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Physical systems usually exhibit quantum behavior, such as superpositions and entanglement, only when they are sufficiently decoupled from a lossy environment. Paradoxically, a specially engineered interaction with the environment can become a resource for the generation and protection of quantum states. This notion can be generalized to the confinement of a system into a manifold of quantum states, consisting of all coherent superpositions of multiple stable steady states. We have confined the state of a superconducting resonator to the quantum manifold spanned by two coherent states of opposite phases and have observed a Schrödinger cat state spontaneously squeeze out of vacuum before decaying into a classical mixture. This experiment points toward robustly encoding quantum information in multidimensional steady-state manifolds.

The transfer of information between different physical forms is a central theme in communication and computation, for example between processing entities and memory. Nowhere is this more crucial than in quantum computation [1], where great effort must be taken to protect the integrity of a fragile quantum bit (qubit) [2]. However, transfer of quantum information is particularly challenging, as the process must remain coherent at all times to preserve the quantum nature of the information [3]. Here we demonstrate the coherent transfer of a superposition state in an electron spin 'processing' qubit to a nuclear spin 'memory' qubit, using a combination of microwave and radiofrequency pulses applied to 31 P donors in an isotopically pure 28 Si crystal [4,5]. The state is left in the nuclear spin on a timescale that is long compared with the electron decoherence time and then coherently transferred back to the electron spin, thus demonstrating the 31 P nuclear spin as a solid-state quantum memory. The overall store/readout fidelity is about 90%, attributed to imperfect rotations which can be improved through the use of composite pulses [6]. The coherence lifetime of the quantum memory element at 5.5 K exceeds one second.Classically, transfer of information can include a copying step, facilitating the identification and correction of errors. However, the no-cloning theorem limits the ability to faithfully copy quantum states across different degrees of freedom [7]; thus error correction becomes more challenging than for classical information and the transfer of information must take place directly. Experimental demonstrations of such transfer include moving a trapped ion qubit in and out of a decoherence-free subspace for storage purposes [8] and optical measurements of NV centres in diamond [9].Nuclear spins are known to benefit from long coherence times compared to electron spins, but are slow to manipulate and suffer from weak thermal polarisation. A powerful model for quantum computation is thus one in which electron spins are used for processing and readout while nuclear spins are used for storage. The storage element can be a single, well-defined nuclear spin, or perhaps a bath of nearby nuclear spins [10]. 31 P donors in silicon provide an ideal combination of long-lived spin-1/2 electron [11] and nuclear spins [12], with the additional advantage of integration with existing technologies [4] and the possibility of single spin detection by electrical measurement [13,14,15]. Direct measurement of the 31 P nuclear spin by NMR has only been possible at very high doping levels (e.g. near the metal insulator transition [16]). Instead, electron-nuclear double resonance (ENDOR) can be used to excite both the electron and nuclear spin associated with the donor site, and measure the nuclear spin via the electron [17]. This was recently used to measure the nuclear spin-lattice relaxation time T 1n , which was found to follow the electron relaxation time T 1e over the range 6 to 12 K with the relationship T 1n ≈ 250T 1e [5,...

We present a semi-classical method for determining the effective low-energy quantum Hamiltonian of weakly anharmonic superconducting circuits containing mesoscopic Josephson junctions coupled to electromagnetic environments made of an arbitrary combination of distributed and lumped elements. A convenient basis, capturing the multi-mode physics, is given by the quantized eigenmodes of the linearized circuit and is fully determined by a classical linear response function. The method is used to calculate numerically the low-energy spectrum of a 3D-transmon system, and quantitative agreement with measurements is found.

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Quantum error-correction codes would protect an arbitrary state of a multi-qubit register against decoherence-induced errors 1 , but their implementation is an outstanding challenge for the development of large-scale quantum computers. A first step is to stabilize a nonequilibrium state of a simple quantum system such as a qubit or a cavity mode in the presence of decoherence. Several groups have recently accomplished this goal using measurementbased feedback schemes [2][3][4][5] . A next step is to prepare and stabilize a state of a composite system [6][7][8] . 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 by an autonomous feedback scheme which combines continuous drives along with a specifically engineered coupling between the two-qubit register and a dissipative reservoir. Similar autonomous feedback techniques have recently been used for qubit reset 9 and the stabilization of a single qubit state 10 , as well as for creating 11 and stabilizing 6 states of multipartite quantum systems. Unlike conventional, measurement-based schemes, an autonomous approach counter-intuitively uses engineered dissipation to fight decoherence [12][13][14][15] , obviating the need 1 arXiv:1307.4349v3 [quant-ph] 23 Oct 2013 for a complicated external feedback loop to correct errors, simplifying implementation. 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 state for quantum information processing. Such autonomous schemes, broadly applicable to a variety of physical systems as demonstrated by a concurrent publication with trapped ion qubits 16 , will be an essential tool for the implementation of quantum-error correction.Here we implement a proposal 17 , tailored to the circuit Quantum Electrodynamics (cQED) architecture 18 , for stabilizing entanglement between two superconducting transmon qubits 19 . The qubits are dispersively coupled to an open cavity which acts as the dissipative reservoir. The cavity in our implementation is furthermore engineered to preferentially decay into a 50 Ω transmission line that we can monitor on demand. We show, using two-qubit quantum state tomography and high-fidelity single-shot readout, that the steady-state of the system reaches the target Bell state with a fidelity of 67 %, well above the 50 % threshold that witnesses entanglement. As discussed in Ref. 17, the fidelity can be further improved by monitoring the cavity output and performing conditional tomography when the output indicates that the two qubits are in the Bell state. We implemented this protocol via post-selection and demonstrated that the fidelity increased to ∼ 77 %.Our cQED setup, outlined schematically in Fig. 1a, consists of two individually addressable qubits, Alice and Bob, coupled dispersively to a three-dimensional (3D) rectangular copper cavity.The setup is described by...

Measuring a quantum system can randomly perturb its state. The strength and nature of this back-action depend on the quantity that is measured. In a partial measurement performed by an ideal apparatus, quantum physics predicts that the system remains in a pure state whose evolution can be tracked perfectly from the measurement record. We demonstrated this property using a superconducting qubit dispersively coupled to a cavity traversed by a microwave signal. The back-action on the qubit state of a single measurement of both signal quadratures was observed and shown to produce a stochastic operation whose action is determined by the measurement result. This accurate monitoring of a qubit state is an essential prerequisite for measurement-based feedback control of quantum systems.

Quantum error correction (QEC) is required for a practical quantum computer because of the fragile nature of quantum information [1]. In QEC, information is redundantly stored in a large Hilbert space and one or more observables must be monitored to reveal the occurrence of an error, without disturbing the information encoded in an unknown quantum state. Such observables, typically multi-qubit parities such as σ , must correspond to a special symmetry property inherent to the encoding scheme. Measurements of these observables, or error syndromes, must also be performed in a quantum non-demolition (QND) way and faster than the rate at which errors occur. Previously, QND measurements of quantum jumps between energy eigenstates have been performed in systems such as trapped ions [2][3][4], electrons [5], cavity quantum electrodynamics (QED) [6, 7], nitrogen-vacancy (NV) centers [8,9], and superconducting qubits [10,11]. So far, however, no fast and repeated monitoring of an error syndrome has been realized. Here, we track the quantum jumps of a possible error syndrome, the photon number parity of a microwave cavity, by mapping this property onto an ancilla qubit. This quantity is just the error syndrome required in a recently proposed scheme for a hardware-efficient protected quantum memory using Schrödinger cat states in a harmonic oscillator [12]. We demonstrate the projective nature of this measurement onto a parity eigenspace by observing the collapse of a coherent state onto even or odd cat states. The measurement is fast compared to the cavity lifetime, has a high single-shot fidelity, and has a 99.8% probability per single measurement of leaving the parity unchanged. In combination with the deterministic encoding of * current address: Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing, P. R. China † current address: Institut für Experimentalphysik, Universität Innsbruck, Technikerstraße 25, A-6020 Innsbruck, Austria; Institut für Quantenoptik und Quanteninformation,Österreichische Akademie der Wissenschaften, Otto-Hittmair-Platz 1, A-6020 Innsbruck, Austria quantum information in cat states realized earlier [13,14], our demonstrated QND parity tracking represents a significant step towards implementing an active system that extends the lifetime of a quantum bit.Besides their necessity in quantum error correction and quantum information, QND measurements play a central role in quantum mechanics. The application of an ideal projective QND measurement yields a result corresponding to an eigenvalue of the measured operator, and projects the system onto the eigenstate associated with that eigenvalue. Moreover, the measurement must leave the system in that state, so that subsequent measure- Experimental device and parity measurement protocol (P) of a photon state. (a) Bottom half of the device containing a transmon qubit located in a trench and coupled to two waveguide cavities. The low frequency cavity, with ωs/2π = 7.216 GHz and a lifetime of τ0 = 5...