Model for monitoring of a charge qubit using a radio-frequency quantum point contact including experimental imperfections

The extension of quantum trajectory theory to incorporate realistic imperfections in the measurement of solid-state qubits is important for quantum computation, particularly for the purposes of state preparation and error correction as well as for readout of computations. Previously this has been achieved for low-frequency (dc) weak measurements. In this paper we extend realistic quantum trajectory theory to include radio frequency (rf) weak measurements where a low-transparency quantum point contact (QPC), coupled to a charge qubit, is used to damp a classical oscillator circuit. The resulting realistic quantum trajectory equation must be solved numerically. We present an analytical result for the limit of large dissipation within the oscillator (relative to the QPC), where the oscillator slaves to the qubit. The rf+dc mode of operation is considered. Here the QPC is biased (dc) as well as subjected to a small-amplitude sinusoidal carrier signal (rf). The rf+dc QPC is shown to be a low-efficiency charge-qubit detector, which may nevertheless be higher than the dc-QPC (which is subject to 1/f noise).

[1]  Kurt Jacobs.  How to project qubits faster using quantum feedback , 2003 .

[2]  H. M. Wiseman,et al.  State and dynamical parameter estimation for open quantum systems , 2001 .

[3]  N. Gisin,et al.  Continuous quantum jumps and infinite-dimensional stochastic equations , 1991 .

[4]  J. Gambetta,et al.  Stochastic simulations of conditional states of partially observed systems, quantum and classical , 2005, quant-ph/0503241.

[5]  Kurt Jacobs,et al.  Quantum error correction for continuously detected errors with any number of error channels per qubit , 2004 .

[6]  Yoshiro Hirayama,et al.  Charge noise analysis of an AlGaAs/GaAs quantum dot using transmission-type radio-frequency single-electron transistor technique , 2000 .

[7]  Wiseman,et al.  Adaptive phase measurements of optical modes: Going beyond the marginal Q distribution. , 1995, Physical review letters.

[8]  B. E. Kane.  A silicon-based nuclear spin quantum computer , 1998, Nature.

[9]  Continuous quantum measurement: Inelastic tunneling and lack of current oscillations , 2003, cond-mat/0307727.

[10]  T. Eiles,et al.  Noise in the Coulomb blockade electrometer , 1992 .

[11]  Neil P. Oxtoby,et al.  Quantum trajectories for the realistic measurement of a solid-state charge qubit , 2005 .

[12]  Stefano Mancini,et al.  Bayesian feedback versus Markovian feedback in a two-level atom , 2002 .

[13]  R. Schoelkopf,et al.  The radio-frequency single-electron transistor (RF-SET): A fast and ultrasensitive electrometer , 1998, Science.

[14]  Büttiker,et al.  Scattering theory of current and intensity noise correlations in conductors and wave guides. , 1992, Physical review. B, Condensed matter.

[15]  Nonideal quantum detectors in Bayesian formalism , 2002, cond-mat/0211647.

[16]  John K. Stockton,et al.  Adaptive homodyne measurement of optical phase. , 2002, Physical review letters.

[17]  H. Mabuchi,et al.  Quantum trajectories for realistic detection , 2002 .

[18]  D A Williams,et al.  Charge-qubit operation of an isolated double quantum dot. , 2005, Physical review letters.

[19]  V. Privman,et al.  QUANTUM COMPUTATION IN QUANTUM-HALL SYSTEMS , 1997, quant-ph/9707017.

[20]  D. DiVincenzo,et al.  Quantum computation with quantum dots , 1997, cond-mat/9701055.

[21]  Milburn,et al.  Quantum theory of optical feedback via homodyne detection. , 1993, Physical review letters.

[22]  A. Gossard,et al.  Fast single-charge sensing with a rf quantum point contact , 2007, 0707.2946.

[23]  G. J. Milburn,et al.  Quantum error correction for continuously detected errors , 2003 .

[24]  H M Wiseman,et al.  Capture and release of a conditional state of a cavity QED system by quantum feedback. , 2002, Physical review letters.

[25]  Alexander N. Korotkov,et al.  Numerical analysis of radio-frequency single-electron transistor operation , 2004 .

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

[27]  D. Pozar.  Microwave Engineering , 1990 .

[28]  K. Jacobs,et al.  Rapid state-reduction of quantum systems using feedback control , 2006, 2006 Conference on Lasers and Electro-Optics and 2006 Quantum Electronics and Laser Science Conference.

[29]  Milburn,et al.  Quantum theory of field-quadrature measurements. , 1993, Physical review. A, Atomic, molecular, and optical physics.

[30]  H. M. Wiseman.  Quantum trajectories and quantum measurement theory , 1996 .

[31]  H. Cheong,et al.  Coherent manipulation of electronic States in a double quantum dot. , 2003, Physical review letters.

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

[33]  G. Milburn,et al.  Dynamics of a mesoscopic charge quantum bit under continuous quantum measurement , 2001, cond-mat/0103005.

[34]  Hei Wong,et al.  Low-frequency noise study in electron devices: review and update , 2003, Microelectron. Reliab..

[35]  H. M. Wiseman,et al.  Quantum measurement of coherent tunneling between quantum dots , 2001 .

[36]  Correlated quantum measurement of a solid-state qubit , 2000, cond-mat/0008003.

[37]  Graham,et al.  Linear stochastic wave equations for continuously measured quantum systems. , 1994, Physical review. A, Atomic, molecular, and optical physics.

[38]  H. Carmichael.  An open systems approach to quantum optics , 1993 .

[39]  P. Warszawski,et al.  Quantum trajectories for realistic photodetection: I. General formalism , 2002 .

[40]  Alexander N. Korotkov,et al.  Quantum feedback control of a solid-state qubit , 2002 .

[41]  D. D. Awschalom,et al.  Quantum information processing using quantum dot spins and cavity QED , 1999 .

[42]  D. Averin,et al.  Counting statistics and detector properties of quantum point contacts. , 2005, Physical review letters.

[43]  Toshiaki Hayashi,et al.  Impedance analysis of a radio-frequency single-electron transistor , 2002 .

[44]  R. Schoelkopf,et al.  Radio-frequency single-electron transistor: Toward the shot-noise limit , 2001 .

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

[46]  A. Korotkov.  Selective quantum evolution of a qubit state due to continuous measurement , 2000, cond-mat/0008461.

[47]  N. Oxtoby,et al.  Sensitivity and back action in charge qubit measurements by a strongly coupled single-electron transistor , 2006, cond-mat/0601035.

[48]  T. Duty,et al.  The single Cooper-pair box as a charge qubit , 2005 .

[49]  Nathan,et al.  Continuous quantum measurement of two coupled quantum dots using a point contact: A quantum trajectory approach , 2000, cond-mat/0006333.

[50]  K. Jacobs,et al.  FEEDBACK CONTROL OF QUANTUM SYSTEMS USING CONTINUOUS STATE ESTIMATION , 1999 .

[51]  Milburn,et al.  Interpretation of quantum jump and diffusion processes illustrated on the Bloch sphere. , 1993, Physical review. A, Atomic, molecular, and optical physics.

[52]  Gerard J. Milburn,et al.  Practical scheme for error control using feedback , 2004 .

[53]  Eli Yablonovitch,et al.  Electron-spin-resonance transistors for quantum computing in silicon-germanium heterostructures , 1999, quant-ph/9905096.

[54]  R J Schoelkopf,et al.  Radio-frequency single-electron transistor as readout device for qubits: charge sensitivity and backaction. , 2001, Physical review letters.

[55]  D. Williams,et al.  Radio-frequency point-contact electrometer , 2006, 0708.2473.