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arXiv:1712.06141 · Physical review. B./Physical review. B

Chip-to-chip entanglement of transmon qubits using engineered measurement fields

Christian Dickel, Jaap J. Wesdorp, Nathan K. Langford, Sarwan Peiter, Ramiro Sagastizabal, Alessandro Bruno, Ben Criger, Felix Motzoi, L. DiCarlo

Published Feb 13, 2018• 39 citations
arXivHTMLPDF

Abstract

While the on-chip processing power in circuit QED devices is growing rapidly, an open challenge is to establish high-fidelity quantum links between qubits on different chips. Here, we show entanglement between transmon qubits on different cQED chips with $49%$ concurrence and $73%$ Bell-state fidelity. We engineer a half-parity measurement by successively reflecting a coherent microwave field off two nearly identical transmon-resonator systems. By ensuring the measured output field does not distinguish $|01\ensuremath{\rangle}$ from $|10\ensuremath{\rangle}$, unentangled superposition states are probabilistically projected onto entangled states in the odd-parity subspace. We use in situ tunability and an additional weakly coupled driving field on the second resonator to overcome imperfect matching due to fabrication variations. To demonstrate the flexibility of this approach, we also produce an even-parity entangled state of similar quality, by engineering the matching of outputs for the $|00\ensuremath{\rangle}$ and $|11\ensuremath{\rangle}$ states. The protocol is characterized over a range of measurement strengths using quantum state tomography showing good agreement with a comprehensive theoretical model.

DOI
10.1103/physrevb.97.064508

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While the on-chip processing power in circuit QED devices is growing rapidly, an open challenge is to establish high-fidelity quantum links between qubits on different chips. Here, we show entanglement between transmon qubits on different cQED chips with 4949%49 concurrence and 7373%73 Bell-state fidelity. We engineer a half-parity measurement by successively reflecting a coherent microwave field off two nearly identical transmon-resonator systems. By ensuring the measured output field does not distinguish ∣01\ensuremath⟩|01\ensuremath{\rangle}∣01\ensuremath⟩ from ∣10\ensuremath⟩|10\ensuremath{\rangle}∣10\ensuremath⟩, unentangled superposition states are probabilistically projected onto entangled states in the odd-parity subspace. We use in situ tunability and an additional weakly coupled driving field on the second resonator to overcome imperfect matching due to fabrication variations. To demonstrate the flexibility of this approach, we also produce an even-parity entangled state of similar quality, by engineering the matching of outputs for the ∣00\ensuremath⟩|00\ensuremath{\rangle}∣00\ensuremath⟩ and ∣11\ensuremath⟩|11\ensuremath{\rangle}∣11\ensuremath⟩ states. The protocol is characterized over a range of measurement strengths using quantum state tomography showing good agreement with a comprehensive theoretical model.
This thesis mainly summarizes two experiments that relate to building a quantum computer out of superconducting transmon qubits. Transmon qubits have emerged as one of the foremost solid state qubits, realizing processors with more than ten qubits and demonstrating small scale quantum algorithms as well as quantum error correction schemes. Right now, there is a race between different academic and industry research groups to scale up transmon qubit processors. The first experiment was a demonstration of qubit control by selective broadcasting in order to reduce the scaling of expensive electronics with the number of qubits for individual single-qubit control. We demonstrated that we can bring two transmon qubits to the same frequency (combining fabrication accuracy and in-situ fine tuning) and use the same hardware to control both, routing the pulses with a nanosecond-timescale vector switch matrix. Despite the compromises required by this technique, we show a scalable path to single qubit control beyond the threshold required for quantum error correction. In benchmarking, we take into account gate leakage due to the fact that transmons are fundamentally multi-level systems. In the second experiment we establish entanglement between two transmon qubits on different chips. We use an entanglement by measurement scheme and demonstrate that we can overcome minor fabrication imperfections by shaping our measurement pulses. Ultimately, performance is mainly limited by photon loss between the chips and up to the amplification chain. This entanglement mediated by traveling photons could be used to make a distributed transmon processor where computations are spread across several chip modules. This modularity could enable connectivities that cannot be realized on chip and ease fabrication requirements, as modules could be individually fabricated and selected. Thus, both of these experiments fit into the larger effort to converge on the hardware, control equipment and architecture of a future large-scale transmon quantum computer. Other experiments I contributed to are summarized in the conclusion chapter to show the diverse physics that can be studied in cQED experiments.
Quantum entanglement is a cornerstone of quantum information science, enabling advancements in quantum computing, cryptography, and metrology. We report a comprehensive experimental study of quantum entanglement in a superconducting circuit comprising two transmon qubits coupled via a tunable bus resonator, operating at ultra-low temperatures (10 mK) in a dilution refrigerator. Using precise microwave control, we generate Bell states with a fidelity of 0.94 ± 0.02 and a concurrence of 0.92 ± 0.03, confirming robust entanglement. Quantum state tomography and coherence measurements yield energy relaxation (T1) times of 92 ± 5 µs and 88 ± 4 µs, and dephasing (T2) times of 85 ± 6 µs and 82 ± 5 µs for qubits Q1 and Q2, respectively, at 10 mK. We systematically investigate the impact of temperature (10 mK, 50 mK, 100 mK) and environmental noise on entanglement persistence. Real-time analysis of recent literature and social media discussions highlights ongoing challenges in scaling superconducting qubit systems due to 1/f noise and material limitations. Our findings demonstrate the viability of superconducting circuits for high-fidelity quantum operations and provide critical insights into optimizing coherence at millikelvin temperatures.
An open challenge in quantum information processing with superconducting circuits is to entangle arbitrary pairs of qubits, not simply nearest neighbors. This can be accomplished by first entangling the qubits with flying microwave oscillators in the form of traveling pulses and then performing joint manipulation and measurement on a pair of such flying oscillators at a distant site. This method has the advantage of avoiding the overhead required to move information over large distances via only nearest neighbor coupling while also possessing an extremely high on/off ratio of coupling. Remarkably, such a process is naturally embedded in the act of phase-preserving amplification, which transforms two input modes, termed signal and idler, into a two-mode squeezed output state. For an ideal system, this operation generates heralded, perfectly entangled states between remote qubits with a fifty percent success rate. For an inefficient system, the partial loss of information from the flying states degrades the purity of the entanglement. Data will be shown on such a protocol involving two transmon qubits embedded in superconducting cavities connected to the signal and idler inputs of a Josephson Parametric Converter (JPC) operated as a nearly-quantum limited phase-preserving amplifier. I will also discuss new devices which will allow us to improve the process and achieve high success rates with imperfect hardware. Light refreshments will be served.
We experimentally and theoretically investigate the quantum trajectories of jointly monitored transmon qubits embedded in spatially separated microwave cavities.Using nearly quantum-noise-limited superconducting amplifiers and an optimized setup to reduce signal loss between cavities, we can efficiently track measurement-induced entanglement generation as a continuous process for single realizations of the experiment.The quantum trajectories of transmon qubits naturally split into low and high entanglement classes.The distribution of concurrence is found at any given time, and we explore the dynamics of entanglement creation in the state space.The distribution exhibits a sharp cutoff in the high concurrence limit, defining a maximal concurrence boundary.The most-likely paths of the qubits' trajectories are also investigated, resulting in three probable paths, gradually projecting the system to two even subspaces and an odd subspace, conforming to a "half-parity" measurement.We also investigate the most-likely time for the individual trajectories to reach their most entangled state, and we find that there are two solutions for the local maximum, corresponding to the low and high entanglement routes.The theoretical predictions show excellent agreement with the experimental entangled-qubit trajectory data.
Using circuit QED, we consider the measurement of a superconducting transmon qubit via a coupled microwave resonator. For ideally dispersive coupling, ringing up the resonator produces coherent states with frequencies matched to transmon energy states. Realistic coupling is not ideally dispersive, however, so transmon-resonator energy levels hybridize into joint eigenstate ladders of the Jaynes--Cummings type. Previous work has shown that ringing up the resonator approximately respects this ladder structure to produce a coherent state in the eigenbasis (a dressed coherent state). We numerically investigate the validity of this coherent-state approximation to find two primary deviations. First, resonator ring-up leaks small stray populations into eigenstate ladders corresponding to different transmon states. Second, within an eigenstate ladder the transmon nonlinearity shears the coherent state as it evolves. We then show that the next natural approximation for this sheared state in the eigenbasis is a dressed squeezed state and derive simple evolution equations for such states by using a hybrid phase--Fock-space description.
Abstract Ternary quantum information processing in superconducting devices poses a promising alternative to its more popular binary counterpart through larger, more connected computational spaces and proposed advantages in quantum simulation and error correction. Although generally operated as qubits, transmons have readily addressable higher levels, making them natural candidates for operation as quantum three-level systems (qutrits). Recent works in transmon devices have realized high fidelity single qutrit operation. Nonetheless, effectively engineering a high-fidelity two-qutrit entanglement remains a central challenge for realizing qutrit processing in a transmon device. In this work, we apply the differential AC Stark shift to implement a flexible, microwave-activated, and dynamic cross-Kerr entanglement between two fixed-frequency transmon qutrits, expanding on work performed for the Z Z interaction with transmon qubits. We then use this interaction to engineer efficient, high-fidelity qutrit CZ † and CZ gates, with estimated process fidelities of 97.3(1)% and 95.2(3)% respectively, a significant step forward for operating qutrits on a multi-transmon device.