev. Appl. 19, 064043 (2023).

[4] F. Yan et al., Phys. Rev. Appl. 10, 054062 (2018).   

Engineering pure 6 photon-interactions with a Josephson dipole - PART 1/2

Two or more superconducting qubits can be efficiently coupled by a driven nonlinear Josephson circuit capable of multi-photon interactions. Such a device typically consists of a flux-biased superconducting loop interrupted by one or more Josephson junctions, and couples to the external circuitry from a pair of its terminals. With adequate design, and choosing a proper flux-bias point, these dipoles can implement strong three-wave mixing Hamiltonians, resulting in a highly efficient photon swap between a pair of superconducting qubits. However, the capability of implementing pure higher order wave mixing has been limited by the difficulty of eliminating undesired Hamiltonian terms. In this talk, we will introduce a new device, which behaves as a pure 6-wave-mixing element.  We will present preliminary theoretical and experimental results, discussing practical applications of such processes, including the simultaneous entanglement of 4 superconducting qubits.

 

Part 1 will present the modeling and fabrication of the 6-wave-mixing element.   

Engineering pure 6 photon-interactions with a Josephson dipole - PART 2/2

Two or more superconducting qubits can be efficiently coupled by a driven nonlinear Josephson circuit capable of multi-photon interactions. Such a device typically consists of a flux-biased superconducting loop interrupted by one or more Josephson junctions, and couples to the external circuitry from a pair of its terminals. With adequate design, and choosing a proper flux-bias point, these dipoles can implement strong three-wave mixing Hamiltonians, resulting in a highly efficient photon swap between a pair of superconducting qubits. However, the capability of implementing pure higher order wave mixing has been limited by the difficulty of eliminating undesired Hamiltonian terms. In this talk, we will introduce a new device, which behaves as a pure 6-wave-mixing element.  We will present preliminary theoretical and experimental results, discussing practical applications of such processes, including the simultaneous entanglement of 4 superconducting qubits.

 

Part 2 will present preliminary experimental results and applications of the 6-wave-mixing element.   

A three qubit system with a common SQUID coupler with increased connectivity for fast gates

The majority of popular superconducting qubit system architectures employ pairwise nearest-neighbor (either fixed or tunable) couplings between qubits and individualized readout resonators. In these systems the localized nearest-neighbor connectivity can create complications for algorithm circuit decomposition requiring numerous SWAP operations. However, there are feasible alternative options to add increased qubit connectivity and shared control and readout resources benefitting scalability. With appropriate parameter choice and frequency allocation, groups of qubits with all-to-all connectivity can be achieved despite the challenge of the quadratic increase in the number of pairwise interactions with increasing qubit count. Our group has developed a design approach of this style consisting of multiple resonant modes, acting as either qubits or cavities, all galvanically coupled to a common tunable SQUID element. This enables high on/off coupling ratios and fast parametrically driven interactions for gates and readout. In this talk, we will review our design and simulation tools for this approach and discuss an example of a three qubit system with all-to-all connectivity. We will highlight some of the design and operational challenges and advantages of this system.   

Control strategies for static ZZ coupling in flux-tunable transmon coupler systems

Flux-tunable transmon couplers are widely used to implement two-qubit gates between superconducting qubits. However, connecting qubits through such couplers induces a ZZ coupling, an energy shift conditioned by the qubits’ state which limits the performance of both one- and two-qubit gates. The performance limitation for two-qubit gates can be comparable to that from decoherence.

 

In this talk, we present strategies to mitigate and control the ZZ coupling in devices based on fixed-frequency transmon qubits and flux-tunable transmon couplers. These strategies, which are based on numerical and analytical modeling, provide information on how to choose the frequencies, anharmonicities, and coupling strengths of the qubit systems. This allows us to create several parameter regions with mitigated ZZ coupling that can be accessed by current technology without major redesigns. We also describe the underlying reasons for the existence of these regions inferred from new diagrammatic perturbation theory.   

Limits to parametric pumping in superconducting circuits

Parametric driving constitutes a promising paradigm for the development of future superconducting quantum processors. However, these systems suffer from a poorly understood effect imposing a lower limit on gate times: as the drive strength is increased, experiments show a sudden onset of leakage due to unwanted excitations. To understand this effect, we theoretically examine a parametrically driven system consisting of a qubit and a driven coupler. We identify the system parameters that govern the onset of leakage. Our study elucidates strategies for achieving faster high-fidelity gates based on parametric driving in systems composed of transmons and SNAILs.   

Modular tunable coupler for superconducting qubits

Tunable coupling elements in superconducting quantum circuits enable fast and high fidelity interactions and have become ubiquitous in quantum processors. Such tunable elements need to provide a combination of high coupling rates and low parasitic (such as ZZ) interactions. Moreover, the circuit needs to be insensitive to variation in the data qubit parameters to enable a modular design of multi-qubit circuits and lower simulation complexity. Here we describe the theory and initial experimental results of a dual ancilla coupler that mediates the interaction between two data transmons. The ancilla transmons are strongly hybridized to enable first order insensitivity to circuit parameters and ZZ interaction cancellation. Our coupler allows static as well as parametric interactions and it is therefore suitable for a variety of superconducting qubit platforms.   

Fast ZZ-Free Entangling Gates for Superconducting Qubits Assisted by a Driven Resonator

Engineering high-fidelity two-qubit gates is an indispensable step toward practical quantum computing. For superconducting quantum platforms, one important setback is the stray interaction between qubits, which causes significant coherent errors. For transmon qubits, protocols for mitigating such errors usually involve fine-tuning the hardware parameters or introducing usually noisy flux-tunable couplers. In this work, we propose a simple scheme to cancel these stray interactions. The coupler used for such cancellation is a driven high-coherence resonator, where the amplitude and frequency of the drive serve as control knobs. Through the resonator-induced-phase (RIP) interaction, the static ZZ coupling can be entirely neutralized. We numerically show that such a scheme can enable short and high-fidelity entangling gates, including cross-resonance CNOT gates within 40 ns and adiabatic CZ gates within 140 ns. Our architecture is not only ZZ free but also contains no extra noisy components, such that it preserves the coherence times of fixed-frequency transmon qubits. With the state-of-the-art coherence times, the error of our cross-resonance CNOT gate can be reduced to below 1e-4.   

ZZ-Free Two-Qubit CZ Gate Based on Fluxonium Coupler

In this talk, we propose an adiabatic, coupler-flux-biased controlled-Z (CZ) gate that is implemented between two transmon qubits coupled via a fluxonium, an architecture we call T-F-T. The coupling mediated by fluxonium allows the ZZ interaction to be completely canceled while the two transmons are outside of the straddling regime. This makes the architecture less susceptible to the microwave crosstalk and frequency crowding. We experimentally verified that complete ZZ cancellation is possible with two-qubits biased in the off-straddling regime. In addition, we will discuss characterization and optimization of CZ gate fidelity.   

Continuous fSim Gate Using Bichromatic Parametric Drives for Superconducting Qubits

Most quantum computation architectures rely on a single specific type of two-qubit gate to form a universal gate set. However, having flexible native entanglement gates can help to reduce circuit complexity, which is highly relevant for the performance of NISQ devices. Here, we propose a scheme to implement a continuous fermionic simulation gate( fSim gate) for superconducting qubits. We simultaneously apply two parametric drives with different frequencies targeting two different transitions. iSWAP-type and CPhase-type of operations can be realized at the same time in one single gate round with tunable angles controlled by drive amplitudes and frequencies. We give analytical formulas of effective coupling strengths covering from dispersive regime to strong drive regime. Numerical simulation estimates that the gate is fast and with high fidelity in a large domain of parameters (subject to qubit T1 and T2 limitations). This gate opens up possibilities for versatile gate architectures.