In this review, we discuss recent experiments that investigate how the quantum sate of a superconducting qubit evolves during measurement. We provide a pedagogical overview of the measurementprocess, when the qubit is dispersively coupled to a microwave frequency cavity, and the qubit state is encoded in the phase of a microwave tone that probes the cavity. A continuous measurement record is used to reconstruct the individual quantum trajectories of the qubit state, and quantum state tomography is performed to verify that the state has been tracked accurately. Furthermore, we discuss ensembles of trajectories, time-symmetric evolution, two-qubit trajectories, and potential applications in measurement-based quantum error correction.
The quantum state of a superconducting transmon qubit inside a three-dimensional cavity is monitored by reflection of a microwave field on the cavity. The information inferred fromthe measurement record is incorporated in a density matrix ρt, which is conditioned on probe results until t, and in an auxiliary matrix Et, which is conditioned on probe results obtained after t. Here, we obtain these matrices from experimental data and we illustrate their application to predict and retrodict the outcome of weak and strong qubit measurements.
We provide a thorough theoretical analysis of qubit state measurement in a setup where a driven, parametrically-coupled cavity system is directly coupled to the qubit, with one of thecavities having a weak Kerr nonlinearity. Such a system could be readily realized using circuit QED architectures. We demonstrate that this setup is capable in the standard linear-response regime of both producing a highly amplified output signal while at the same time achieving near quantum-limited performance: the measurement backaction on the qubit is near the minimal amount required by the uncertainty principle. This setup thus represents a promising route for performing efficient large-gain qubit measurement that is completely on-chip, and that does not rely on the use of circulators or complex non-reciprocal amplifiers.
The length of time that a quantum system can exist in a superposition state is determined by how strongly it interacts with its environment. This interaction entangles the quantum statewith the inherent fluctuations of the environment. If these fluctuations are not measured, the environment can be viewed as a source of noise, causing random evolution of the quantum system from an initially pure state into a statistical mixture-a process known as decoherence. However, by accurately measuring the environment in real time, the quantum system can be maintained in a pure state and its time evolution described by a quantum trajectory conditioned on the measurement outcome. We employ weak measurements to monitor a microwave cavity embedding a superconducting qubit and track the individual quantum trajectories of the system. In this architecture, the environment is dominated by the fluctuations of a single electromagnetic mode of the cavity. Using a near-quantum-limited parametric amplifier, we selectively measure either the phase or amplitude of the cavity field, and thereby confine trajectories to either the equator or a meridian of the Bloch sphere. We perform quantum state tomography at discrete times along the trajectory to verify that we have faithfully tracked the state of the quantum system as it diffuses on the surface of the Bloch sphere. Our results demonstrate that decoherence can be mitigated by environmental monitoring and validate the foundations of quantum feedback approaches based on Bayesian statistics. Moreover, our experiments suggest a new route for implementing what Schrodinger termed „quantum steering“-harnessing action at a distance to manipulate quantum states via measurement.
When a frequency chirped excitation is applied to a classical high-Q
nonlinear oscillator, its motion becomes dynamically synchronized to the drive
and large oscillation amplitude isobserved, provided the drive strength
exceeds the critical threshold for autoresonance. We demonstrate that when such
an oscillator is strongly coupled to a quantized superconducting qubit, both
the effective nonlinearity and the threshold become a non-trivial function of
the qubit-oscillator detuning. Moreover, the autoresonant threshold is
sensitive to the quantum state of the qubit and may be used to realize a high
fidelity, latching readout whose speed is not limited by the oscillator Q.
We demonstrate quantum bath engineering for a superconducting artificial atom
coupled to a microwave cavity. By tailoring the spectrum of microwave photon
shot noise in the cavity,we create a dissipative environment that autonomously
relaxes the atom to an arbitrarily specified coherent superposition of the
ground and excited states. In the presence of background thermal excitations,
this mechanism increases the state purity and effectively cools the dressed
atom state to a low temperature.
We observe measurement-induced qubit state mixing in a transmon qubit
dispersively coupled to a planar readout cavity. Our results indicate that
dephasing noise at the qubit-readoutdetuning frequency is up-converted by
readout photons to cause spurious qubit state transitions, thus limiting the
nondemolition character of the readout. Furthermore, we use the qubit
transition rate as a tool to extract an equivalent flux noise spectral density
at f ~ 1 GHz and find agreement with values extrapolated from a $1/f^alpha$
fit to the measured flux noise spectral density below 1 Hz.
The act of measurement bridges the quantum and classical worlds by projecting
a superposition of possible states into a single, albeit probabilistic,
outcome. The time-scale of this„instantaneous“ process can be stretched using
weak measurements so that it takes the form of a gradual random walk towards a
final state. Remarkably, the interim measurement record is sufficient to
continuously track and steer the quantum state using feedback. We monitor the
dynamics of a resonantly driven quantum two-level system — a superconducting
quantum bit –using a near-noiseless parametric amplifier. The high-fidelity
measurement output is used to actively stabilize the phase of Rabi
oscillations, enabling them to persist indefinitely. This new functionality
shows promise for fighting decoherence and defines a path for continuous
quantum error correction.
We demonstrate high-fidelity, quantum nondemolition, single-shot readout of a
superconducting flux qubit in which the pointer state distributions can be
resolved to below one part in1000. In the weak excitation regime, continuous
measurement permits the use of heralding to ensure initialization to a fiducial
state, such as the ground state. This procedure boosts readout fidelity to
93.9% by suppressing errors due to spurious thermal population. Furthermore,
heralding potentially enables a simple, fast qubit reset protocol without
changing the system parameters to induce Purcell relaxation.