Two Qubits and a Cavity: Three's Company (original) (raw)
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Tripartite interactions between two phase qubits and a resonant cavity | NIST
Nature, 2010
Multipartite entanglement is essential for quantum computation 1 and communication 2-4 , and for fundamental tests of quantum mechanics 5 and precision measurements 6. It has been achieved with various forms of quantum bits (qubits), such as trapped ions 7,8 , photons 9 and atoms passing through microwave cavities 10. Quantum systems based on superconducting circuits, which are potentially more scalable, have been used to control pair-wise interactions of qubits 11-16 and spectroscopic evidence for three-particle entanglement was observed 17,18. Here, we report the demonstration of coherent interactions in the time domain for three directly coupled superconducting quantum systems, two phase qubits and one resonant cavity. We provide evidence for the deterministic evolution from a simple product state, through a tripartite W state, into a (bipartite) Bell state. The cavity can be thought of as a multiphoton register or an entanglement bus, and arbitrary preparation of multiphoton states in this cavity using one of the qubits 19 and subsequent interactions for entanglement distribution should allow for the deterministic creation of another class of entanglement, a Greenberger-Horne-Zeilinger state. With the development of quantum information science 1 , entanglement of multiparticle systems has become a resource for a new information technology. In particular, three-particle or tripartite entanglement allows for teleportation 2 , secret sharing 4 and dense coding 20 , with connections to cosmology 21. Over the past decade, the development of exquisite control over quantum systems has led to various demonstrations of tripartite entanglement 8-10. Genuine tripartite entanglement is delineated by two inequivalent classes of states 22 : Greenberger-Horne-Zeilinger and W, where the W state involves only a single photon shared amongst three systems. Using multipartite entanglement in a solid-state-qubit system has only recently received theoretical attention 23-25. Thus far in superconducting systems, bipartite entanglement has been verified by two-qubit quantum state tomography 13 and used to carry out a quantum algorithm 15. Spectroscopic evidence for three-particle entanglement was observed for two current-biased phase qubits coupled to a lumped element consisting of an inductor-capacitor circuit and a cavity as well as for transmon qubits 17,18. In the experiments described below, we first verified the spectroscopic signature of three coupled systems. Next, we demonstrated coherent interactions. Frequency detuning of the third system was used to verify the proper change in the time evolution of two versus three coupled systems. Finally, we describe a free-evolution process as a means of deterministically preparing arbitrary single-photon tripartite entangled states and a corresponding visualization LETTERS NATURE PHYSICS
Generation of three-qubit entangled states using superconducting phase qubits
2010
Entanglement is one of the key resources required for quantum computation[1], so experimentally creating and measuring entangled states is of crucial importance in the various physical implementations of a quantum computer . In superconducting qubits[3], two-qubit entangled states have been demonstrated and used to show violations of Bell's Inequality and to implement simple quantum algorithms . Unlike the two-qubit case, however, where all maximally-entangled two-qubit states are equivalent up to local changes of basis, three qubits can be entangled in two fundamentally different ways[6], typified by the states |GHZ = (|000 +|111 )/ √ 2 and |W = (|001 +|010 +|100 )/ √ 3. Here we demonstrate the operation of three coupled superconducting phase qubits[7] and use them to create and measure |GHZ and |W states 1 . The states are fully characterized using quantum state tomography [8] and are shown to satisfy entanglement witnesses [9], confirming that they are indeed examples of three-qubit entanglement and are not separable into mixtures of two-qubit entanglement. arXiv:1004.4246v2 [cond-mat.supr-con]
Entanglement of superconducting qubits via microwave fields: Classical and quantum regimes
Physical Review B, 2008
We study analytically and numerically the problem of two qubits with fixed coupling irradiated with quantum or classical fields. In the classical case, we derive an effective Hamiltonian and describe its entangling properties. We identify a coupling/decoupling switching protocol and we construct composite pulse sequences leading to a CNOT gate. In the quantum case, we show that qubit-qubit-photon multiparticle entanglement and maximally entangled two-qubit states can be obtained by driving the system at very low powers (one quanta of excitation). Our results can be applied to a variety of systems of two superconducting qubits coupled to resonators.
Continuous joint measurement and entanglement of qubits in remote cavities
Physical Review A, 2015
We present a first principles theoretical analysis of the entanglement of two superconducting qubits in spatially separated microwave cavities by a sequential (cascaded) probe of the two cavities with a coherent mode, that provides a full characterization of both the continuous measurement induced dynamics and the entanglement generation. We use the SLH formalism to derive the full quantum master equation for the coupled qubits and cavities system, within the rotating wave and dispersive approximations, and conditioned equations for the cavity fields. We then develop effective stochastic master equations for the dynamics of the qubit system in both a polaronic reference frame and a reduced representation within the laboratory frame. We compare simulations with and analyze tradeoffs between these two representations, including the onset of a non-Markovian regime for simulations in the reduced representation. We provide conditions for ensuring persistence of entanglement and show that using shaped pulses enables these conditions to be met at all times under general experimental conditions. The resulting entanglement is shown to be robust with respect to measurement imperfections and loss channels. We also study the effects of qubit driving and relaxation dynamics during a weak measurement, as a prelude to modeling measurement-based feedback control in this cascaded system.
Physical Review Letters, 2012
We report a system where fixed interactions between non-computational levels make bright the otherwise forbidden two-photon |00 → |11 transition. The system is formed by hand selection and assembly of two discrete component transmon-style superconducting qubits inside a rectangular microwave cavity. The application of a monochromatic drive tuned to this transition induces twophoton Rabi-like oscillations between the ground and doubly-excited states via the Bell basis. The system therefore allows all-microwave two-qubit universal control with the same techniques and hardware required for single qubit control. We report Ramsey-like and spin echo sequences with the generated Bell states, and measure a two-qubit gate fidelity of Fg = 90% (unconstrained) and 86% (maximum likelihood estimator).
Quasi-lattice chains and multipartite entanglement in a cavity
The mesoscopic scale of superconducting qubits makes their inter-spacings comparable to the scale of wavelength of a circuit cavity field to which they commonly couple. This comparability results in inhomogeneous coupling strengthes for each qubit and hence asynchronous Rabi excitation cycles among the qubits that form a quasi-lattice. We find that such inhomogeneous coupling benefits the formation of multi-photon resonances between the single-mode cavity field and the quasi-lattice. The multi-photon resonances lead, in turn, to the simultaneous generation of inequivalent |GHZ and |W types of multipartite entanglement states, which are not transformable to each other through local operations with classical communications. Applying the model on the 3-qubit quasilattice and using the entanglement measures of both concurrence and 3-tangle, we verify that the inhomogeneous coupling specifically promotes the generation of the totally inseparable |GHZ state.
Generating entanglement via measurement between two remote superconducting qubits
Bulletin of the American Physical Society, 2014
Measurement has traditionally been viewed as a means to restore classical behavior to a quantum system: a coherent superposition, once observed, transforms into a single classical state. However, it is possible to design a measurement that instead projects into an entangled state, thereby purifying, rather than destroying, quantum correlations. We use continuous measurement to generate entanglement between two superconducting qubits that are separated by more than a meter of cable, demonstrating that quantum information can be transferred over the metallic wires that comprise a low-loss channel for microwave photon propagation. We further generate a faithful, time-resolved record of single quantum trajectories. Studying the statistics of these trajectories and of the ensemble of measurements provides insight into the dynamics of measurement-induced entanglement in an extended quantum network.
Deterministic Entanglement of Photons in Two Superconducting Microwave Resonators
Physical Review Letters, 2011
Quantum entanglement, one of the defining features of quantum mechanics, has been demonstrated in a variety of nonlinear spin-like systems. Quantum entanglement in linear systems has proven significantly more challenging, as the intrinsic energy level degeneracy associated with linearity makes quantum control more difficult. Here we demonstrate the quantum entanglement of photon states in two independent linear microwave resonators, creating N -photon NOON states as a benchmark demonstration. We use a superconducting quantum circuit that includes Josephson qubits to control and measure the two resonators, and we completely characterize the entangled states with bipartite Wigner tomography. These results demonstrate a significant advance in the quantum control of linear resonators in superconducting circuits.