Comptes Rendus
Quantum trajectories of superconducting qubits
[Trajectoires quantiques de qubits supraconducteurs]
Comptes Rendus. Physique, Volume 17 (2016) no. 7, pp. 766-777.

Dans ce compte rendu, nous présentons des expériences récentes permettant d'observer l'évolution d'un qubit supraconducteur pendant une mesure. Nous couvrons de manière pégagogique le processus de mesure dans le cas où le qubit est couplé dispersivement à une cavité micro-ondes de manière à ce que son état soit encodé dans la phase d'un ton micro-onde sondant la cavité. Un enregistrement étalé dans le temps est utilisé pour reconstruire les trajectoires quantiques individuelles de l'état du qubit, et la précision de ces trajectoires est vérifiée par une tomographie d'état quantique. De plus, nous discutons les ensembles de trajectoires, l'évolution symmétrique par renversement du temps, les trajectoires à deux qubits et les applications potentielles en correction d'erreur quantique basée sur la mesure.

In this review, we discuss recent experiments that investigate how the quantum sate of a superconducting qubit evolves during measurement. We provide a pedagogical overview of the measurement process, when the qubit is dispersively coupled to a microwave frequency cavity, and the qubit state is encoded in the phase of a microwave tone that probes the cavity. A continuous measurement record is used to reconstruct the individual quantum trajectories of the qubit state, and quantum state tomography is performed to verify that the state has been tracked accurately. Furthermore, we discuss ensembles of trajectories, time-symmetric evolution, two-qubit trajectories, and potential applications in measurement-based quantum error correction.

Publié le :
DOI : 10.1016/j.crhy.2016.07.007
Keywords: Quantum measurement, Quantum information processing, Microwave quantum optics, Superconducting qubits, Parametric amplifiers
Mot clés : Mesure quantique, Processus d'information quantique, Optique quantique au régime micro-onde, Qubits supraconducteurs, Amplificateurs paramétriques

Steven J. Weber 1 ; Kater W. Murch 2 ; Mollie E. Kimchi-Schwartz 1 ; Nicolas Roch 3 ; Irfan Siddiqi 1

1 Quantum Nanoelectronics Laboratory, Department of Physics, University of California, Berkeley, CA 94720, USA
2 Department of Physics, Washington University, St. Louis, MO 63130, USA
3 CNRS and Université Grenoble Alpes, Institut Néel, 38042 Grenoble, France
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Steven J. Weber; Kater W. Murch; Mollie E. Kimchi-Schwartz; Nicolas Roch; Irfan Siddiqi. Quantum trajectories of superconducting qubits. Comptes Rendus. Physique, Volume 17 (2016) no. 7, pp. 766-777. doi : 10.1016/j.crhy.2016.07.007. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/j.crhy.2016.07.007/

[1] H.J. Carmichael An Open Systems Approach to Quantum Optics, Springer, Berlin, 1993

[2] C. Gardiner; P. Zoller Quantum Noise, Springer, 2004

[3] J. Dalibard; Y. Castin; K. Mølmer Wave-function approach to dissipative processes in quantum optics, Phys. Rev. Lett., Volume 68 (1992), pp. 580-583 | DOI

[4] C. Gardiner; A. Parkins; P. Zoller Wave-function quantum stochastic differential equations and quantum-jump simulation methods, Phys. Rev. A, Volume 46 (1992), pp. 4363-4381 | DOI

[5] R. Schack; T.A. Brun; I.C. Percival Quantum state diffusion, localization and computation, J. Phys. A, Volume 28 (1995), pp. 5401-5413

[6] H.M. Wiseman; G.J. Milburn Quantum Measurement and Control, Cambridge University Press, 2010

[7] T.A. Brun A simple model of quantum trajectories, Am. J. Phys., Volume 70 (2002), p. 7

[8] N. Gisin Quantum measurements and stochastic processes, Phys. Rev. Lett., Volume 52 (1984) no. 19, pp. 1657-1660 | DOI

[9] L. Diosi Quantum stochastic processes as models for state vector reduction, J. Phys. A, Math. Gen., Volume 21 (1988) no. 13, pp. 2885-2898 | DOI

[10] N. Gisin; I.C. Percival The quantum-state diffusion model applied to open systems, J. Phys. A, Math. Gen., Volume 25 (1992) no. 21, pp. 5677-5691 | DOI

[11] R.B. Griffiths Consistent histories and the interpretation of quantum mechanics, J. Stat. Phys., Volume 36 (1984) no. 1–2, pp. 219-272 | DOI

[12] W. Nagourney; J. Sandberg; H. Dehmelt Shelved optical electron amplifier: observation of quantum jumps, Phys. Rev. Lett., Volume 56 (1986) no. 26, pp. 2797-2799 | DOI

[13] T. Sauter; W. Neuhauser; R. Blatt; P. Toschek Observation of quantum jumps, Phys. Rev. Lett., Volume 57 (1986) no. 14, pp. 1696-1698 | DOI

[14] J. Bergquist; R. Hulet; W. Itano; D. Wineland Observation of quantum jumps in a single atom, Phys. Rev. Lett., Volume 57 (1986) no. 14, pp. 1699-1702 | DOI

[15] R. Vijay; D.H. Slichter; I. Siddiqi Observation of quantum jumps in a superconducting artificial atom, Phys. Rev. Lett., Volume 106 (2011) no. 11 | DOI

[16] C. Guerlin; J. Bernu; S. Deléglise; C. Sayrin; S. Gleyzes; S. Kuhr; M. Brune; J.-M. Raimond; S. Haroche Progressive field-state collapse and quantum non-demolition photon counting, Nature, Volume 448 (2007) no. 7156, pp. 889-893 | DOI

[17] C.J. Hood The atom-cavity microscope: single atoms bound in orbit by single photons, Science, Volume 287 (2000) no. 5457, pp. 1447-1453 | DOI

[18] A. Korotkov Continuous quantum measurement of a double dot, Phys. Rev. B, Volume 60 (1999) no. 8, pp. 5737-5742 | DOI

[19] H.-S. Goan; G. Milburn; H. Wiseman; H. Bi Sun Continuous quantum measurement of two coupled quantum dots using a point contact: a quantum trajectory approach, Phys. Rev. B, Volume 63 (2001) no. 12 | DOI

[20] E.V. Sukhorukov; A.N. Jordan; S. Gustavsson; R. Leturcq; T. Ihn; K. Ensslin Conditional statistics of electron transport in interacting nanoscale conductors, Nat. Phys., Volume 3 (2007) no. 4, pp. 243-247 | DOI

[21] J. Gambetta; A. Blais; M. Boissonneault; A.A. Houck; D.I. Schuster; S.M. Girvin Quantum trajectory approach to circuit QED: quantum jumps and the Zeno effect, Phys. Rev. A, At. Molec. Opt. Phys., Volume 77 (2008) no. 1 | DOI

[22] A.N. Korotkov Quantum Bayesian approach to circuit QED measurement, 2011 | arXiv

[23] M. Hatridge; S. Shankar; M. Mirrahimi; F. Schackert; K. Geerlings; T. Brecht; K.M. Sliwa; B. Abdo; L. Frunzio; S.M. Girvin; R.J. Schoelkopf; M.H. Devoret Quantum back-action of an individual variable-strength measurement, Science, Volume 339 (2013), pp. 178-181 | DOI

[24] P. Campagne-Ibarcq; L. Bretheau; E. Flurin; A. Auffèves; F. Mallet; B. Huard Observing interferences between past and future quantum states in resonance fluorescence, Phys. Rev. Lett., Volume 112 (2014) no. 18 | DOI

[25] K.W. Murch; S.J. Weber; C. Macklin; I. Siddiqi Observing single quantum trajectories of a superconducting quantum bit, Nature, Volume 502 (2013) no. 7470, pp. 211-214 | DOI

[26] S.J. Weber; A. Chantasri; J. Dressel; A.N. Jordan; K.W. Murch; I. Siddiqi Mapping the optimal route between two quantum states, Nature, Volume 511 (2014), pp. 570-573 | DOI

[27] N. Roch; M. Schwartz; F. Motzoi; C. Macklin; R. Vijay; A. Eddins; A. Korotkov; K. Whaley; M. Sarovar; I. Siddiqi Observation of measurement-induced entanglement and quantum trajectories of remote superconducting qubits, Phys. Rev. Lett., Volume 112 (2014) no. 17 | DOI

[28] D. Tan; S. Weber; I. Siddiqi; K. Mølmer; K.W. Murch Prediction and retrodiction for a continuously monitored superconducting qubit, 2014 | arXiv

[29] C. Sayrin; I. Dotsenko; X. Zhou; B. Peaudecerf; T. Rybarczyk; S. Gleyzes; P. Rouchon; M. Mirrahimi; H. Amini; M. Brune; J.-M. Raimond; S. Haroche Real-time quantum feedback prepares and stabilizes photon number states, Nature, Volume 477 (2011) no. 7362, pp. 73-77 | DOI

[30] R. Vijay; C. Macklin; D.H. Slichter; S.J. Weber; K.W. Murch; R. Naik; A.N. Korotkov; I. Siddiqi Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback, Nature, Volume 490 (2012) no. 7418, pp. 77-80 | DOI

[31] G. de Lange; D. Ristè; M. Tiggelman; C. Eichler; L. Tornberg; G. Johansson; A. Wallraff; R. Schouten; L. DiCarlo Reversing quantum trajectories with analog feedback, Phys. Rev. Lett., Volume 112 (2014) no. 8 | DOI

[32] J.P. Groen; D. Ristè; L. Tornberg; J. Cramer; P.C. De Groot; T. Picot; G. Johansson; L. Dicarlo Partial-measurement backaction and nonclassical weak values in a superconducting circuit, Phys. Rev. Lett., Volume 111 (2016) | DOI

[33] M.S. Blok; C. Bonato; M.L. Markham; D.J. Twitchen; V.V. Dobrovitski; R. Hanson Manipulating a qubit through the backaction of sequential partial measurements and real-time feedback, Nat. Phys., Volume 10 (2014) no. 3, pp. 189-193 | DOI

[34] J. Koch; T. Yu; J. Gambetta; A. Houck; D. Schuster; J. Majer; A. Blais; M. Devoret; S. Girvin; R. Schoelkopf Charge-insensitive qubit design derived from the Cooper pair box, Phys. Rev. A, Volume 76 (2007) no. 4 | DOI

[35] A. Megrant; C. Neill; R. Barends; B. Chiaro; Y. Chen; L. Feigl; J. Kelly; E. Lucero; M. Mariantoni; P.J.J. O'Malley; D. Sank; A. Vainsencher; J. Wenner; T.C. White; Y. Yin; J. Zhao; C.J. Palmstrom; J.M. Martinis; A.N. Cleland Planar superconducting resonators with internal quality factors above one million, Appl. Phys. Lett., Volume 100 (2012) no. 11, p. 113510 | DOI

[36] J.B. Chang; M.R. Vissers; A.D. Córcoles; M. Sandberg; J. Gao; D.W. Abraham; J.M. Chow; J.M. Gambetta; M. Beth Rothwell; G.A. Keefe; M. Steffen; D.P. Pappas Improved superconducting qubit coherence using titanium nitride, Appl. Phys. Lett., Volume 103 (2013) no. 1 | DOI

[37] H. Paik; D.I. Schuster; L.S. Bishop; G. Kirchmair; G. Catelani; A.P. Sears; B.R. Johnson; M.J. Reagor; L. Frunzio; L.I. Glazman; S.M. Girvin; M.H. Devoret; R.J. Schoelkopf Observation of high coherence in Josephson Junction qubits measured in a three-dimensional circuit QED architecture, Phys. Rev. Lett., Volume 107 (2011) no. 24 | DOI

[38] A. Blais; R.-S. Huang; A. Wallraff; S. Girvin; R. Schoelkopf Cavity quantum electrodynamics for superconducting electrical circuits: an architecture for quantum computation, Phys. Rev. A, Volume 69 (2004) no. 6 | DOI

[39] V.B. Braginsky; F.Y. Khalili Qunatum Measurement, Cambridge University Press, 1992

[40] N. Bergeal; F. Schackert; M. Metcalfe; R. Vijay; V.E. Manucharyan; L. Frunzio; D.E. Prober; R.J. Schoelkopf; S.M. Girvin; M.H. Devoret Phase-preserving amplification near the quantum limit with a Josephson ring modulator, Nature, Volume 465 (2010) no. 7294, pp. 64-68 | DOI

[41] C. Caves Quantum limits on noise in linear amplifiers, Phys. Rev. D, Volume 26 (1982) no. 8, pp. 1817-1839 | DOI

[42] M. Hatridge; R. Vijay; D.H. Slichter; J. Clarke; I. Siddiqi Dispersive magnetometry with a quantum limited SQUID parametric amplifier, Phys. Rev. B, Volume 83 (2011) no. 13 | DOI

[43] K. Jacobs; D. Steck A straightforward introduction to continuous quantum measurement, Contemp. Phys., Volume 47 (2006), p. 279

[44] A. Chantasri; J. Dressel; A.N. Jordan Action principle for continuous quantum measurement, Phys. Rev. A, Volume 88 (2013) no. 4 | DOI

[45] H.M. Wiseman Weak values, quantum trajectories, and the cavity-QED experiment on wave-particle correlation, Phys. Rev. A, Volume 65 (2002) | DOI

[46] S. Gammelmark; B. Julsgaard; K. Mølmer Past quantum states of a monitored system, Phys. Rev. Lett., Volume 111 (2013) | DOI

[47] M. Tsang Time-symmetric quantum theory of smoothing, Phys. Rev. Lett., Volume 102 (2009) | DOI

[48] M. Tsang Optimal waveform estimation for classical and quantum systems via time-symmetric smoothing, Phys. Rev. A, Volume 80 (2009) | DOI

[49] M. Tsang; H.M. Wiseman; C.M. Caves Fundamental quantum limit to waveform estimation, Phys. Rev. Lett., Volume 106 (2011) | DOI

[50] M.A. Armen; A.E. Miller; H. Mabuchi Spontaneous dressed-state polarization in the strong driving regime of cavity QED, Phys. Rev. Lett., Volume 103 (2009) | DOI

[51] T.A. Wheatley; D.W. Berry; H. Yonezawa; D. Nakane; H. Arao; D.T. Pope; T.C. Ralph; H.M. Wiseman; A. Furusawa; E.H. Huntington Adaptive optical phase estimation using time-symmetric quantum smoothing, Phys. Rev. Lett., Volume 104 (2010) | DOI

[52] T. Rybarczyk; S. Gerlich; B. Peaudecerf; M. Penasa; B. Julsgaard; K. Mølmer; S. Gleyzes; M. Brune; J.-M. Raimond; S. Haroche; I. Dotsenko Past quantum state analysis of the photon number evolution in a cavity, 2014 | arXiv

[53] N. Williams; A. Jordan Entanglement genesis under continuous parity measurement, Phys. Rev. A, Volume 78 (2008) no. 6

[54] A. Silberfarb; P. Jessen; I. Deutsch Quantum state reconstruction via continuous measurement, Phys. Rev. Lett., Volume 95 (2005) no. 3 | DOI

[55] A. Smith; C. Riofrío; B. Anderson; H. Sosa-Martinez; I. Deutsch; P. Jessen Quantum state tomography by continuous measurement and compressed sensing, Phys. Rev. A, Volume 87 (2013) no. 3 | DOI

[56] J.E. Johnson; C. Macklin; D.H. Slichter; R. Vijay; E.B. Weingarten; J. Clarke; I. Siddiqi Heralded state preparation in a superconducting qubit, Phys. Rev. Lett., Volume 109 (2012) no. 5 | DOI

[57] D. Ristè; C.C. Bultink; K.W. Lehnert; L. DiCarlo Feedback control of a solid-state qubit using high-fidelity projective measurement, Phys. Rev. Lett., Volume 109 (2012) no. 24 | DOI

[58] P. Campagne-Ibarcq; E. Flurin; N. Roch; D. Darson; P. Morfin; M. Mirrahimi; M.H. Devoret; F. Mallet; B. Huard Persistent control of a superconducting qubit by stroboscopic measurement feedback, Phys. Rev. X, Volume 3 (2013) no. 2 | DOI

[59] S. Bravyi; A. Kitaev Quantum codes on a lattice with boundary, 1998 | arXiv

[60] J.M. Chow; J.M. Gambetta; E. Magesan; D.W. Abraham; A.W. Cross; B.R. Johnson; N.A. Masluk; C.A. Ryan; J.A. Smolin; S.J. Srinivasan; M. Steffen Implementing a strand of a scalable fault-tolerant quantum computing fabric, Nat. Commun., Volume 5 (2014), p. 4015 | DOI

[61] R. Barends; J. Kelly; A. Megrant; A. Veitia; D. Sank; E. Jeffrey; T.C. White; J. Mutus; A.G. Fowler; B. Campbell; Y. Chen; Z. Chen; B. Chiaro; A. Dunsworth; C. Neill; P. O'Malley; P. Roushan; A. Vainsencher; J. Wenner; A.N. Korotkov; A.N. Cleland; J.M. Martinis Superconducting quantum circuits at the surface code threshold for fault tolerance, Nature, Volume 508 (2014) no. 7497, pp. 500-503 | DOI

[62] J. Kelly; R. Barends; A.G. Fowler; A. Megrant; E. Jeffrey; T.C. White; D. Sank; J.Y. Mutus; B. Campbell; Y. Chen; Z. Chen; B. Chiaro; A. Dunsworth; I.C. Hoi; C. Neill; P.J.J. O'Malley; C. Quintana; P. Roushan; A. Vainsencher; J. Wenner; A.N. Cleland; J.M. Martinis State preservation by repetitive error detection in a superconducting quantum circuit, 2014 | arXiv

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