QUROPE Quantum Information Processing and Communication in Europe

A. Physical approach and perspective

Quantum computation with superconducting Josephson junction (JJ) based circuits exploits the intrinsic coherence of the superconducting state, into which all electrons are condensed. The systems form effective two(multi)-level artifical atoms where quantum information is stored in different degrees of freedom: charge, flux or phase. The "old" distinction in terms of charge, flux, and phase qubits is however a bit outdated: all JJ-qubits are now closer to the phase regime than to the charge regime in order to defeat charge noise and achieve long coherence times. Systems are fabricated with thin film technology and operated at temperatures below 100 mK. Measurements are performed with integrated on-chip detectors. Coupling between qubits can be made strong, especially using microwave resonators and cavities - circuit/cavity quantum electrodynamics (cQED). This also provides opportunities for coupling widely different types of qubits in hybrid devices, inluding atoms, ions and impurity spins in quantum dots, crystals, and microtraps. The state of the art is described in [1-5], including comprehensive technical accounts in [4,5].

About 30 groups work on superconducting quantum bits in Europe, Japan, China and the USA. European experimental groups: Saclay, France (D. Esteve, D. Vion, P. Bertet); Delft, The Netherlands (J. Mooij, C.P.J.M. Harmans); Chalmers, Sweden (P. Delsing, C. Wilson); ETH Zürich, Switzerland (A. Wallraff); PTB, Germany (A. Zorin); Jena, Germany (E. Ilichev); KIT Karlsruhe, Germany (A. Ustinov); Grenoble, France (O. Buisson); HUT, Helsinki, Finland (S. Paraoanu); TUM Munich (R. Gross); and others. European theory groups: KIT Karlsruhe , Germany (G. Schön, A. Shnirman); SNS Pisa, Italy (R. Fazio); LMU Munich (F. Marquardt); Chalmers, Sweden (V. Shumeiko, G. Johansson, G. Wendin); Catania, Italy (G. Falci, E. Paladino); Basel, Switzerland (C. Bruder); Grenoble, France (F. Hekking); Toulouse, France (D. Shepelyansky); Bilbao, Spain (E. Solano, J. Siewert); and others.

B. State of the art

Referring to the seven DiVincenzo criteria [6], the state of the art for QIP with JJ-qubits can be described as follows:

1. Qubits: systems with 2-4 qubits (charge, flux and phase) have been fabricated and investigated. Recent hybrid JJ-qubits (transmon [7,8], fluxonium [9]) are showing great promise due to lower sensitivity to noise.
2. Initialization: this proceeds via relaxation into the ground state on a timescale of microseconds.
3. Universal gate operations: high fidelity single qubit operations are performed with microwave and DC pulses. Two qubit gate operations and entangling gates with moderate-to-good fidelity have been achived for all major types of qubits (transmon [8], flux [10], phase [11]). Violation of a Bell inequality has been demonstrated with phase qubits [12].
4. Readout: a variety of qubit readout schemes is available, including single-shot switching [10-12] and dispersive [13,14] readout. QND measurement has been demonstrated with dispersive readout methods [13,14]. Low cross-correlation, simultaneous individual readout of two coupled qubits has been achieved for phase [12] and flux [13] qubits.
5. Long coherence times: coherence times of 1-10 microseconds have been observed in transmon and flux qubits, and of about 200 ns in phase qubits [5]. The shortest time needed for basic 1- and 2-qubit quantum operation is a few nanoseconds.
6. Quantum interfaces for qubit interconversion: there are currently several demonstrations of coherent transfer between JJ-qubits and microwave resonators (both lumped circuits and microwave cavities) (see [1-14]), including systematic population of a harmonic oscillator with 0-10 photons in pure Fock states and in arbitrary superpositions [15]. Of great interest for microwave engineering is the development of rapidly tunable microwave resonators [16].
7. Quantum interfaces to flying qubits for optical communication: research is at an embryonic stage, and there are so far no experimental investigations. 

It should be emphasized that spectacular progress has been accomplished during the last few years (2010-2012) by Josephson qubit quantum processors. Without quoting all articles, a nine-quantum-element solid-state quantum processor has been implemented, and used to run a three-qubit compiled version of Shor's algorithm to factor the number 15, and successfully find the prime factors 48% of the time. A Toffoli gate has been implemented with three superconducting transmon qubits coupled to a microwave resonator, with a fidelity of 68.5%. A "quantum machine" has been demonstrated, with seven quantum elements: two superconducting qubits coupled through a quantum bus, two quantum memories, and two zeroing registers. This machine has been used to implement quantum Fourier transform, with 66% process fidelity, and the 3-qubit Toffoli-class OR phase gate, with 98\% phase fidelity. Other experiments involve the deterministic production of 3-qubit GHZ states with fidelity 88%, and a QND detection scheme that measures the number of photons inside a high-quality-factor microwave cavity on a chip.

Though this topic remains controversial, it may be time to quote also the Canadian company D-Wave, which has built devices of increasing scale based on inductively coupled superconducting flux qubits. Several recent experiments report interesting physics in this device, providing evidence of macroscopic tunneling [17] and quantum annealing [18] in cells of 8 qubits and over timescales that far exceed the individual qubit coherence time. More studies are needed to understand the capabilities of these devices as optimization processors.

C. Strengths and weaknesses

Strengths:

• High potential for scalable integrated technology;
• Strong coupling between qubits using microwave resonators and cavities;
• Flexible opportunities with different types of superconducting qubits;
• Mature background technology, 20 years of experience;
• Long history of pushing the limits of measurement towards quantum limits;
• Great potential for providing a platform for large scale integration of solid-state qubits and QIP devices;
• Driver of applications in solid-state quantum engineering;
• Low-temperature or superconducting technologies necessary for integration with solid state microtraps for hybrid systems with atom and ions, or cold atoms and molecules;
• Great potential for meeting the challenge of developing microwave-optical interfaces;

Weaknesses:

• Qubits manufactured, not natural, and therefore sensitive to imperfections;
• Coherence times presently limited by defects in tunnel barriers and substrates to the 1-10 microsecond range;
• Coherence times seem to be limited by relaxation. Ulltimate limits of achievable relaxation times not known;

D. Short-term goals (3-5 years)

• Realize high-fidelity universal two-qubit gates in the most promising types of qubits;
• Realize non-destructive, high-fidelity single shot readout of individual qubits in multi-qubit circuits;
• Improve fidelity of operation and readout;
• Investigate and eliminate main sources of decoherence;
• Develop junctions with lower 1/f noise;
• Realize fully controllable three-qubit clusters within a generally scalable architecture;
• Develop switchable coupling with large on/off ratio between qubits;
• Realize systems of multiple qubits of different types coupled through common harmonic oscillator buses - solid-state cavity QED;
• Demonstrate teleportation and qubit coding for quantum error correction;
• Make first experimental tests of quantum algorithms with 3-5 qubits.

E. Long-term goals (10 years and beyond)

• Develop multi-qubit circuits connecting several 5-6 qubit clusters (multi-core circuits);
• Improve fidelity to the level needed for large-scale application;
• Develop interfaces to microwave and optical transmission lines;
• Develop quantum interfaces between qubits with typical microwave frequencies and atoms with optical transitions;
• Develop interfaces for hybrid solutions to long term storage and communication;
• Demonstrate elementary quantum error correction, quantum feed-forward (pulse optimization) and quantum feedback.
• Simulation of simple quantum systems.

F. Key references

[1] Proceedings of Nobel Symposium 141: Qubits for Future Quantum Computers (ed. G. Johansson), Phys. Scr. T137 (2010).
[2] J. Clarke and F.K. Wilhelm: “Superconducting Qubits”, Nature Insight 453, 1031 (2008).
[3] R. J. Schoelkopf and S. M. Girvin, "Wiring up quantum systems", Nature 451, 664 (2008).
[4] G. Wendin and V.S. Shumeiko, "Quantum bits with Josephson junctions", Low Temp. Phys. 33, 724 (2007).
[5] J.M. Martinis, "Superconducting Phase Qubits", Quantum Information Processing 8, 81 (2009).
[6] http://qt.tn.tudelft.nl/~lieven/qip2007/QIP3_divincenzo_criteria.pdf [7] J.M. Fink, R. Bianchetti, M. Baur, M. Goeppl, L. Steffen, S. Filipp, P.J. Leek, A. Blais, and A. Wallraff: “Collective Qubit States and the Tavis-Cummings Model in Circuit QED”, Phys. Rev. Lett. 103, 083601 (2009).
[8] L. DiCarlo, J. M. Chow, J. M. Gambetta, L.S. Bishop, D. I. Schuster, J. Majer, A. Blais, L. Frunzio, S. M. Girvin, and R. J. Schoelkopf: “Demonstration of Two-Qubit Algorithms with a Superconducting Quantum Processor”, Nature 460, 240 (2009).
[9] V.E. Manucharyan et al., "Fluxonium: single Cooper pair circuit free of charge offsets", Science 326, 113-116 (2009).
[10] J.H. Plantenberg, P.C. de Groot, C.J.P.M. Harmans and J. E. Mooij, "Demonstration of controlled-NOT quantum gates on a pair of superconducting quantum bits", Nature 447, 14 (2007).
[11] R.C. Bialczak, M. Ansmann, M. Hofheinz, E. Lucero, M. Neeley, A. O'Connell, D. Sank, H. Wang, J. Wenner, M. Steffen, A. Cleland, J. Martinis, "Quantum Process Tomography of a Universal Entangling Gate Implemented with Josephson Phase Qubits", Nature Physics 6, 409–413 (2010).
[12] M. Ansmann, H. Wang, R.C. Bialczak, M.. Hofheinz, E. Lucero, M. Neeley, A. D. O'Connell, D. Sank, M. Weides, J. Wenner, A. N. Cleland and J..M. Martinis, "Violation of Bell's inequality in Josephson phase qubits", Nature 461, 504-506 (2009).
[13] P.C. de Groot, A.F. van Loo, J. Lisenfeld,2, R.N. Schouten, A. Lupascu, C.J.P.M Harmans, and J.E. Mooij, "Low-crosstalk bifurcation detectors for coupled flux qubits", submitted to Applied Physics Letters (2009).
[14] F. Mallet, F.R. Ong, A. Palacios-Laloy, F. Nguyen, P. Bertet, D. Viuon, and D. Esteve, "Single-shot qubit readout in circuit quantum electrodynamics" Nature Physics 5, 791 (2009).
[15] M. Hofheinz, H. Wang, M. Ansmann, R.C. Bialczak, E. Lucero, M. Neeley, A. D. O'Connell, D. Sank, J. Wenner, J.M. Martinis and A.N. Cleland, "Synthesizing arbitrary quantum states in a superconducting resonator", Nature 459, 546-549 (2009).
[16] M. Sandberg, C.M. Wilson, F. Persson, T. Bauch, G. Johansson, V. Shumeiko, T. Duty, and P. Delsing, "Tuning the field in a microwave resonator faster than the photon lifetime", Appl. Phys. Lett. 92, 203501 (2008).
[17]M. W. Johnson et al. , Nature 473, 194–198 (2011).
[18] S. Boixo, T. Albash, F. M. Spedalieri, N. Chancellor, and Daniel A. Lidar, arXiv:1212.1739.