Session D47: Superconducting Qubits: Tunable Couplers & Gates II

Geometric Gates via Parametric Control of a SQUID Coupler

Quantum gates involving topologically protected geometric phases and implemented via adiabatic evolution are more likely to be robust against pulse imperfections and parameter uncertainties. Recent techniques for implementing accelerated two-qubit adiabatic gates have used multiple control drives and a common auxiliary mode to imprint the geometric phase for a CZ gate. We propose a similar geometric CZ gate between two fluxonia implemented via parametric flux control of a tunable SQUID coupler. The SQUID coupler has the advantage of minimizing residual static ZZ interactions when idling at its off point while still enabling rapid parametric control.   

High-Fidelity Two-Qubit Gates Between Fluxonium Qubits Using a Tunable Coupler

Tunable couplers provide a promising platform for the realization of efficient two-qubit gates, capitalizing on their potential for achieving a substantial on/off coupling ratio and eliminating residual interactions within a single design. In this work, we theoretically explore designs for fast, high-fidelity two-qubit gates between superconducting fluxonium qubits using a floating SQUID as a tunable coupler. We investigate the performance of both fast-flux and parametric gate designs by modulating the flux through the coupler and consider the impact of junction asymmetry. We also explore the possibility of using this coupler to achieve fast, high fidelity readout for fluxonium qubits beyond what is possible with capacitively coupling to the readout resonator.   

Design of fluxonium coupling and readout via SQUID couplers

The superconducting fluxonium qubit has emerged as a promising alternative to the widely-studied transmon qubit due to increased coherence times at the half-flux quantum sweet-spot, large anharmonicity, and robust charge-noise insensitivity. Scaling to multi-qubit fluxonium systems requires implementation of fast, high-fidelity, and highly expressive quantum gates, with small residual coupling when the gate is off. In this work, we present the design of a 2D tunable coupler composed of a floating SQUID element achieving these requirements. We study the family of gates realizable with the phase coupling realized by the SQUID, and investigate their limits with regard to gate time, leakage, and drive-induced decoherence. We also study the element’s suitability for fast, high-fidelity readout for highly detuned fluxonium qubits retaining decoherence protection at half-flux quantum.   

Designing Two-Fluxonium Qubits with a Tunable Coupler

The scalability of quantum systems is an important consideration as we strive for large-scale quantum computing. A candidate for a superconducting qubit architecture is the fluxonium qubit which offers numerous advantages, including low error rates. Compared to the conventional transmon qubit, the fluxonium is realized with one additional element: a linear inductor. The imposing challenge for fluxonium qubits is to design two coupled fluxonium qubits and realize two-qubit gate implementations with high fidelity.  In this talk, I will present a design for a two-fluxonium device with the qubit-qubit coupling enabled by a transmon coupler. The device is implemented using our established fluxonium design that we have integrated into IBM Qiskit Metal. In particular, I will discuss the analysis of the device parameters and how we have optimized the design to enable the desired high-fidelity two-qubit gate.   

Two Fluxonium CZ Gate using a Transmon Coupler

There have been increasing efforts to improve the coherence times and gate fidelities for superconducting qubits. Recently, fluxonium qubits have been gaining atention due to its large anharmonicity, millisecond coherence times, and higher gate fidelities. In this work we study two fluxoniums capacitively coupled by a flux-tunable transmon. We implement a CZ gate by selectively driving the transmon levels. Specifically, we cycle the transmon-population through non-computational states conditional on the state of the fluxoniums, thus, accumulating a conditional phase. Our circuit is designed to have optimal frequency selectivity. Using numerical simulations, we demonstrate high fidelities, low leakage, and very low residual ZZ-interaction. We will also present our first results on our experimental implementation.   

Tunable inductive coupler with >99.9% two-qubit gate fidelity between fluxonia

The fluxonium qubit is a promising candidate for quantum computation due to its long coherence times and large anharmonicity. We present a tunable coupler that realizes strong inductive coupling between two heavy-fluxonium qubits, each with ∼ 50MHz frequencies and ∼ 5 GHz anharmonicities. The coupler enables the qubits to have a large tuning range of XX coupling strengths (−35 to 75 MHz). The ZZ coupling strength is < 3kHz across the entire coupler bias range, and < 100Hz at the coupler off-position. These qualities lead to fast, high-fidelity single- and two-qubit gates. By driving at the difference frequency of the two qubits, we realize a √iSWAP gate in 258ns with fidelity 99.72%, and by driving at the sum frequency of the two qubits, we achieve a √bSWAP gate in 102ns with fidelity 99.91%. This latter gate is only 5 qubit Larmor periods in length. We run cross-entropy benchmarking for over 20 consecutive hours and measure stable gate fidelities, with √bSWAP drift (2σ) < 0.02% and √iSWAP drift < 0.08%.   

Inductive coupling scheme for quantum simulation with superconducting qubits

Superconducting qubits provides a promising platform for quantum simulation of Bose-Hubbard Hamiltonians due to the flexibility of tuning system parameters. Changing the ratio of on-site interaction strength due to qubit anharmonicity and coupling strength between qubits allows exploration of different quantum phases in the Bose-Hubbard model. Probing these quantum phase transitions requires the ability to dynamically tune the coupling strength. An inductive coupling scheme can make use of the nonlinearity of a Josephson junction to dynamically change the mutual inductance between two qubits by applying a DC magnetic flux [1]. The relative mutual inductances between the qubits and couplers can be engineered to achieve a large range of coupling strengths. Having both a high coupling strength and the ability to tune between positive and negative couplings enables quantum simulation experiments in various parameter regimes. We present our experimental realization and characterization of a tunable inductive coupler between transmon qubits.

[1] Geller et al., PRA 92, 012320 (2015)   

Reinforcement learning for optimization of fluxonium two-qubit gates

Among superconducting qubits, the fluxonium is a promising alternative to the transmon for gate-based quantum information processing. Here we will discuss our recent demonstration (arXiv:2304.06087) of an architecture for fluxonium-fluxonium two-qubit gates mediated by transmon couplers (FTF, for fluxonium-transmon-fluxonium). Relative to architectures that exclusively rely on a direct coupling between fluxonium qubits, FTF enables stronger couplings for gates using non-computational states while simultaneously suppressing the static controlled-phase entangling rate (ZZ) down to kHz levels, all without requiring strict parameter matching. We implemented FTF with a flux-tunable transmon coupler and demonstrated a microwave-activated controlled-Z (CZ) gate whose operation frequency could be tuned over a 2 GHz range, adding frequency allocation freedom for FTF in larger systems. To optimize this gate, we implemented model-free reinforcement learning of the pulse parameters to boost the mean gate fidelity up to 99.922±0.009%, averaged over roughly an hour between scheduled training runs. In this talk, we will discuss the details of this calibration procedure and opportunities for improvements.   

Towards High-fidelity Two-qubit Gates: Static ZZ Suppression via Multipath Coupling in Inductively Coupled Fluxonium Qubits - Part I

Compared to capacitive coupling, inductively coupled fluxoniums provide enhanced hybridization of computational states, facilitating entanglement with suppressed ZZ crosstalk. Utilizing a tunable coupler, high-fidelity gates between inductively coupled fluxonium qubits were demonstrated.[1] Here we demonstrate the implementation of static ZZ suppression through multipath coupling in directly inductively coupled fluxonium qubits. This scheme, designed for high-fidelity gate operations, can benefit advancing fluxonium-based quantum processors and broadening the horizons of universal quantum computing. In this part, we present an exhaustive circuit analysis for these multipath-coupled fluxonium qubits. 

[1] arXiv preprint arXiv:2309.0572 (2023)   

Towards high-fidelity two-qubit gates: Static ZZ Suppression via Multipath Coupling in inductively coupled fluxonium qubits - part II

Compared to capacitive coupling, inductively coupled fluxoniums provide enhanced hybridization of computational states, facilitating entanglement with suppressed ZZ crosstalk. Utilizing a tunable coupler, high-fidelity gates between inductively coupled fluxonium qubits were demonstrated. [1] Here we demonstrate the implementation of static ZZ suppression through multipath coupling in directly inductively coupled fluxonium qubits. This scheme, designed for high-fidelity gate operations, can benefit advancing fluxonium-based quantum processors and broadening the horizons of universal quantum computing. This part, we present analysis of gate operations for these multipath coupled fluxonium qubits. 

[1] arXiv preprint arXiv:2309.0572 (2023)   

Fast two-qubit gates between inductively-capacitively coupled fluxoniums

Among various superconducting qubits, fluxonium qubit has the advantage of longer than 1ms coherence time and large nonlinearity. However, to build a quantum processor, one problem in scaling up the qubits is the residual ZZ-coupling between connected qubits, which introduces unwanted crosstalk between qubits and prevents local operation. Introducing a tunable coupler is one approach to suppressing the ZZ coupling to the sub-MHz values. We present an alternative approach when the ZZ interaction is reduced to a kHz range thanks to direct capacitive and inductive interactions between a pair of fluxoniums. We analyze the interplay between these two interactions that reduce unwanted ZZ couplings. We then analyze several other fluxonium gate schemes, such as microwave-activated CZ, cross-resonance CNOT, and SWAP gates. We find optimal parameters for these gates to achieve high fidelity.   

Title: Frequency tunable single photon emitter using double transmon coupler architecture

Single photon emitters and detectors enable entanglement distribution on quantum networks. Here we present a compact and straightforward single photon emitter at microwave frequencies based on the recently developed double transmon coupler (DTC) superconducting circuit architecture. One DTC transmon stores a photon while the other transmon releases the photon into the waveguide radiation field. The two transmons do not have the same frequency, which makes state preparation bleedthrough into the radiation field ignorable or filterable. We use parametric modulation of the DTC flux to shape the outgoing waveform of the emitted photon while the steady state flux bias sets the frequency of the outgoing photon.   

Implementation of a Quantum Switch with Superconducting Circuits: Part 1 - Theory

A quantum switch (QSwitch) is a four-node quantum router that swaps a single photon between an input and two outputs based on a quantum address. In contrast to previous quantum routers, which require the output qubit to be classically selected, a QSwitch can route to a superposition of outputs. A QSwitch is a necessary component for building a quantum RAM (QRAM), as the gate that it enables forms the basis of the memory access operation upon which QRAM usage relies. 

This is the first part of a two-part talk. In this part we will focus on a new protocol that relies on a strong ZZ coupling between a control qubit and the input and output qubits. We will show that this protocol is much more gate efficient. We will also show how this design can be efficiently scaled to design a QRAM.   

Implementation of a Quantum Switch with Superconducting Circuits: Part 2 - Experiment

A quantum switch (QSwitch) is a four-node quantum router that swaps a single photon between an input and two outputs based on a quantum address. In contrast to previous quantum routers, which require the output qubit to be classically selected, a QSwitch can route to a superposition of outputs. A QSwitch is a necessary component for building a quantum RAM (QRAM), as the gate that it enables forms the basis of the memory access operation upon which QRAM usage relies. In this talk, we present experimental updates on a QSwitch implemented using four fixed-frequency transmons. We will first discuss its circuit geometry and explain how our device is calibrated. We will then characterize and compare the performance of different implementations of the quantum routing protocol.   

Generating Extensible High-Dimensional Entanglement via Two-Photon Qudit-Qudit Interactions

Quantum computing with D-level systems (or qudits) represents a promising alternative to traditional qubit based approaches by deploying a larger, and more connected Hilbert space for the same number of quantum units (in our case transmons). In our work, we explore extensible methods based on coherent two-photon XX-YY interactions in transmon qudits. These interactions realize relevant Hamiltonians for qudit based quantum simulation, allow subspace entangling interactions in larger coupled qudit architectures, and may enable high-dimensional quantum computing through improved circuit compilation. Specifically, we leverage these two-photon qudit-qudit interactions to experimentally demonstrate multi-controlled qubit Toffoli gates such as the CCZ and CCCZ gate, and also generate and tomographically reconstruct two-qudit Bell states up to D=4.