Session H48: Entanglement in Superconducting Circuits

Entanglement of remote transmon qubits by concurrent photon detection - Part 1

One proposed realization for a quantum computer is the modular architecture, which consists of error-corrected quantum memories that are connected via a quantum router. A fundamental requirement for this modular quantum computer is the ability to entangle arbitrary, distant qubits on demand. This can be realized in circuit QED using a protocol inspired by recent experiments based on trapped ions and nitrogen-vacancy centers. First, each qubit is entangled with a single cavity photon (Fock state n=1) using sideband pulses. On their way out of the cavity, the now flying photons interfere on a beam-splitter and are concurrently detected by a novel microwave photo-multiplier that employs a third qubit-cavity system. In this protocol, the presence of losses in the photon flight path only affect the success probability of creating an entangled state but not its fidelity. In this talk, we present the experimental realization of this protocol for entangling two transmon qubits, focusing on the implementation and optimization of the microwave photo-multiplier.   

Entanglement of remote transmon qubits by concurrent photon detection - Part 2

One proposed realization for a quantum computer is the modular architecture, which consists of error-corrected quantum memories that are connected via a quantum router. A fundamental requirement for this modular quantum computer is the ability to entangle arbitrary, distant qubits on demand. This can be realized in circuit QED using a protocol inspired by recent experiments based on trapped ions and nitrogen-vacancy centers. First, each qubit is entangled with a single cavity photon (Fock state n=1) using sideband pulses. On their way out of the cavity, the now flying photons interfere on a beam-splitter and are concurrently detected by a novel microwave photo-multiplier that employs a third qubit-cavity system. In this protocol, the presence of losses in the photon flight path only affect the success probability of creating an entangled state but not its fidelity. In this talk, we present experimental results for this protocol and discuss the factors influencing the success probability and the fidelity of the generated entangled states.   

Using a Superconducting Resonator with Frequency-Compensated Tunable Coupling to Transfer a Quantum State Deterministically and Directly

Deterministic direct quantum state transfer between devices on different chips requires the ability to transfer quantum states between traveling qubits and fixed logic qubits. Reflections must be minimized to avoid energy loss and phase interference; this requires tunable coupling to an inter-chip line while the two devices are at equal frequencies. To achieve this, we use a 6GHz superconducting coplanar resonator with tunable coupling to a 50 Ohm transmission line. We compensate for the resulting shift in resonator frequency by simultaneously tuning a second SQUID. We measure the device coherence and demonstrate the ability to release a single-frequency shaped pulse into the transmission line, efficiently capture a shaped pulse, and deterministically and directly transfer a quantum state.   

Controlled release of cavity states into propagating modes induced via a single qubit

Photonic states stored in long-lived cavities are a promising platform for scalable quantum computing and for the realization of quantum networks. An important aspect in such a cavity-based architecture will be the controlled conversion of stored photonic states into propagating ones. This will allow, for instance, quantum state transfer between remote cavities. We demonstrate the controlled release of quantum states from a microwave resonator with millisecond lifetime in a 3D circuit QED system. Dispersive coupling of the cavity to a transmon qubit allows us to enable a four-wave mixing process that transfers the stored state into a second resonator from which it can leave the system through a transmission line. This permits us to evacuate the cavity on time scales that are orders of magnitude faster than the intrinsic lifetime. This Q-switching process can in principle be fully coherent, making our system highly promising for quantum state transfer between nodes in a quantum network of high-Q cavities.   

Concurrent remote entanglement with continuous variables

A necessary ingredient for large scale quantum information processing is the ability to entangle distant qubits on demand. In the field of superconducting quantum information, this process can be achieved by entangling stationary superconducting qubits with flying coherent states of microwave light, which are then co-amplified by a Josephson Parametric Converter (JPC). The JPC also serves as a which-path information eraser, causing the probabilistic continuous measurement process to concurrently entangle the qubits. We discuss the sensitivity of the experiment to the loss of quantum information during the flight of the coherent states, as well as strategies to improve which-path information erasure and reduce information loss to the degree required for entanglement generation.   

Preparation of a narrowband, itinerant microwave qubit for quantum information transfer

Narrowband microwave-frequency signals are compatible with many quantum information processing technologies and can coherently transfer quantum information between devices. The creation of itinerant, microwave single photon states has been successfully demonstrated. Here, we show progress towards generating a narrowband, itinerant microwave qubit in a coherent superposition of zero and one Fock states. Specifically, we use the red-sideband transition of a transmon to map a superposition of qubit states onto a propagating microwave signal. This signal should have a bandwidth sufficiently narrow to be absorbed by a quantum-enabled electro-optic converter [1], potentially enabling the transfer of quantum information from a transmon qubit to the optical domain.   

Characterizing an itinerant microwave Fock state compatible with transfer to a macroscopic mechanical oscillator

Transferring propagating single-photon signals generated by a qubit to a mechanical oscillator offers a way to prepare non-classical motional states of a macroscopic object. In this concept, a highly coherent transmon qubit in a cavity is used to create single itinerant microwave photons. These photons can then be directed towards a tunable electromechanical circuit where they can be converted into single phonons. In this talk, we present measurements of itinerant single photons engineered to realize this concept. In particular, we: characterize their quantum state tomographically, demonstrate that they have sufficiently narrow bandwidth for capture by an electromechanical circuit, and measure the efficiency with which they travel between microwave cavities.   

Entangled Schrodinger cats in circuit QED: Experimental Architecture

The development of quantum information technology relies on creating and controling entanglement over an increasingly large Hilbert space. Superconducting cavities offer high-dimensional spaces for quantum states in a low-loss and hardware-efficient fashion, making it an ideal memory of quantum information and an important element towards fault-tolerant quantum computation. In this talk we present a cQED architecture that allows quantum control over the coherent state basis of two superconducting cavities with millisecond coherence. In particular, we show deterministic entanglement of coherent-state microwave fields in two superconducting cavities of the form: $\frac{1}{\sqrt 2 }\left( {\left| \right.\left. {\beta_{a} } \right\rangle \left| \right.\left. {\beta_{a} } \right\rangle \pm \left| - \right.\left. {\beta_{a} } \right\rangle \left| - \right.\left. {\beta_{a} } \right\rangle } \right)$. We engineer the capability to measure the joint photon number parity to achieve complete state tomography of the two-cavity state. Following widespread efforts of realizing ``Schrodinger's cat''-like mesoscopic superposition in various physical systems, this experiment demonstrates mesoscopic entanglement between two ``Schrodinger's cats''.   

Entangled Schrodinger cats in circuit QED: Joint Wigner Tomography

Creating and controlling entanglement of quantum states over large Hilbert space is an important element of quantum information processing. Using the cQED architecture consisting of two long-lived superconducting cavities dispersively coupled to a transmon qubit, we successfully created an entangled coherent-state microwave fields in two superconducting cavities. In this talk, we will present the full joint Wigner tomography of the state, measured using the method of joint photon number parity measurement introduced in the previous talk. Furthermore, we will show the redundant encoding and efficient read-out of two logical bits of information in such entangled state and hence demonstrating that the entangled ``Schrodinger cats'' is a viable candidate as an error-correctable quantum memory as well as a valuable platform for implementation of two-qubit logical operations.   

Generating entanglement via symmetry-selective bath engineering in superconducting qubits

Bath engineering, which utilizes coupling to lossy modes in a quantum system to generate non-trivial steady states, is a potential alternative to gate- and measurement-based quantum science. In this talk, we discuss autonomous stabilization of entanglement between two superconducting transmon qubits in a symmetry-selective manner. Our experiments are implemented using two 3D transmons housed in separate copper cavities. The cavities are coupled via an aperture, and hybridize into nondegenerate symmetric and antisymmetric bath modes. We utilize the engineered symmetries of the dissipative environment to stabilize a target Bell state $\frac{1}{\sqrt{2}}\left(|ge\rangle \pm |eg\rangle\right)$ in the qubit sector; we further demonstrate suppression of the Bell state of opposite symmetry due to parity selection rules. This implementation is resource-efficient, achieves a steady-state fidelity $\mathcal{F} = 0.70$, and is scalable to multiple qubits. http://arxiv.org/abs/1511.00702   

Multimode Entanglement Generation in a Parametric Superconducting Cavity

Parametric microwave resonators implemented with superconducting circuits have become increasingly important in various application within quantum information processing. For example, quantum-limited parametric amplifiers based on these devices have now become commonplace as first-stage amplifiers for qubit experiments. Here we study the generation of multimode entangled states of propagating microwave photons, which can be used a resource in quantum computing and communication applications. We use a CPW resonator with a low fundamental resonance frequency that than has a number of modes in the common frequency band of 4-12 GHz. These modes are all parametrically coupled by a single SQUID that terminates the resonator. When parametrically pumping the system at the sum of two mode frequencies, we observe parametric downconversion and two-mode squeezing. By pumping at the difference frequency, we observe a beamsplitter-like mode conversion. By using multiple pump tones that combine these different processes, theory predicts we can construct multimode entangled states with a well-controlled entanglement structure, e.g., cluster states. Preliminary measurements will be presented.   

Simultaneous measurement of non-commuting observables in circuit QED: Theory

We describe the theory of a novel technique for simultaneously and continuously measuring a pair of non-commuting qubit observables, which has until now not been realized experimentally. Our proposed experimental platform consists of a qubit dispersively coupled to two linear cavity modes. Driving the qubit on resonance realizes an effective two-level system with energy splitting given by the Rabi frequency. Non-commuting measurements are performed on this system by application of sideband tones detuned from the cavity resonance frequencies by the Rabi frequency. We show that this realizes cooling and back-action free measurements constituting destructive and QND measurements, respectively, along an arbitrary axis of the Bloch sphere. Simultaneous application of a distinct pair of measurements may then be achieved by choosing a different axis for each cavity mode. We show that existing high quantum efficiency homodyne measurement techniques will enable the reconstruction of quantum trajectories of the qubit. Finally, we describe methods for characterizing the system's dynamics and verifying that the scheme does enable access to incommensurate, competing degrees of freedom.   

Simultaneous measurement of non-commuting observables in circuit QED: Experiment

The existence of incompatible measurements lies at the heart of numerous fundamental concepts in quantum mechanics, such as entanglement, contextuality and measurement-disturbance tradeoffs. We implement a novel technique for simultaneously and continuously measuring a pair of non-commuting observables in a circuit-QED architecture, which features a transmon qubit coupled to two modes of an electromagnetic cavity. By driving the transmon on resonance, we form an effective, low-frequency two-level system on which we perform the non-commuting measurements. To this end, we use microwave tones near the cavity's resonances to implement cooling and backaction-evading measurements familiar from optomechanics. Control of the relative amplitude and phase of these sideband tones enables qubit state measurement along an arbitrary axis of the Bloch sphere. We apply this technique to both modes of the cavity simultaneously, with distinct axes chosen for each mode. This realizes a continuous and simultaneous measurement of two non-commuting observables. We use high quantum-efficiency parametric amplifiers to track the resulting quantum trajectories of the qubit, enabling a measurement of the mutual disturbance of the two observables.   

Optimized entanglement purification schemes for modular based quantum computers

The choice of entanglement purification scheme strongly depends on the fidelities of quantum gates and measurements, as well as the imperfection of initial entanglement. For instance, the purification scheme optimal at low gate fidelities may not necessarily be the optimal scheme at higher gate fidelities. We employ an evolutionary algorithm that efficiently optimizes the entanglement purification circuit for given system parameters. Such optimized purification schemes will boost the performance of entanglement purification, and consequently enhance the fidelity of teleportation-based non-local coupling gates, which is an indispensible building block for modular-based quantum computers. In addition, we study how these optimized purification schemes affect the resource overhead caused by error correction in modular based quantum computers.