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arXiv:1801.04858 · Physical review. B./Physical review. B

Coupling two spin qubits with a high-impedance resonator

Shannon P. Harvey, C. G. L. Bøttcher, Lucas Orona, Stephen D. Bartlett, Andrew C. Doherty, Amir Yacoby

Published Jun 7, 2018• 49 citations
arXivHTMLPDF

Abstract

Fast, high-fidelity single and two-qubit gates are essential to building a viable quantum information processor, but achieving both in the same system has proved challenging for spin qubits. We propose and analyze an approach to perform a long-distance two-qubit controlled phase (CPHASE) gate between two singlet-triplet qubits using an electromagnetic resonator to mediate their interaction. The qubits couple longitudinally to the resonator, and by driving the qubits near the resonator's frequency, they can be made to acquire a state-dependent geometric phase that leads to a CPHASE gate independent of the initial state of the resonator. Using high impedance resonators enables gate times of order 10 ns while maintaining long coherence times. Simulations show average gate fidelities of over 96% using currently achievable experimental parameters and over 99% using state-of-the-art resonator technology. After optimizing the gate fidelity in terms of parameters tuneable in situ, we find it takes a simple power-law form in terms of the resonator's impedance and quality and the qubits' noise bath.

DOI
10.1103/physrevb.97.235409

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Fast, high-fidelity single and two-qubit gates are essential to building a viable quantum information processor, but achieving both in the same system has proved challenging for spin qubits. We propose and analyze an approach to perform a long-distance two-qubit controlled phase (CPHASE) gate between two singlet-triplet qubits using an electromagnetic resonator to mediate their interaction. The qubits couple longitudinally to the resonator, and by driving the qubits near the resonator's frequency, they can be made to acquire a state-dependent geometric phase that leads to a CPHASE gate independent of the initial state of the resonator. Using high impedance resonators enables gate times of order 10 ns while maintaining long coherence times. Simulations show average gate fidelities of over 96% using currently achievable experimental parameters and over 99% using state-of-the-art resonator technology. After optimizing the gate fidelity in terms of parameters tuneable in situ, we find it takes a simple power-law form in terms of the resonator's impedance and quality and the qubits' noise bath.
Coupling qubits to a superconducting resonator provides a mechanism to enable long-distance entangling operations in a quantum computer based on spins in semiconducting materials. Here, we demonstrate a controllable spin-photon coupling based on a longitudinal interaction between a spin qubit and a resonator. We show that coupling a singlet-triplet qubit to a high-impedance superconducting resonator can produce the desired longitudinal coupling when the qubit is driven near the resonator's frequency. We measure the energy splitting of the qubit as a function of the drive amplitude and frequency of a microwave signal applied near the resonator antinode, revealing pronounced effects close to the resonator frequency due to longitudinal coupling. By tuning the amplitude of the drive, we reach a regime with longitudinal coupling exceeding 1 MHz. This mechanism for qubit-resonator coupling represents a stepping stone towards producing high-fidelity two-qubit gates mediated by a superconducting resonator.
To scale superconducting quantum processors, it is essential to achieve long coherence times while engineering interactions that do not introduce additional decoherence channels. In superconducting qubit systems, this can be realized using multimode circuits that feature a protected qubit mode alongside a distinct mediator mode. Building on this concept, our recently developed P-mon qubit provides intrinsic protection against decoherence from the readout environment. We extend this approach to controlled two-qubit interactions, by exploiting the mediator modes of P-mons for on-demand coupling. Because direct interactions between the qubit modes are strongly suppressed, unwanted ZZZZZZ-type interactions are significantly reduced to below 3.6(5) kHz3.6(5)~\text{kHz}3.6(5) kHz in the idle state. When tuning the coupled mediator modes on resonance, the cross-Kerr interaction between the qubit and the hybridized mediator modes leads to a qubit-state dependent frequency shift. By selectively addressing these transitions, we implement a 180 ns180~\text{ns}180 ns long CZ gate and determine a fidelity of $99.62(4)~\text{%}$. These results represent a significant step toward a scalable superconducting architecture that maintains high performance at scale.
Single-spin qubits in semiconductor quantum dots proposed by Loss and DiVincenzo (LD qubits) hold promise for universal quantum computation with demonstrations of a high single-qubit gate fidelity above 99.9 % and two-qubit gates in conjunction with a long coherence time. However, initialization and readout of a qubit is orders of magnitude slower than control, which is detrimental for implementing measurement-based protocols such as error-correcting codes. In contrast, a singlet-triplet (ST) qubit, encoded in a two-spin subspace, has the virtue of fast readout with high fidelity and tunable coupling to the electric field. Here, we present a hybrid system which benefits from the different advantages of these two distinct spin-qubit implementations. A quantum interface between the two codes is realized by electrically tunable inter-qubit exchange coupling. We demonstrate a controlled-phase (CPHASE) gate that acts within 5.5 ns, much faster than the measured dephasing time of 211 ns. The presented hybrid architecture will be useful to settle remaining key problems with building scalable spin-based quantum computers.
Geometric gates that use the global property of the geometric phase is believed to be a powerful tool to realize fault-tolerant quantum computation. However, for singlet-triplet qubits in semiconductor quantum dot, the low Rabi frequency of the microwave control leads to overly long gating time, and thus the constructing geometric gate suffers more from the decoherence effect. Here we investigate the key issue of whether the fast geometric gate can be realized for singlet-triplet qubits without introducing an extra microwave-driven pulse, while maintaining the high-fidelity gate operation at the same time. We surprisingly find that both the single- and two-qubit geometric gates can be implemented via only modulating the time-dependent exchange interaction of the Hamiltonian, which can typically be on the order of $\ensuremath{\sim}\mathrm{GHz}$, and thus the corresponding gate time is of several nanoseconds. Furthermore, the obtained geometric gates are superior to their counterparts, i.e., the conventional dynamical gates for singlet-triplet qubits, with a relatively high fidelity surpassing 99%. Therefore our scheme is particularly applied to singlet-triplet qubits to obtain fast and high-fidelity geometric gates. Our scheme can also be extended to other systems without a microwave drive.
Over the past two decades, many quantum systems have been explored as candidate qubits for quantum information processing. Qubits based on nuclear spins enjoy exceptionally long coherence times, especially compared to other solid-state platforms. However, this usually comes at the cost of slow gate operations and weak interqubit interactions, aspects which have so far prevented the development of multi-qubit processors comprised of solid-state nuclear spins. An exception to this is the TbPc2_22​ single-molecule magnet, a nuclear spin qubit which features a remarkable combination of long-lived coherence and fast electrical control. Despite this promise, it has remained an open question how to couple such qubits together to create the entanglement needed for quantum information applications. Given the sensitivity of the TbPc2_22​ molecule to electric fields via the hyperfine Stark effect, it is natural to consider the possibility of using a superconducting transmission line resonator to mediate a long-distance coupling between multiple TbPc2_22​ qubits. We use recent experimental results on single-qubit Rabi oscillations to deduce the strength and nature of the hyperfine Stark effect, information we then use to estimate the qubit-resonator coupling and to design two-qubit entangling gates with fidelities exceeding 99%. Our results suggest that the qubit-resonator interaction is near the edge of the strong coupling regime and could potentially pass into it with further improvements in device designs and components.
Implementing high-fidelity two-qubit gates in single-electron spin qubits in silicon double quantum dots is still a major challenge. In this work we employ analytical methods to design control pulses that generate high-fidelity entangling gates for quantum computers based on this platform. Using realistic parameters and initially assuming a noise-free environment, we present simple control pulses that generate cnot, cphase, and cz gates with average fidelities greater than 99.99% and gate times as short as 45 ns. Moreover, using the local invariants of the system's evolution operator, we show that a simple square pulse generates a cnot gate in less than 27 ns and with a fidelity greater than 99.99%. Last, we use the same analytical methods to generate two-qubit gates locally equivalent to CNOT\sqrt{\mathrm{CNOT}}CNOT​ and CZ\sqrt{\mathrm{CZ}}CZ​ that are used to implement simple two-piece pulse sequences that produce high-fidelity cnot and cz gates in the presence of low-frequency noise.