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...

Superconducting circuits have attracted growing interest in recent years as a promising candidate for fault-tolerant quantum information processing. Extensive efforts have always been taken to completely shield these circuits from external magnetic fields to protect the integrity of the superconductivity. Here we show vortices can improve the performance of superconducting qubits by reducing the lifetimes of detrimental single-electron-like excitations known as quasiparticles. Using a contactless injection technique with unprecedented dynamic range, we quantitatively distinguish between recombination and trapping mechanisms in controlling the dynamics of residual quasiparticle, and show quantized changes in quasiparticle trapping rate because of individual vortices. These results highlight the prominent role of quasiparticle trapping in future development of superconducting qubits, and provide a powerful characterization tool along the way.

Summary The article is a short opinionated review of the quantum treatment of electromagnetic circuits, with no pretension to exhaustiveness. This review, which is an updated and modernized version of a previous set of Les Houches School lecture notes, has three main parts. The first part describes how to construct a Hamiltonian for a general circuit, which can include dissipative elements. The second part describes the quantization of the circuit, with an emphasis on the quantum treatment of dissipation. The final part focuses on the Josephson nonlinear element and the main linear building blocks from which superconducting circuits are assembled. It also includes a brief review of the main types of superconducting artificial atoms, elementary multi‐level quantum systems made from basic circuit elements. Copyright © 2017 John Wiley & Sons, Ltd.

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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 state purity and effectively cools the dressed atom state to a low temperature.

As the energy relaxation time of superconducting qubits steadily improves, non-equilibrium quasiparticle excitations above the superconducting gap emerge as an increasingly relevant limit for qubit coherence. We measure fluctuations in the number of quasiparticle excitations by continuously monitoring the spontaneous quantum jumps between the states of a fluxonium qubit, in conditions where relaxation is dominated by quasiparticle loss. Resolution on the scale of a single quasiparticle is obtained by performing quantum non-demolition projective measurements within a time interval much shorter than T1, using a quantum limited amplifier (Josephson Parametric Converter). The quantum jumps statistics switches between the expected Poisson distribution and a non-Poissonian one, indicating large relative fluctuations in the quasiparticle population, on time scales varying from seconds to hours. This dynamics can be modified controllably by injecting quasiparticles or by seeding quasiparticle-trapping vortices by cooling down in magnetic field.A mesoscopic superconducting circuit, of typical size smaller than 1 mm 3 , cooled to a temperature well below the superconducting gap should be completely free of thermal quasiparticle (QP) excitations. However, in the last decade there has been growing experimental evidence that the QP density at low temperatures saturates to values orders of magnitude above the value expected at thermal equilibrium [1][2][3][4][5]. These non-equilibrium QP excitations limit the performance of a variety of superconducting devices, such as single-electron turnstiles [6], kinetic inductance [7, 8] and quantum capacitance [9] detectors, micro-coolers [10, 11], as well as Andreev bound state nano-systems [12,13]. Moreover, QP's are an important intrinsic decoherence mechanism for superconducting two level systems (qubits) [14][15][16][17][18][19]. In particular, a recent experiment performed on the fluxonium qubit showed energy relaxation times in excess of 1 ms, limited by QP's [20]. Surprisingly, the sources generating these QP excitations are not yet positively identified. The measurement of non-equilibrium QP dynamics at low temperatures could provide insight into their origin as well as an efficient tool to quantify QP suppression solutions.In this letter, we show that the quantum jumps[21] of a qubit whose lifetime is limited by QP tunneling, such as the fluxonium artificial atom, can serve as a sensitive probe of QP dynamics. A jump in the state of the qubit indicates an interaction of the qubit with a QP, and therefore fluctuations in the rate of quantum jumps are directly linked to changes in QP number. Tracking the state of the qubit in real time requires fast, single-shot projective measurement with minimal added noise, made possible by the advent of quantum-limited amplifiers [22][23][24]. In this work, we use a Josephson Parametric Converter (JPC) quantum limited amplifier [23,25] to monitor the state of our qubit with a resolution of 5 µs, two orders of magnitude faster than the qubi...

Parametric conversion and amplification based on three-wave mixing are powerful primitives for efficient quantum operations. For superconducting qubits, such operations can be realized with a quadrupole Josephson junction element, the Josephson Ring Modulator (JRM), which behaves as a loss-less three-wave mixer. However, combining multiple quadrupole elements is a difficult task so it would be advantageous to have a three-wave dipole element that could be tessellated for increased power handling and/or information throughput. Here, we present a dipole circuit element with third-order nonlinearity, which implements three-wave mixing. Experimental results for a non-degenerate amplifier based on the proposed third-order nonlinearity are reported.In quantum devices based on superconductors, Josephson junctions provide a nonlinear interaction between electromagnetic modes which is purely dispersive. However, because the Josephson potential is an even function of the superconducting phase difference ϕ, this nonlinearity is, to lowest order, of the form ϕ 4 . This Kerr nonlinearity is useful for engineering interactions between modes, but it imparts undesired frequency shifts. This problem is analogous to that generated by χ (3) media in nonlinear optics [1]. Such frequency shifts become especially problematic as the number of interacting modes, and therefore frequency crowding, increases. An alternative strategy is to use a minimal ϕ 3 nonlinearity for engineering the same useful interactions between modes while minimizing these unwanted Kerr frequency shifts.A form of this ϕ 3 nonlinearity has been realized with four Josephson junctions arranged in a ring threaded by DC magnetic flux. This device, called the Josephson ring modulator (JRM) [2,3], specifically provides a trilinear Hamiltonian term of the form ϕ x ϕ y ϕ z between three modes named X, Y , and Z. However, the JRM is a quadrupole element, i.e. it imposes a current and phase relation between four nodes of a circuit. Thus, a question naturally arises, would it be possible to engineer a a third-order ϕ 3 nonlinearity in a dipole device similar to the Josephson junction?An inherent advantage of such a dipole element is that it is more modular and easier to integrate into complex circuits. In particular, such an element can be tessellated, as with a Josephson junction [4], for improved power handling capabilities and information throughput. Furthermore, it can provide a three-wave coupling between a superconducting qubit and an oscillator.In this Letter, we report an experimental realization of a pure ϕ 3 nonlinear dipole element, demonstrating its performance in a non-degenerate parametric amplifier. Because this dispersive element is asymmetric in the transformation of ϕ → −ϕ, in contrast with the SQUID [5,6] Superconducting Nonlinear Asymmetric Inductive eLement (SNAIL). After the completion of our work, we became aware of a theoretical proposal for a similar element, given in Ref.9. Fig. 1a shows the circuit we propose to achieve cubic nonlinearity in a di...

Encoding quantum states in complex multiphoton fields can overcome loss during signal transmission in a quantum network. Transmitting quantum information encoded in this way requires that locally stored states can be converted to propagating fields. Here we experimentally show the controlled conversion of multiphoton quantum states, like "Schrödinger cat" states, from a microwave cavity quantum memory into propagating modes. By parametric conversion using the nonlinearity of a single Josephson junction, we can release the cavity state in ∼ 500 ns, about 3 orders of magnitude faster than its intrinsic lifetime. This 'catapult' faithfully converts arbitrary cavity fields to traveling signals with an estimated efficiency of > 90 %, enabling on-demand generation of complex itinerant quantum states. Importantly, the release process can be controlled precisely on fast time scales, allowing us to generate entanglement between the cavity and the traveling mode by partial conversion. Our system can serve as the backbone of a microwave quantum network, paving the way towards error-correctable distribution of quantum information and the transfer of highly non-classical states to hybrid quantum systems.A powerful way to tame complexity when scaling up a quantum system is to construct it as a network. Breaking up the whole into small, testable modules that are connected through well-defined communication channels reduces undesired crosstalk and minimizes the spreading of errors through the system. Therefore, quantum networks have been proposed for quantum information processing (QIP) [1] and it has been shown theoretically that there are favorable thresholds for quantum error correction for such modular architectures, even with noisy quantum communication channels [2]. Experiments with multiple platforms are currently underway to realize prototypes of quantum networks [3][4][5]. The key requirement hereby is the ability to interface quantum states stored and processed in network nodes with propagating states that connect the nodes.Quantum continuous variables (CV) allow versatile and robust encoding of quantum information in higherdimensional Hilbert spaces. For instance, encoding quantum bits in CV systems can provide the redundancy required to enable quantum error correction [6]. NonGaussian CV states that could be used as QIP-enabling resources have been created experimentally in the states of ion motion [7] and atomic spins [8,9], as well as optical [10,11] and microwave photons [12][13][14][15]. In particular, microwave cavities in superconducting circuits have recently further enabled the storage [16] and protection [17] of quantum information encoded in non-Gaussian oscillator states. Using these locally stored states as resources in an error-protected, network-based QIP architecture hinges on the ability to interface them with traveling signals (Fig. 1a). However, the controlled map- * wolfgang.pfaff@yale.edu ping of general multiphoton states between a CV quantum memory and traveling signals has so far remained an o...