Real-time quantum state estimation in circuit QED via the Bayesian approach

Using a circuit QED device, we present a theoretical study of real-time quantum state estimation via quantum Bayesian approach. Suitable conditions under which the Bayesian approach can accurately update the density matrix of the qubit are analyzed. We also consider the correlation between some basic and physically meaningful parameters of the circuit QED and the performance of the Bayesian approach. Our results advance the understanding of quantum Bayesian approach and pave the way to study quantum feedback control and adaptive control.

[1]  F. Nori,et al.  Hybrid quantum circuits: Superconducting circuits interacting with other quantum systems , 2012, 1204.2137.

[2]  Stephen Becker,et al.  Quantum state tomography via compressed sensing. , 2009, Physical review letters.

[3]  A. Jordan,et al.  Mapping the optimal route between two quantum states , 2014, Nature.

[4]  Franco Nori,et al.  Feedback control of Rabi oscillations in circuit QED , 2013 .

[5]  Steven T. Flammia,et al.  Quantum tomography via compressed sensing: error bounds, sample complexity and efficient estimators , 2012, 1205.2300.

[6]  R. J. Schoelkopf,et al.  Quantum Back-Action of an Individual Variable-Strength Measurement , 2013, Science.

[7]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[8]  Wei Feng,et al.  Exact quantum Bayesian rule for qubit measurements in circuit QED , 2015, Scientific Reports.

[9]  Pierre Rouchon,et al.  Quantum state tomography with noninstantaneous measurements, imperfections, and decoherence , 2015, 1510.01726.

[10]  A. N. Korotkov,et al.  Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback , 2012, Nature.

[11]  A. Korotkov.  Continuous quantum measurement of a double dot , 1999, cond-mat/9909039.

[12]  Xin-Qi Li,et al.  Quantum Bayesian rule for weak measurements of qubits in superconducting circuit QED , 2014, 1404.3870.

[13]  P. Bertet,et al.  Coherent dynamics of a flux qubit coupled to a harmonic oscillator , 2004, Nature.

[14]  S. Girvin,et al.  Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics , 2004, Nature.

[15]  J M Gambetta,et al.  Measurement-induced qubit state mixing in circuit QED from up-converted dephasing noise. , 2012, Physical review letters.

[16]  Hideo Mabuchi,et al.  Quantum feedback control and classical control theory , 1999, quant-ph/9912107.

[17]  Alexandre Blais,et al.  Quantum trajectory approach to circuit QED: Quantum jumps and the Zeno effect , 2007, 0709.4264.

[18]  G. Milburn,et al.  Quantum Measurement and Control , 2009 .

[19]  G. Chiribella,et al.  Optimal Quantum Tomography , 2009, IEEE Journal of Selected Topics in Quantum Electronics.

[20]  Franco Nori,et al.  Quantum feedback: theory, experiments, and applications , 2014, 1407.8536.

[21]  Alexandre Blais,et al.  Qubit-photon interactions in a cavity: Measurement-induced dephasing and number splitting , 2006 .

[22]  K J Resch,et al.  Experimental feedback control of quantum systems using weak measurements. , 2009, Physical review letters.

[23]  Robert L. Kosut,et al.  Quantum tomography protocols with positivity are compressed sensing protocols , 2015, npj Quantum Information.

[24]  Alexander N. Korotkov.  Quantum Bayesian approach to circuit QED measurement with moderate bandwidth , 2016 .

[25]  Wei Feng,et al.  Qubit state tomography in a superconducting circuit via weak measurements , 2016, 1606.04659.

[26]  S. Girvin,et al.  Cavity quantum electrodynamics for superconducting electrical circuits: An architecture for quantum computation , 2004, cond-mat/0402216.

[27]  W. Marsden.  I and J , 2012 .

[28]  Daoyi Dong,et al.  Quantum State Tomography via Linear Regression Estimation , 2013, Scientific Reports.