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Register a new userNonlinear oscillators and high fidelity qubit state measurement in circuit quantum electrodynamics
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In this book chapter we analyze the high excitation nonlinear response of the Jaynes-Cummings model in quantum optics when the qubit and cavity are strongly coupled. We focus on the parameter ranges appropriate for transmon qubits in the circuit quantum electrodynamics architecture, where the system behaves essentially as a nonlinear quantum oscillator and we analyze the quantum and semi-classical dynamics. One of the central motivations is that under strong excitation tones, the nonlinear response can lead to qubit quantum state discrimination and we present initial results for the cases when the qubit and cavity are on resonance or far off-resonance (dispersive).
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We demonstrate a qubit readout scheme that exploits the Jaynes-Cummings nonlinearity of a superconducting cavity coupled to transmon qubits. We find that in the strongly-driven dispersive regime of this system, there is the unexpected onset of a high-transmission bright state at a critical power which depends sensitively on the initial qubit state. A simple and robust measurement protocol exploiting this effect achieves a single-shot fidelity of 87% using a conventional sample design and experimental setup, and at least 61% fidelity to joint correlations of three qubits.
We analyze a two qubit parity measurement based on dispersive read-out in circuit quantum electrodynamics. The back-action on the qubits has two qualitatively different contributions. One is an unavoidable dephasing in one of the parity subspaces, arising during the transient time of switching on the measurement. The other part is a stochastic rotation of the phase in the same subspace, which persists during the whole measurement. The latter can be determined from the full measurement record, using the method of state estimation. Our main result is that the outcome of this phase determination process is {em independent} of the initial state in the state estimation procedure. The procedure can thus be used in a measurement situation, where the initial state is unknown. We discuss how this feed-back method can be used to achieve a high fidelity parity measurement for realistic values of the cavity-qubit coupling strength. Finally, we discuss the robustness of the feed-back procedure towards errors in the measurement record.
Circuit quantum electrodynamics allows spatially separated superconducting qubits to interact via a quantum bus, enabling two-qubit entanglement and the implementation of simple quantum algorithms. We combine the circuit quantum electrodynamics architecture with spin qubits by coupling an InAs nanowire double quantum dot to a superconducting cavity. We drive single spin rotations using electric dipole spin resonance and demonstrate that photons trapped in the cavity are sensitive to single spin dynamics. The hybrid quantum system allows measurements of the spin lifetime and the observation of coherent spin rotations. Our results demonstrate that a spin-cavity coupling strength of 1 MHz is feasible.
Traditionally, quantum entanglement has played a central role in foundational discussions of quantum mechanics. The measurement of correlations between entangled particles can exhibit results at odds with classical behavior. These discrepancies increase exponentially with the number of entangled particles. When entanglement is extended from just two quantum bits (qubits) to three, the incompatibilities between classical and quantum correlation properties can change from a violation of inequalities involving statistical averages to sign differences in deterministic observations. With the ample confirmation of quantum mechanical predictions by experiments, entanglement has evolved from a philosophical conundrum to a key resource for quantum-based technologies, like quantum cryptography and computation. In particular, maximal entanglement of more than two qubits is crucial to the implementation of quantum error correction protocols. While entanglement of up to 3, 5, and 8 qubits has been demonstrated among spins, photons, and ions, respectively, entanglement in engineered solid-state systems has been limited to two qubits. Here, we demonstrate three-qubit entanglement in a superconducting circuit, creating Greenberger-Horne-Zeilinger (GHZ) states with fidelity of 88%, measured with quantum state tomography. Several entanglement witnesses show violation of bi-separable bounds by 830pm80%. Our entangling sequence realizes the first step of basic quantum error correction, namely the encoding of a logical qubit into a manifold of GHZ-like states using a repetition code. The integration of encoding, decoding and error-correcting steps in a feedback loop will be the next milestone for quantum computing with integrated circuits.
We investigate a hybrid quantum system consisting of spatially separated resonant exchange qubits, defined in three-electron semiconductor triple quantum dots, that are coupled via a superconducting transmission line resonator. Drawing on methods from circuit quantum electrodynamics and Hartmann-Hahn double resonance techniques, we analyze three specific approaches for implementing resonator-mediated two-qubit entangling gates in both dispersive and resonant regimes of interaction. We calculate entangling gate fidelities as well as the rate of relaxation via phonons for resonant exchange qubits in silicon triple dots and show that such an implementation is particularly well-suited to achieving the strong coupling regime. Our approach combines the favorable coherence properties of encoded spin qubits in silicon with the rapid and robust long-range entanglement provided by circuit QED systems.
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