Designing quantum memories with embedded control: photonic circuits for autonomous quantum error correction.

We propose an approach to quantum error correction based on coding and continuous syndrome readout via scattering of coherent probe fields, in which the usual steps of measurement and discrete restoration are replaced by direct physical processing of the probe beams and coherent feedback to the register qubits. Our approach is well matched to physical implementations that feature solid-state qubits embedded in planar electromagnetic circuits, providing an autonomous and "on-chip" quantum memory design requiring no external clocking or control logic.

[1]  Andrei Faraon,et al.  Generation and transfer of single photons on a photonic crystal chip. , 2007, Optics express.

[2]  K. Parthasarathy.  An Introduction to Quantum Stochastic Calculus , 1992 .

[3]  Hideo Mabuchi,et al.  Coherent-feedback quantum control with a dynamic compensator , 2008, 0803.2007.

[4]  M.R. James,et al.  $H^{\infty}$ Control of Linear Quantum Stochastic Systems , 2008, IEEE Transactions on Automatic Control.

[5]  Matthew R. James,et al.  An Introduction to Quantum Filtering , 2006, SIAM Journal of Control and Optimization.

[6]  Andrew J. Landahl,et al.  Continuous quantum error correction via quantum feedback control , 2002 .

[7]  Hideo Mabuchi,et al.  Cavity-QED models of switches for attojoule-scale nanophotonic logic , 2009, 0907.2720.

[8]  Ramon van Handel,et al.  Approximation and limit theorems for quantum stochastic models with unbounded coefficients , 2007, 0712.2276.

[9]  Robin L. Hudson,et al.  Quantum Ito's formula and stochastic evolutions , 1984 .

[10]  Jens Koch,et al.  Coupling superconducting qubits via a cavity bus , 2007, Nature.

[11]  Sze M. Tan,et al.  A computational toolbox for quantum and atomic optics , 1999 .

[12]  Matthew R. James,et al.  Quantum Dissipative Systems and Feedback Control Design by Interconnection , 2007, IEEE Transactions on Automatic Control.

[13]  Franco Fagnola,et al.  On quantum stochastic differential equations with unbounded coefficients , 1990 .

[14]  Matthew R. James,et al.  The Series Product and Its Application to Quantum Feedforward and Feedback Networks , 2007, IEEE Transactions on Automatic Control.

[15]  M. Markham,et al.  Ultralong spin coherence time in isotopically engineered diamond. , 2009, Nature materials.

[16]  Panos Aliferis,et al.  Subsystem fault tolerance with the Bacon-Shor code. , 2007, Physical review letters.

[17]  Charles Santori,et al.  Hybrid photonic crystal cavity and waveguide for coupling to diamond NV-centers. , 2009, Optics express.

[18]  Hideo Mabuchi,et al.  Physical model of continuous two-qubit parity measurement in a cavity-QED network , 2008, 0812.1246.

[19]  C. Gardiner,et al.  Quantum Noise: A Handbook of Markovian and Non-Markovian Quantum Stochastic Methods with Applications to Quantum Optics , 2004 .

[20]  D. Gottesman.  An Introduction to Quantum Error Correction and Fault-Tolerant Quantum Computation , 2009, 0904.2557.