Session D36: Quantum Control: Quantum Gates

Qutrit Entanglement With Differential AC Stark Shift

Ternary quantum information processing in circuit quantum electrodynamics devices poses a promising alternative to its more popular binary counterpart through larger computational spaces and proposed more efficient error correction schemes. Recent advancements in ternary quantum computing, such as qutrit randomized benchmarking and quantum information scrambling on a qutrit device, have been key in enabling qutrit development and in demonstrating its value in quantum simulation. However, effectively engineering two qutrit entanglement remains a central challenge towards realizing ternary quantum information processing. In this work, we present a generalized Joint Amplification of ZZ (JAZZ) method for measuring the entanglement between two nearest neighbor transmon qutrits. Leveraging this method, we apply the differential AC Stark shift to enable larger driven ZZ interactions and implement a scheme for an efficient two qutrit C-Phase gate.   

A quantum module with all-to-all gates via parametric control

For quantum computing in the NISQ era, most platforms for superconducting systems, including surface code, employ a network of two-body interactions between nearest-neighbor qubits. Alternatively, modular quantum computers seek to create networks with dense local couplings among small 'quantum modules' which are in turn connected via a quantum bus. In this talk, we present such a quantum module comprised of a central Superconducting Nonlinear Asymmetric Inductive eLement (SNAIL) coupled with four transmon qubits. Two-qubit interactions are created via three-wave coupling driving the SNAIL at the difference frequency of a pair of qubits. The module's architecture allows us to realize all-to-all two-qubit couplings with experimental SWAP times of ~100 ns in our prototype. Moreover, we can also drive single qubit gates in the module as fast as ~20 ns by driving the central SNAIL at one half of each qubit's resonant frequency, allowing the entire module's gates to be implemented via a single drive line. The module is also directly compatible with our previously realized quantum state router (C. Zhou, et al. arXiv (2021)).  We will present data characterizing the device's performance and discuss the prospects for its integration into larger-scale modular quantum machines.    

Modular coupling approach using ancilla transmons with flux-tunable hybridization

Recent demonstrations of small quantum processors (tens of qubits) based upon superconducting circuits have incorporated coupling elements to facilitate fast multi-qubit operation without sacrificing data storage fidelity. A recently proposed [Yan2018] and now state-of-the-art coupling approach leverages the interference of a static interaction between two data transmons and a separate virtual interaction through a non-computational flux tunable ancilla transmon to produce an effective tunable coupling. The resultant coupling is a non-trivial function of all three transmons’ frequencies and the static interactions between them. Consequently, adapting the coupler to new architectures and use cases can require considerable remodeling. To overcome this challenge, we introduce a new ancilla-based coupler that utilizes the hybridization of two ancillas to mediate the interaction of external circuitry across the coupler. Our proposed coupler is modular in design and simulation, has first order insensitivity to data-transmon parameters, and can mediate both degenerate and parametric interactions to implement a diverse set of entangling operations.

Reference: Yan F, et al. Tunable Coupling Scheme for Implementing High-Fidelity Two-Qubit Gates. Phys. Rev. Applied 10, 054062 (2018).   

Mitigating off-resonant error in the cross-resonance gate

Off-resonant error for a driven quantum system refers to interactions due to the input drives having non-zero spectral overlap with unwanted system transitions. Here, we quantify off-resonant error for the cross-resonance interaction with application to a direct CNOT gate implementation [1, 2]. We show that pulse parameters should be optimized so that off-resonant transition frequencies coincide with the local minima due to the pulse spectrum sidebands. Additionally, we show that a Y-DRAG [3, 4] pulse on the control qubit can significantly help to mitigate the effects of off-resonant error. Depending on system parameters, the proposed methods can improve the average off-resonant error by up to an order of magnitude for a direct CNOT calibration.

[1] Petar Jurcevic, Ali Javadi-Abhari, Lev S Bishop, Isaac Lauer, Daniela F Bogorin, Markus Brink, Lauren Capelluto, Oktay Gunluk, Toshinari Itoko, Naoki Kanazawa, et al. “Demonstration of quantum volume 64 on a superconducting quantum computing system”, Quantum Science and Technology, 6(2):025020, 2021.

[2] Abhinav Kandala, Ken X. Wei, Srikanth Srinivasan, Easwar Magesan, Santino Carnevale, George A. Keefe, David Klaus, Oliver Dial, and David C. McKay, “Demonstration of a high-fidelity cnot for fixed-frequency transmons with engineered ZZ suppression”, arXiv preprint quant-ph/2011.07050, 2020.

[3] F. Motzoi, J. M. Gambetta, P. Rebentrost, and F. K. Wilhelm, “Simple pulses for elimination of leakage in weakly nonlinear qubits”. Phys. Rev. Lett., 103:110501, 2009.

[4] Jay M Gambetta, F Motzoi, ST Merkel, and Frank K Wilhelm. “Analytic control methods for high-fidelity unitary operations in a weakly nonlinear oscillator”. Physical Review A, 83(1):012308, 2011.   

Towards high-fidelity two-qubit gates on fluxonium qubits

Recently we demonstrated microwave two-qubit gate schemes [1, 2] using high levels of fluxoniums, where the gate fidelity is limited by the decoherence outside the computational space. To solve this problem, here we demonstrate the implementation of microwave two-qubit gates using only computational states. By applying a strong microwave drive between the two qubit frequencies, we can flip 00 to 11 in ~80 ns through the two-photon transition. On the other hand, we can induce a ZZ interaction (~5 MHz) by off-resonantly driving near the qubit frequencies. With these techniques, we can construct a bSWAP gate and a CZ gate and over 99.9% fidelities can be expected. These high-fidelity two-qubit gates on fluxoniums can benefit the development of Noisy Intermediate Scale Quantum (NISQ) processors and universal quantum computing.

[1] Physical Review X 11(2) (2021): 021026

[2] arXiv preprint arXiv:2103.04491 (2021)   

Microwave activated two-qubit gate for fluxonium qubits via a tunable-transmon coupler

Qubit lifetimes in superconducting transmon based quantum computers are a leading cause of gate infidelity. Furthermore, the transmon’s anharmonicity gives rise to frequency crowding on multi-qubit devices and limits the gate speed. The fluxonium qubit is a promising alternative to transmons, with coherence times reaching the order of milliseconds and anharmonicities on the order of gigahertz. In this work, we present a device containing two fluxonium qubits connected by a tunable-transmon coupler. By utilizing the higher levels of the fluxonium qubits and the transmon excited state, we explore the potential of a microwave activated CPHASE gate. We present results on a device designed to operate in a parameter space that has large qubit-to-qubit couplings and a reduced always-on ZZ interaction. This architecture is expected to facilitate faster, higher fidelity two-qubit gates.   

The siZZle Gate – Using AC Stark tones to modulate ZZ in Superconducting Transmon Qubits

Fixed frequency superconducting transmon qubits are an attractive technology for scaling due to their high coherence and stability. However, there are a number of challenges associated with always on coupling. In particular, the higher levels cause shifts in the computational levels that leads to unwanted ZZ quantum crosstalk. Here, we will discuss a novel technique to manipulate the energy levels and mitigate this crosstalk via a simultaneous AC Stark effect on coupled qubits. This breaks a fundamental deadlock between qubit-qubit coupling and crosstalk, leading to a 90ns CNOT with a gate error of (0.19 ± 0.02)% and the demonstration of a novel CZ gate with fixed-coupling single-junction transmon qubits. Furthermore, we show a definitive improvement in circuit performance with crosstalk cancellation over seven qubits, demonstrating the scalability of the technique. This talk is based on work published in arXiv:2106.00675 (2021).   

Understanding the speed limits of parametrically pumped quantum gates

Controllable couplings between qubits are vital for realizing large-scale quantum machines. In superconducting systems, high-fidelity two-qubit gates can be performed by off-resonant parametric pumping of a non-linear element dispersively coupled to two qubits. In this scheme, the performance of fast high-fidelity gates requires strong pumping. However, high drive strengths may activate unwanted transitions which can ruin gate fidelity and coherence properties. Moreover, strong coupling between the pump port and the non-linear mode may limit the lifetime of the quantum modes being controlled. In this work we will use our previously built quantum state router [Zhou and Lu, arxiv: (2021)] and a new 4-qubit quantum module as platforms (which both operated via 3-wave-based parametric gates) to study how to characterize and control the factors that limit our gate speed. We show how to identify and mitigate the effects of parasitic parametric processes while maintaining qubit lifetimes, and engineer the drive port's impedance to allow stronger parametric drives while maintaining mode lifetimes. In total, our results open a pathway to realizing a modular qubit architecture featuring high-fidelity parametric gates.   

Robust entangling shaped pulses for cavity-coupled silicon quantum dot spin qubits with always-on coupling

The fidelity of cavity-mediated long-range entanglement between singly-loaded double quantum dot spin qubits in silicon is ultimately limited by charge noise. Leading order effects of quasistatic charge noise can be suppressed by using a composite pulse sequence provided that the coupling can be switched on and off rapidly by pulsing on the tunnel barrier voltage [1]. However, a different approach is needed when bandwidth limitations [2] preclude rapid pulsing of the tunnel barrier. Here, we report a robust iSWAP gate for such a system, with both qubits driven slightly off-resonantly using a shaped pulse obtained using a physics informed neural network [3], in the presence of an always-on exchange coupling. The resulting gate is robust against quasistatic charge noise as well as driving amplitude errors, and the control requirements are within experimental limitations.

[1] A. Warren, U. Güngördü, J. P. Kestner, E. Barnes, S. E. Economou, Phys. Rev. B 104, 115308 (2021)

[2] W. Huang et al Nature (London) 569, 532 (2019)

[3] U. Güngördü, J. P. Kestner, arXiv:2011.02512 (2020)   

Crosstalk resistant CZ gate robust against charge noise in silicon two qubit devices

Although silicon is a promising and scalable platform for quantum computing the fidelity of two qubit gates in silicon is limited by charge noise and potential crosstalk. Schemes to deal with either individually have been proposed, but this work presents a method of dealing with both at the same time. The presence of crosstalk and charge noise results in a unitary error propagator that involves all 15 generators of SU(4), making it very difficult to create a robust pulse analytically. Therefore a robust pulse shape is determined by numerically optimizing a neural network. The effects of crosstalk are taken into account exactly through the hamiltonian while also being computationally efficient. Neural networks are computationally efficient to optimize because of the rapid evaluation of the high-dimensional gradient of the cost function through back propagation. This approach was then also applied to create robust sections of the composite pulse sequence of Ref [1] that suppresses exchange noise and Zeeman energy fluctuations. The resulting pulse sequence has an infidelity of 10^-3 for quasi static noise fluctuations in exchange J of 10% or fluctuations in Zeeman energy of 10kHz.

 

[1] U. Güngördü and J. P. Kestner, Phys. Rev. B98, 165301(2018).   

Demonstration of an entangling gate between non-interacting qubits using the quantum Zeno effect

The quantum Zeno effect occurs in systems when frequent measurements are applied to effectively freeze the system dynamics, holding it at an eigenstate of the measurement observable. The measurements divide the Hilbert space into subspaces with distinct eigenvalues of the measured observable, and give rise to 'Zeno dynamics' within each. Transitions between subspaces are suppressed by measurement, but the evolution inside each subspace is completely coherent. We show that Zeno dynamics can deterministically create entanglement between two

non-interacting qubits in a process we call Zeno gate. We demonstrate the Zeno gate on two

transmons far detuned from each other and coupled to a 3D cavity that acts as a non-local measurement device. We study the dynamics of the system and model it using the Lindblad master equation.   

Crosstalk Cancellation in The Tunable-Coupling Architecture with Fixed-Frequency Qubits

Scalability of superconducting quantum processors is undermined by both quantum and classical crosstalk between qubits. Here, we implement a set of scalable and robust techniques for characterizing and cancelling crosstalk in a tunable-coupling architecture with fixed-frequency transmon qubits, and show improvement in simultaneous benchmarking results.    

Implementing dispersive readout of superconducting qubits with simultaneous resonator reset

A key challenge in quantum computing is speeding up measurement and initialization. Here, we experimentally demonstrate a dispersive measurement method for superconducting qubits that simultaneously returns the readout resonator to its initial state. The approach is based on analytical pulses [1] and requires knowledge of the qubit and resonator parameters, but needs no direct optimization of the pulse shape. Moreover, the method generalizes to an arbitrary number of modes. In the case of qubit readout, we are able to drive the resonator to 10² and back to 10^-2 photons in less than 4/κ, achieving a T₁-limited assignment fidelity of 98.5%. We also present results for qutrit readout. 

[1] F. Motzoi, L. Buchmann, C. Dickel: Simple, smooth and fast pulses for dispersive measurements in cavities and quantum networks, arXiv:1809.04116v1 [quant-ph]   

Halving ion-trap two-qubit gate time while enhancing frequency-drift robustness

Two-qubit gate performance is vital for scaling up ion-trap quantum computing, and reducing gate time τ and gate error rate is achieved by quantum-control methods. We develop a full model for two-qubit gates effected in a Paul trap with multiple ions, described by a master equation incorporating the single-ion quadrupolar effective Rabi frequency,

an Autler-Townes shift, off-resonant transitions, photon scatterings, laser-power fluctuations, motional heating, cross-Kerr phonon coupling and laser spillover with no fitting parameters. To minimize τ, while maintaining fixed gate fidelity, we articulate and solve the feasibility problem: given the seven-ion master equation with all ions prepared in the ground state and given vibrational modes initially in a ∼μK thermal state, and with the target being two of the ions evolving over time τ into a Bell state, and subject to a strict upper bound on laser power, design an amplitude-modulated Raman laser pulse that deterministically yields a close approximation to this Bell state. We solve our problem by global optimization and obtain a pulse sequence that executes in half the time required by state-of-the-art methods. Our pulse is robust against long-term drift in the frequency detuning and an imperfect initial motional ground state.