Session P29: Focus Session: Superconducting Qubits: Multiple Qubits and Entanglement

Prospects for a prototype quantum processor based on three-dimensional superconducting cavities and qubits

Superconducting qubits embedded in three-dimensional waveguide resonators (recently pioneered by Paik, et al., arXiv:1105.4652) have shown excellent coherence properties and an ease of implementation that make them an enticing core component for small prototype quantum processors. The relatively large physical dimensions of the microwave modes of these 3D-cQED systems may lead one to discount their prospects for scaling. We argue that the larger characteristic dimensions, among others factors, in fact facilitate scaling for currently practicable prototype systems of $\sim $10 to 1,000 qubits. This emerges from significantly reduced fabrication complexity and costs, larger tolerances to parameter deviations, a more prevalent role for off-the-shelf components, and greater amenability to full-device electromagnetic simulation. At IBM we are working towards a modular quantum processor prototype based on 3D-cQED. Multi-qubit cavities, each implementing an artificial NMR molecule, are to be connected in an array by non-linear elements which double as tunable couplers between qubits in adjacent cavities and as single-shot readout circuitry. The resulting lattice of physical qubits provides a fabric on which surface code error correction can take place, implying a fault-tolerant threshold error rate for this architecture of $\sim $1{\%}. We describe recent experiments demonstrating a two-qubit gate with a two qubit/one cavity device and progress toward tunable coupling of qubits in adjacent cavities.   

Prime factoring using a Josephson phase-qubit architecture: $15 = 3*5$

We demonstrate a compiled version of Shor's algorithm using a quantum processor. The processor consists of ``off-the-shelf" components: qubits and resonators arranged in the ReZQu architecture. We have performed the algorithm for N=15 and the period r=2. The required two and three qubit entanglement is observed during the computation, which exemplifies the quantum nature of the algorithm.   

Building Transmon Qubits in the ReZQu Architecture

Transmon qubits are promising candidates for use in a superconducting quantum computer because of their long coherence times, but traditionally involve a difficult measurement scheme. By reading out each transmon through a phase qubit, we are able to take advantage of the single shot and multiplexed readout technologies already in use. This allows us to drop transmons into the ReZQu architecture. However, fabricating a transmon and phase qubit on the same chip comes with its own set of challenges. We present fabrication techniques and preliminary data as we move toward our next generation of qubits.   

High-fidelity CZ gate for the quantum Von Neumann architecture

The building block of a scalable superconducting quantum computer has recently been demonstrated [M. Mariantoni et al., Science 334, 61 (2011)]. This architecture consists of superconducting phase qubits capacitively coupled both to individual memory resonators as well as a common bus. In this work we investigate the fidelity of a CZ logic gate between a qubit and bus in a multi-qubit device. Our results show that it is possible to implement the CZ gate with 99.99\% intrinsic fidelity in 30ns with a simple two-parameter pulse profile (plus two Z rotations). An analytical error model is also developed to explain and extend this result.   

High-fidelity gates towards a scalable superconducting quantum processor

We experimentally explore the implementation of high-fidelity gates on multiple superconducting qubits coupled to multiple resonators. Having demonstrated all-microwave single and two qubit gates with fidelities $> 90\%$ on multi-qubit single-resonator systems, we expand the application to qubits across two resonators and investigate qubit coupling in this circuit. The coupled qubit-resonators are building blocks towards two-dimensional lattice networks for the application of surface code quantum error correction algorithms.   

Driving two-qubit entanglement with an enhanced ZZ interaction in circuit QED

The quantum bus architecture is fast becoming a popular approach for coupling superconducting qubits [1,2]. With two fixed-frequency qubits coupled by a resonator, it is possible to engineer the system's frequencies such that the qubits experience a strong ZZ interaction. This interaction can be used as a resource for creating entanglement when needed, but can also be suppressed at will using appropriate decoupling sequences. We will show measurements of a device where this ZZ interaction is enhanced by interactions with higher-levels of superconducting transmon qubits. To achieve high-fidelity control in this regime, we employ robust composite pulses and optimal control methods to decouple the two-qubit interaction during single-qubit operations. The resulting system serves as a testbed for adapting control techniques from liquid-state NMR to fixed-frequency superconducting qubits.\\[4pt] [1] L. DiCarlo {\it el al}. Nature {\bf 460}, 240-244 (2009).\\[0pt] [2] Matteo Mariantoni {\it et al}. Science {\bf 334}, 61-65 (2011).   

Controlling superconducting qubits in the presence of a strong, constant ZZ interaction

We look at the problem of optimal gate design in a system of two superconducting qubits coupled by a cavity. The system is designed to have a strong ``always on'' ZZ interaction, which is essential for two-qubit entangling gates, but presents a challenge for single qubit manipulation. Using pulse shaping ideas from NMR we are able to analytically derive single qubit gates that remove this unwanted coupling to 3rd order in the Magnus expansion, and applying DRAG corrections prevents leakage to higher oscillator levels. In the limit of strong cross-talk these pulses break down when the qubit being manipulated has a resonance close to the higher transition frequencies of the other, however we are still able to find high fidelity pulses numerically.   

Implementation of a Toffoli Gate with Superconducting Circuits

The Toffoli gate is an important primitive in many quantum circuits and quantum error correction schemes. Here we demonstrate the implementation of a Toffoli gate with three superconducting transmon qubits coupled to a microwave resonator [1]. Following Ralph \emph{et~al.}~[2] we used the third energy level of the transmon qubit to significantly reduce the number of elementary gates needed to implemente the Toffoli gate in comparison to approaches using two-level systems only. A similar scheme to realize a Toffoli-class gate has independently been devised on a system of three logical qubits encoded in the states of two qubits and a resonator [3]. Our gate fidelity evaluated by both full process tomography and Monte Carlo process certification is $68.5\pm0.5$\%. The results reinforce the potential of macroscopic superconducting qubits for implementation of complex quantum operations and point at the possibility to implement quantum error correction schemes~[4]. \newline [1] A. Fedorov \emph{et~al.}, arXiv:1108.3966. \newline [2] T.~C.~Ralph, K.~J.~Resch, A.~Gilchrist, Phys. Rev. A \textbf{75}, 022313 (2007).\newline [3] M. Mariantoni, \emph{et~al.} Science \textbf{334}, 61 (2011).\newline [4] M.~D. Reed, \emph{et~al.}, arXiv:1109.4948.   

Multiple photon effects in coupled anharmonic oscillators for circuit QED architectures

In recent years many superconducting qubits have emerged that are essentially weak anharmonic oscillators. When these systems are coupled, due to the weak anharmonicity the major source of error in this system is leakage. In this talk I will present a method for reducing leakage when implementing a two qubit gate. I will also show that due to this weak anharmonicity new multi-photon transitions emerge that can be used for implementing new types of two qubit gates.   

Observing Resonant Entanglement Dynamics in Circuit QED

We study the resonant interaction of up to three two-level systems and a single mode of an electromagnetic field in a circuit QED setup. Our investigation is focused on how a single excitation is dynamically shared in this fourpartite system. The underlying theory of the experiment is governed by the Tavis-Cummings-model, which on resonance predicts dynamics known as vacuum Rabi oscillations. The resonant situation has already been studied spectroscopically with three qubits [1] and time resolved measurements have been carried out in a tripartite system [2]. Here we are able to observe the coherent oscillations and their $\sqrt{N}$- enhancement by tracking the populations of all three qubits and the resonator. Full quantum state tomography is used to verify that the dynamics generates the maximally entangled 3-qubit W-state when the cavity state factorizes. The $\sqrt{N}$-speed-up offers the possibility to create W-states within a few ns with a fidelity of 75\%. We compare the resonant collective method to an approach, which achieves entanglement by sequentially tuning qubits into resonance with the cavity.\\[4pt] [1] J.~M.~Fink, Physical Review Letters \textbf{103}, 083601 (2009)\\[0pt] [2] F. Altomare, Nature Physics \textbf{6}, 777--781 (2010)   

Benchmarking a Teleportation Protocol realized in Circuit QED

Teleportation of a quantum state may be used for distributing entanglement between distant qubits in quantum communication and for realizing universal and fault-tolerant quantum computation. Here we demonstrate the implementation of a teleportation protocol, up to the single-shot measurement step, with superconducting qubits coupled to a microwave resonator [1]. Using full quantum state tomography and evaluating an entanglement witness, we show that the protocol generates a genuine tripartite entangled state of all three-qubits. Calculating the projection of the measured density matrix onto the basis states of two qubits allows us to reconstruct the teleported state. Repeating this procedure for a complete set of input states we find an average output state fidelity of 86\% for the teleported state.\newline [1] M.~Baur, A.~Fedorov, L.~Steffen, S.~Filipp, M.P.~da~Silva, and A.~Wallraff, arXiv:1107.4774.   

Characterization of a two-transmon processor with individual single-shot qubit readout

We report the characterization of a two-qubit processor implemented with two capacitively coupled tunable superconducting qubits of the transmon type, each qubit having its own non-destructive single-shot readout. The fixed capacitive coupling yields the $\sqrt{iSWAP}$ two-qubit gate for a suitable interaction time. We reconstruct by state tomography the coherent dynamics of the two-bit register as a function of the interaction time, observe a violation of the Bell inequality by 22 standard deviations after correcting readout errors, and measure by quantum process tomography a gate fidelity of 90\%.   

Demonstrating quantum speed-up in a superconducting two-qubit processor

We operate a superconducting quantum processor consisting of two tunable transmon qubits coupled by a swapping interaction, and equipped with non destructive single-shot readout of the two qubits [1]. With this processor, we run the Grover search algorithm among four objects and find that the correct answer is retrieved after a single run with a success probability between 0.52 and 0.67, significantly larger than the 0.25 achieved with a classical algorithm. This constitutes a proof-of-concept for the quantum speed-up of electrical quantum processors [2].\\[4pt] [1] arXiv:1109.6735v1 \\[0pt] [2] arXiv:1110.5170v1