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Quantum physics was invented to account for two fundamental features of measurement resultstheir discreetness and randomness. Emblematic of these features is Bohr's idea of quantum jumps between two discrete energy levels of an atom 1 . Experimentally, quantum jumps were first observed in an atomic ion driven by a weak deterministic force while under strong continuous energy measurement 2-4 . The times at which the discontinuous jump transitions occur are reputed to be fundamentally unpredictable. Can there be, despite the indeterminism of quantum physics, a possibility to know if a quantum jump is about to occur or not? Here, we answer this question affirmatively by experimentally demonstrating that the jump from the ground to an excited state of a superconducting artificial three-level atom can be tracked as it follows a predictable "flight," by monitoring the population of an auxiliary energy level coupled to the ground state. The experimental results demonstrate that the jump evolution when completed is continuous, coherent, and deterministic. Furthermore, exploiting these features and using real-time monitoring and feedback, we catch and reverse a quantum jump mid-flight, thus deterministically preventing its completion. Our results, which agree with theoretical predictions essentially without adjustable parameters, support the modern quantum trajectory theory 5-9 and provide new ground for the exploration of real-time intervention techniques in the control of quantum systems, such as early detection of error syndromes.Bohr conceived of quantum jumps 1 in 1913, and while Einstein elevated their hypothesis to the level of a quantitative rule with his AB coefficient theory 10,11 , Schrödinger strongly objected to their existence 12 . The nature and existence of quantum jumps remained a subject of controversy for seven decades until they were directly observed in a single system 2-4 . Since then, quantum jumps have been observed in a variety of atomic [13][14][15][16] and solid-state 17-21 systems. Recently, quantum jumps have been recognized as an essential phenomenon in quantum feedback control 22,23 , and in particular, for detecting and correcting decoherence-induced errors in quantum information systems 24,25 .

Entangling two remote quantum systems that never interact directly is an essential primitive in quantum information science and forms the basis for the modular architecture of quantum computing. When protocols to generate these remote entangled pairs rely on using traveling single-photon states as carriers of quantum information, they can be made robust to photon losses, unlike schemes that rely on continuous variable states. However, efficiently detecting single photons is challenging in the domain of superconducting quantum circuits because of the low energy of microwave quanta. Here, we report the realization of a robust form of concurrent remote entanglement based on a novel microwave photon detector implemented in the superconducting circuit quantum electrodynamics platform of quantum information. Remote entangled pairs with a fidelity of 0.57 AE 0.01 are generated at 200 Hz. Our experiment opens the way for the implementation of the modular architecture of quantum computation with superconducting qubits.

Manipulating the state of a logical quantum bit (qubit) usually comes at the expense of exposing it to decoherence. Fault-tolerant quantum computing tackles this problem by manipulating quantum information within a stable manifold of a larger Hilbert space, whose symmetries restrict the number of independent errors. The remaining errors do not affect the quantum computation and are correctable after the fact. Here we implement the autonomous stabilization of an encoding manifold spanned by Schrödinger cat states in a superconducting cavity. We show Zeno-driven coherent oscillations between these states analogous to the Rabi rotation of a qubit protected against phase flips. Such gates are compatible with quantum error correction and hence are crucial for fault-tolerant logical qubits. DOI: 10.1103/PhysRevX.8.021005 Subject Areas: Quantum Physics, Quantum InformationThe quantum Zeno effect (QZE) is the apparent freezing of a quantum system in one state under the influence of a continuous observation. This continuous observation can be performed by a dissipative environment [1][2][3]. It can be further generalized to the stabilization of a manifold spanned by multiple quantum states, an operation which requires a dissipation that is blind to the manifold observables [4]. Harnessing this effect is crucial for the design of quantum computation schemes, since autonomous stabilization is a form of the feedback needed for quantum error correction. When employing manifold QZE for correcting errors, motion inside the manifold can still subsist and can be driven by the combination of the dissipative stabilization and an external force [5][6][7][8][9][10]. Therefore, manifold QZE offers a pathway towards the realization of logical gates compatible with quantum error correction. An example of such a system is provided by a superconducting microwave cavity, in which a dissipative process that annihilates photons in pairs at rate κ 2 , acting together with a twophoton drive of strength ϵ 2 , projects the system onto the manifold spanned by Schrödinger cat states jCand N is a normalization factor [11][12][13]. Each one of these states has a well-defined photon number parity, which is conserved by the engineered dissipation. In this Schrödinger cat state manifold, the displacement operator DðαÞ ¼ expðαa † − α Ã aÞ (where a is the annihilation operator acting on the harmonic oscillator) has two effects: it changes the photon number parity and it changes the amplitude of its component coherent states. The engineered dissipation leaves the change in parity invariant and cancels the change in amplitude [ Fig. 1(a)]. The net result of this quantum Zeno dynamics is to continuously vary the parity of Schrödinger cat states.These parity oscillations constitute the basis of an X gate on a qubit encoded in the protected manifold j0/1i P ¼ N ðjα ∞ i AE j−α ∞ iÞ. Encoding quantum information in superpositions of Schrödinger cat states is compatible with quantum error correction realized with quantum nondemolition parity measurements [14]...

We introduce a driven-dissipative two-mode bosonic system whose reservoir causes simultaneous loss of two photons in each mode and whose steady states are superpositions of pair-coherent/Barut-Girardello coherent states. We show how quantum information encoded in a steady-state subspace of this system is exponentially immune to phase drifts (cavity dephasing) in both modes. Additionally, it is possible to protect information from arbitrary photon loss in either (but not simultaneously both) of the modes by continuously monitoring the difference between the expected photon numbers of the logical states. Despite employing more resources, the two-mode scheme enjoys two advantages over its one-mode cat-qubit counterpart with regards to implementation using current circuit QED technology. First, monitoring the photon number difference can be done without turning off the currently implementable dissipative stabilizing process. Second, a lower average photon number per mode is required to enjoy a level of protection at least as good as that of the cat-codes. We discuss circuit QED proposals to stabilize the code states, perform gates, and protect against photon loss via either active syndrome measurement or an autonomous procedure. We introduce quasiprobability distributions allowing us to represent two-mode states of fixed photon number difference in a twodimensional complex plane, instead of the full four-dimensional two-mode phase space. The twomode codes are generalized to multiple modes in an extension of the stabilizer formalism to nondiagonalizable stabilizers. The M -mode codes can protect against either arbitrary photon losses in up to M − 1 modes or arbitrary losses and gains in any one mode.