Quantum back-action of an individual variable-strength measurement

Observing single quantum trajectories of a superconducting quantum bit

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 state with 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' determined by the measurement outcome. Here we use weak measurements to monitor a microwave cavity containing a superconducting quantum bit (qubit), and track the individual quantum trajectories of the system. In this set-up, 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 the 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 foundation of quantum feedback approaches based on Bayesian statistics. Moreover, our experiments suggest a new means of implementing 'quantum steering'--the harnessing of action at a distance to manipulate quantum states through measurement.

Autonomously stabilized entanglement between two superconducting quantum bits

Quantum error correction codes are designed to protect an arbitrary state of a multi-qubit register from decoherence-induced errors, but their implementation is an outstanding challenge in the development of large-scale quantum computers. The first step is to stabilize a non-equilibrium state of a simple quantum system, such as a quantum bit (qubit) or a cavity mode, in the presence of decoherence. This has recently been accomplished using measurement-based feedback schemes. The next step is to prepare and stabilize a state of a composite system. Here we demonstrate the stabilization of an entangled Bell state of a quantum register of two superconducting qubits for an arbitrary time. Our result is achieved using an autonomous feedback scheme that combines continuous drives along with a specifically engineered coupling between the two-qubit register and a dissipative reservoir. Similar autonomous feedback techniques have been used for qubit reset, single-qubit state stabilization, and the creation and stabilization of states of multipartite quantum systems. Unlike conventional, measurement-based schemes, the autonomous approach uses engineered dissipation to counteract decoherence, obviating the need for a complicated external feedback loop to correct errors. Instead, the feedback loop is built into the Hamiltonian such that the steady state of the system in the presence of drives and dissipation is a Bell state, an essential building block for quantum information processing. Such autonomous schemes, which are broadly applicable to a variety of physical systems, as demonstrated by the accompanying paper on trapped ion qubits, will be an essential tool for the implementation of quantum error correction.

Past quantum states of a monitored system

A density matrix ρ(t) yields probabilistic information about the outcome of measurements on a quantum system. We introduce here the past quantum state, which, at time T, accounts for the state of a quantum system at earlier times t<T. The past quantum state Ξ(t) is composed of two objects, ρ(t) and E(t), conditioned on the dynamics and the probing of the system until t and in the time interval [t, T], respectively. The past quantum state is characterized by its ability to make better predictions for the unknown outcome of any measurement at t than the conventional quantum state at that time. On the one hand, our formalism shows how smoothing procedures for estimation of past classical signals by a quantum probe [M. Tsang, Phys. Rev. Lett. 102, 250403 (2009)] apply also to describe the past state of the quantum system itself. On the other hand, it generalizes theories of pre- and postselected quantum states [Y. Aharonov and L. Vaidman, J. Phys. A 24, 2315 (1991)] to systems subject to any quantum measurement scenario, any coherent evolution, and any Markovian dissipation processes.

Deterministically encoding quantum information using 100-photon Schrödinger cat states

In contrast to a single quantum bit, an oscillator can store multiple excitations and coherences provided one has the ability to generate and manipulate complex multiphoton states. We demonstrate multiphoton control by using a superconducting transmon qubit coupled to a waveguide cavity resonator with a highly ideal off-resonant coupling. This dispersive interaction is much greater than decoherence rates and higher-order nonlinearities to allow simultaneous manipulation of hundreds of photons. With a tool set of conditional qubit-photon logic, we mapped an arbitrary qubit state to a superposition of coherent states, known as a "cat state." We created cat states as large as 111 photons and extended this protocol to create superpositions of up to four coherent states. This control creates a powerful interface between discrete and continuous variable quantum computation and could enable applications in metrology and quantum information processing.

Partial-measurement backaction and nonclassical weak values in a superconducting circuit

We realize indirect partial measurement of a transmon qubit in circuit quantum electrodynamics by interaction with an ancilla qubit and projective ancilla measurement with a dedicated readout resonator. Accurate control of the interaction and ancilla measurement basis allows tailoring the measurement strength and operator. The tradeoff between measurement strength and qubit backaction is characterized through the distortion of a qubit Rabi oscillation imposed by ancilla measurement in different bases. Combining partial and projective qubit measurements, we provide the solid-state demonstration of the correspondence between a nonclassical weak value and the violation of a Leggett-Garg inequality.

Three-wave mixing with three incoming waves: signal-idler coherent attenuation and gain enhancement in a parametric amplifier

We demonstrate the time-reversed process of nondegenerate three-wave parametric amplification from three distinct sources in the fully nonlinear regime using a Josephson amplifier. In the reverse process, coherent attenuation, signal and idler beams destructively interfere in the presence of a pump to generate additional pump photons. This effect is observed through the symmetric phase-dependent amplification and attenuation of the signal and idler beams and, in the depleted pump regime, through the phase-dependent modulation of the amplifier gain, directly probing the enhancement of the pump. Results are found to be in good agreement with theory.

Full coherent frequency conversion between two propagating microwave modes

We demonstrate full frequency conversion in the microwave domain using a Josephson three-wave mixing device pumped at the difference between the frequencies of its fundamental eigenmodes. By measuring the signal output as a function of the intensity and phase of the three input signal, idler, and pump tones, we show that the device functions as a controllable three-wave beam splitter or combiner for propagating microwave modes at the single-photon level, in accordance with theory. Losses at the full conversion point are found to be less than 10(-2). Potential applications of the device include quantum information transduction and realization of an ultrasensitive interferometer with controllable feedback.