Hybrid quantum devices, in which dissimilar quantum systems are combined in order to attain qualities not available with either system alone, may enable far-reaching control in quantum measurement, sensing, and information processing. A paradigmatic example is trapped ultracold atoms, which offer excellent quantum coherent properties, coupled to nanoscale solid-state systems, which allow for strong interactions. We demonstrate a deterministic interface between a single trapped rubidium atom and a nanoscale photonic crystal cavity. Precise control over the atom's position allows us to probe the cavity near-field with a resolution below the diffraction limit and to observe large atom-photon coupling. This approach may enable the realization of integrated, strongly coupled quantum nano-optical circuits.

The realization of an all-optical transistor, in which one "gate" photon controls a "source" light beam, is a long-standing goal in optics. By stopping a light pulse in an atomic ensemble contained inside an optical resonator, we realized a device in which one stored gate photon controls the resonator transmission of subsequently applied source photons. A weak gate pulse induces bimodal transmission distribution, corresponding to zero and one gate photons. One stored gate photon produces fivefold source attenuation and can be retrieved from the atomic ensemble after switching more than one source photon. Without retrieval, one stored gate photon can switch several hundred source photons. With improved storage and retrieval efficiency, our work may enable various new applications, including photonic quantum gates and deterministic multiphoton entanglement.

Continuously monitoring the environment of a quantum many-body system reduces the entropy of (purifies) the reduced density matrix of the system, conditional on the outcomes of the measurements. We show that, for mixed initial states, a balanced competition between measurements and entangling interactions within the system can result in a dynamical purification phase transition between (i) a phase that locally purifies at a constant system-size-independent rate and (ii) a "mixed" phase where the purification time diverges exponentially in the system size. The residual entropy density in the mixed phase implies the existence of a quantum error-protected subspace, where quantum information is reliably encoded against the future nonunitary evolution of the system. We show that these codes are of potential relevance to fault-tolerant quantum computation as they are often highly degenerate and satisfy optimal trade-offs between encoded information densities and error thresholds. In spatially local models in 1 þ 1 dimensions, this phase transition for mixed initial states occurs concurrently with a recently identified class of entanglement phase transitions for pure initial states. The purification transition studied here also generalizes to systems with long-range interactions, where conventional notions of entanglement transitions have to be reformulated. We numerically explore this transition for monitored random quantum circuits in 1 þ 1 dimensions and all-to-all models. Unlike in pure initial states, the mutual information of an initially completely mixed state in 1 þ 1 dimensions grows sublinearly in time due to the formation of the error-protected subspace. Purification dynamics is likely a more robust probe of the transition in experiments, where imperfections generically reduce entanglement and drive the system towards mixed states. We describe the motivations for studying this novel class of nonequilibrium quantum dynamics in the context of advanced quantum computing platforms and fault-tolerant quantum computation.

We numerically study the measurement-driven quantum phase transition of Haar-random quantum circuits in 1 + 1 dimensions. By analyzing the tripartite mutual information we are able to make a precise estimate of the critical measurement rate pc = 0.17(1). We extract estimates for the associated bulk critical exponents that are consistent with the values for percolation, as well as those for stabilizer circuits, but differ from previous estimates for the Haar-random case. Our estimates of the surface order parameter exponent appear different from that for stabilizer circuits or percolation, but we are unable to definitively rule out the scenario where all exponents in the three cases match. Moreover, in the Haar case the prefactor for the entanglement entropies Sn depends strongly on the Rényi index n; for stabilizer circuits and percolation this dependence is absent. Results on stabilizer circuits are used to guide our study and identify measures with weak finite-size effects. We discuss how our numerical estimates constrain theories of the transition.Nonequilibrium quantum systems can undergo various phase transitions in their dynamics; characterizing such transitions is a key open question in modern quantum statistical physics. So far, these nonequilibrium phase transitions have been studied primarily for isolated quantum systems [1, 2] and for steady states of dissipative systems [3,4]. One much-studied case is the many-body localization transition [2], which can be seen either (i) as a dynamical transition at which thermalization slows down and stops as a parameter (e.g., the disorder strength in a spin chain) is tuned or (ii) as an entanglement transition at which the many-body eigenstates of the system change from volume-law to area-law entangled. Recently, a different type of entanglement transition was discovered [5][6][7] in the steady-state entanglement of the states produced by individual quantum trajectories [8-11] of a repeatedly-measured quantum many-body system. As the system is measured at an increasing rate, this single-trajectory entanglement goes from volume-law to area-law (see Fig. 1(a)), as has been demonstrated both numerically, and analytically in certain tractable limits [6, 7,[12][13][14][15][16][17]. This measurementdriven non-equilibrium quantum phase transition can also be interpreted as a purification transition [18] that can collapse a mixed state to a pure state through a sufficiently large rate of local projective measurements.A measurement driven transition is expected to occur for any form of quantum chaotic dynamics, e.g. in both random circuit [6, 7] and Hamiltonian [19] dynamics. Current studies have mainly focused on quantum circuits, acting on an array of qudits (of local Hilbert space dimension q); these are believed to be generic models of chaotic quantum dynamics [20][21][22][23][24][25][26]. Various choices of gates have been explored numerically [6, 7, 15]. In specific limiting cases, analytic results (or large-scale simu-lations) exist. Specifically, the transition in...

Significant advances have been made towards fault-tolerant operation of silicon spin qubits, with single qubit fidelities exceeding 99.9%, several demonstrations of two-qubit gates based on exchange coupling, and the achievement of coherent single spin-photon coupling. Coupling arbitrary pairs of spatially separated qubits in a quantum register poses a significant challenge as most qubit systems are constrained to two dimensions with nearest neighbor connectivity. For spins in silicon, new methods for quantum state transfer should be developed to achieve connectivity beyond nearest-neighbor exchange. Here we demonstrate shuttling of a single electron across a linear array of nine series-coupled silicon quantum dots in ~50 ns via a series of pairwise interdot charge transfers. By constructing more complex pulse sequences we perform parallel shuttling of two and three electrons at a time through the array. These experiments demonstrate a scalable approach to physically transporting single electrons across large silicon quantum dot arrays.