Session L29: Superconducting Qubits: Quantum Gates

Fast Parametric Gates with Superconducting Qubits

We discuss a system with two transmon qubits coupled parametrically through a shared dc-SQUID coupler. The coupling can be tuned from nominally zero to up to more than 100 MHz. This coupling mechanism can be used to perform a two-qubit controlled Z-gate. We present the latest experiment results on the gate operation.   

Fault-tolerant photon-number selective phase gate in circuit quantum electrodynamics

In circuit quantum electrodynamics (QED), it has been demonstrated that universal control of the cavity states can be realized by quantum control of a transmon coupled to the cavity in the strongly dispersive regime. An important class of quantum gates are the selective number-dependent arbitrary phase (SNAP) gates, which impart arbitrary phases to the different Fock states of the cavity by cyclically driving the transmon. However, the SNAP gate fidelity is limited by the transmon relaxation and dephasing. Here we show that by using a multi-level transmon and conditional evolution on the transmon state after the gate, the SNAP gate can be made fault-tolerant to the dominant transmon relaxation and dephasing errors. The simulations show that the SNAP gate infidelity can be reduced compared to that of non-fault-tolerant SNAP gate. The fault-tolerant SNAP gates combined with the displacement operations on the cavity can realize fault-tolerant quantum computation in circuit QED.   

High-fidelity conditional two-qubit swapping gate using tunable ancillas

Scalable quantum computing relies crucially on high-fidelity entangling operations. Here we demonstrate that four coupled qubits can operate as a high-fidelity two-qubit entangling gate that swaps two target qubits and adds a relative sign on the |11〉 state (ZSWAP). The gate operation is controlled by the state of two ancilla (control) qubits. The system is readily implementable with superconducting qubits, using capacitively coupled qubits arranged in a diamond-shaped architecture. By using realistic device and noise parameters from state-of-the-art superconducting qubits, we show that the conditional ZSWAP operation can be implemented with a fidelity above 0.99 in a time of about 65 ns.   

Implementation of a Walsh-Hadamard gate in a superconducting qutrit

We present the experimental demonstration of a generalized Walsh-Hadamard gate, which is a Quantum Fourier Transform gate, for a qutrit embedded in the lowest three energy levels of a superconducting circuit. This circuit is a three Josephson junction flux qubit in which all three junctions are shunted by large coplanar capacitors. We use a decomposition of the quantum gate into two unitary operations, one implemented by an off-diagonal Hamiltonian and the other implemented by a diagonal Hamiltonian. The off-diagonal Hamiltonian is obtained by the simultaneous driving of the transitions between levels 0-1, 1-2, and 0-2, with the latter being a two-photon process. The diagonal Hamiltonian is effectively implemented by appropriately shifting the phases of the driving fields. We find that multi-level ac-Stark shifts play an important role in the dynamics, and we adjust the pulse parameters to correct for these shifts. The gate is characterized using tomography of the generated output states corresponding to a set of input states. The average fidelity exceeds 90%, in good agreement with numerical simulations that take into account the multi-level structure of the system.   

Microwave-based CPHASE gates for transmon qubits

Superconducting transmon qubits are of great interest for quantum simulation of quantum chemistry. A key component of these algorithms is breaking up the evolution into small steps, which naturally leads to the need for non-maximally entangling, arbitrary CPHASE gates. Here we design such microwave-based gates using an analytically solvable approach leading to smooth, simple pulses. Our protocol allows for the continuous tuning of the phase. We find CPHASE fidelities of more than 0.999 and typical gate times less than 100ns.   

Limitations and improvements of two qubit gates in superconducting circuit QED

Remarkable progress has been made towards creating and operating processors for quantum computation and simulation with superconducting circuits, with respect to qubit count and coherence time. This has allowed for the implementation of a variety of quantum algorithms on small quantum processors, with promising results thus far. However, significant limitations on the fidelity of multi-qubit entangling gates remain, placing constraints on the scalability of current processors with respect to algorithmic circuit depth. We explore the sources of errors in these gates, include designs with employ cross-resonance and parametric interactions, and attempt to correct and/or mitigate the errors with hardware improvements, control sophistication, and algorithmic error suppression.   

Novel Two-qubit Gate Through Raman-type Transition

Two-qubit gates are essential for quantum computing. Presently, the low fidelity of these operations is a major factor limiting the physical implementation of long quantum algorithms. In this talk, we propose an entangling gate for directly coupled superconducting qubits based on a Raman-type transition and numerically show that it is fast and high fidelity. This gate is all-microwave and does not require additional hardware compared to standard cQED experiments.   

Operation and error budget of the Cross-Resonance gate

We analyze operation of the Cross-Resonance (CR) gate, in which control qubit is driven at the frequency of target qubit to realize the CNOT gate after additional single-qubit rotations. Numerical simulations for multi-level transmons and particular pulse shapes are used to find the CNOT time and parameters of single-qubit rotations as functions of the drive amplitude ε. To understand these dependences, including saturation of the CNOT time at large ε, we develop analytical and semi-analytical theories, which agree well with the numerics. We also calculate intrinsic infidelity of the CR gate as a function of ε and find a minimum, created by the interplay between leakage and imperfect unitary evolution. The error budget of the CR gate can be approximately described analytically or semi-analytically.   

DEMUXYZ Gate Using Single Microwave Drive Line for Multiple Qubits

Superconducting qubits have the potential to lead to large-scale quantum computers with 10⁵ or more qubits in 2D arrays. As the number of qubits increases, finding methods to connect all the necessary control lines to each qubit can become a serious challenge. In this talk, we introduce a new one-qubit gate: DEMUXYZ. This gate makes it possible to decrease the number of microwave control lines from N² to 1 by allowing multiple qubits to share a single microwave line. The shared line carries a continuous wave (CW) microwave tone, which is initially detuned from the qubits’ idle frequency. When a qubit must undergo an arbitrary rotation on the Bloch sphere, the qubit is tuned on resonance with the CW tone and allowed to interact with the drive for the duration required to achieve the desired rotation. The rotation phase is tuned by detuning the qubit frequency away from the drive and idle frequency for the required time length. We demonstrate a first proof of concept for this gate performing experiments on two Xmon transmon qubits.   

Realistic simulations of flux-pulse-based controlled-phase gates in superconducting qubits

We study the performance of the controlled-phase gate in flux-pulsed transmons by running extensive numerical simulations. We include thermal relaxation, dephasing due to fast and quasi-static components of the noise, leakage, and pulse-shape distortions, validating our model with experimental data. We first consider the conventional Geller-Martinis pulse and find that the leakage strongly depends on the dephasing times and that there is an optimal tradeoff between fidelity, leakage and pulse length. Also, we show that state-of-the-art distortion correction techniques can sufficiently reduce pulse distortions so that they are not a limiting factor. Finally, we compare the Geller-Martinis pulse with a novel double-sided pulse that we call net-zero, which has a built-in echo effect. We find better performance for net-zero than for the conventional pulse with respect to the same noise parameters.   

Toward a Universal Gate Set on a Qubit Encoded in Superconducting Cavities

Superconducting microwave cavities coupled to transmon ancillae are an attractive platform for the storage and manipulation of continuous variable (CV) quantum states. Each cavity is a bosonic mode that provides a long coherence time and a large Hilbert space that can be used to redundantly encode quantum information. The coupled transmon ancilla enables nearly arbitrary control over the state of each mode and can be used to perform high quality quantum nondemolition (QND) measurements of the cavity state. Further, it has been demonstrated that the nonlinearity of these ancilla transmons can be driven to enact parametric operations on the system, such as a bilinear coupling between two modes (Gao, et al., PRX 2018). Performing these operations with high fidelity requires mitigating dephasing effects arising from intrinsic properties of the transmon-cavity system as well as external drives. Here, we present our experimental progress towards mitigating these effects and enabling successive, high-fidelity pumped operations on states stored in these cavities.   

Two-Qubit Gates with Fluxonium Circuits.

Among superconducting qubits, the fluxonium offers a unique advantage of the possibility to use different transitions for memory storage and gate realizations [1]. In this talk, we discuss various ways to make entangling gates between fluxoniums using noncomputational levels of the two-qubit system. In one example, a controlled-Z gate is activated by driving a transition leading out of the computational subspace while two qubits are kept at fixed frequencies at their sweet spots [2]. The second example is based on adiabatic tuning of one or both of the qubits away from their sweet spots towards the avoided level crossing between a computational and noncompuational levels [3]. One more possible gate is mediated through a common resonator mode. We compare all the techniques and discuss their advantages and limitations.

[1] L. B. Nguyen, et. al., arXiv:1810.11006 (2018).
[2] K. N. Nesterov, et. al., Phys. Rev. A 98, 030301 (2018).
[3] L. DiCarlo, et. al., Nature (London) 460, 240 (2009).   

Superadiabatic Stimulated Raman adiabatic passage in a three-level transmon

Quantum control by adiabatic pulses presents the advantage of robustness under errors in the control parameters, yet it is inherently slow. Here I present an implementation of the superadiabatic protocol in a three-level system realized with a transmon superconducting circuit, where an additional control pulse is used to cancel the non-adiabatic evolution of the system. This enables the transfer of population from the ground state to the second excited state by stimulated Raman adiabatic passage in only a few tens of nanoseconds, approaching the quantum speed limit. As a bridge between adiabatic and direct methods, superadiabatic concept allows a continuous interpolation between the speed and robustness of the population transfer. As a result, it is possible to choose an optimal protocol speed that meets the given robustness criteria. This is particularly important in the field of circuit quantum electrodynamics, where the acceptable duration of the protocol is limited by the coherence time. Additionally, combination of two superadiabatic passages can be used to form a robust rotation gate in the {|0> - |2>} subspace.   

Realization of two-qubit gates with tunable couplers in superconducting circuits

The realization of two-qubit gates with high fidelity and low crosstalk is a key requirement for the scale-up of quantum processors based on superconducting circuits. Two-qubit gates are typically based on either microwave-controlled interactions or on the in-situ tunability of qubit frequencies. Alternative approaches using tunable coupling elements have also been investigated more recently. Here, we report on the design and implementation of a flux-tunable coupler, featuring small residual qubit-qubit interactions when gates are idle. We study gate operations based on both fast DC flux control and parametric flux modulation.