Method and circuit for reading a value {circumflex over (σ)}z stored in a quantum information unit (qubit) memory having a qubit frequency ωa, with a resonator defined by a resonator damping rate κ, a resonator frequency ωr, a resonator electromagnetic field characterized by â† and â, a longitudinal coupling strength gz, an output âout and a longitudinal coupling gz{circumflex over (σ)}z(â†+â). At a quantum non-demolition (QND) longitudinal modulator, periodically modulating the longitudinal coupling strength gz with a signal of amplitude {tilde over (g)}z at least three (3) times greater than the resonator damping rate κ and of frequency ωm with ωm+κ resonant with ωr, wherein the longitudinal coupling strength gz varies over time (t) in accordance with gz(t)=gz+{tilde over (g)}z cos(ωmt) with gz representing an average value of gz and at a QND homodyne detector, measuring the value {circumflex over (σ)}z of the qubit memory from a phase reading of the output {circumflex over (σ)}out.
Please help me write a proper abstract based on the patent claims. CLAIM: 1. A circuit quantum electrodynamics (circuit QED) implementation of a quantum information unit (qubit) memory having a qubit frequency ωa and holding a value {circumflex over (σ)}z, the circuit QED implementation comprising: a resonator defined by: a resonator damping rate κ; a resonator frequency ωr; a resonator electromagnetic field characterized by â† and â; a longitudinal coupling strength gz; an output âout; a quantum non-demolition (QND) longitudinal coupling gz{circumflex over (σ)}z(â†+â); and a modulator periodically modulating the longitudinal coupling strength gz with a signal of amplitude {tilde over (g)}z greater than or equal to the resonator damping rate κ and of frequency ωm with ωm±κ resonant with ωr±a correction factor, wherein the correction factor is smaller than |ωr/10| and the longitudinal coupling strength gz varies over time (t) in accordance with: gz(t)=gz+{tilde over (g)}z cos(ωmt) with gz representing an average value of gz; and a homodyne detector for measuring the value {circumflex over (σ)}z of the qubit memory from a reading of the output âout. 2. The circuit QED implementation of claim 1, wherein the correction factor is between 0 and |ωr/100|. 3. The circuit QED implementation of claim 1, the homodyne detector is for measuring the value {circumflex over (σ)}z of the qubit memory from a phase reading of the output âout. 4. The circuit QED implementation of claim 1, wherein the signal amplitude {tilde over (g)}z is at least three (3) times greater than the resonator damping rate κ or wherein the signal amplitude {tilde over (g)}z is at least ten (10) times greater than the resonator damping rate κ. 5. The circuit QED implementation of claim 1, further comprising a signal injector providing a single-mode squeezed input on the resonator such that noise on the phase reading from the output âout is reduced while noise is left to augment on one or more interrelated characteristics of the output âout. 6. The circuit QED implementation of claim 3, wherein the average value of gz, gz=0 and the single-mode squeezed input is QND. 7. The circuit QED implementation of claim 1, wherein the qubit memory is a transmon comprising two Josephson junctions with substantially equivalent capacitive values and the longitudinal modulator comprises an inductor-capacitor (LC) oscillator with a phase drop δ across a coupling inductance placed between the two Josephson junctions, the longitudinal coupling resulting from mutual inductance between the oscillator and the transmon, the oscillator varying a flux Φx in the transmon. 8. The circuit QED implementation of claim 7, wherein the transmon has a flux sweet spot at integer values of a magnetic flux quantum Φ0, Josephson energy asymmetry of the transmon is below 0.02 and Φx varies by ±0.05Φ0 around Φx=0. 9. The circuit QED implementation of claim 7, wherein a 3-Wave mixing Josephson dipole element is used to couple the qubit and the resonator. 10. The circuit QED implementation of claim 6, wherein the resonator is detuned from the qubit frequency ωa by |Δ|≧{tilde over (g)}z. 11. The circuit QED implementation of claim 6, wherein the oscillator inductance is provided by an array of Josephson junctions or by one or more Superconducting Quantum Interference Device (SQUID). 12. A method for reading a value {circumflex over (σ)}z stored in a quantum information unit (qubit) memory having a qubit frequency ωa, with a resonator defined by a resonator damping rate κ, a resonator frequency ωr, a resonator electromagnetic field characterized by â† and â, a longitudinal coupling strength gz, an output âout and a quantum non-demolition (QND) longitudinal coupling gz{circumflex over (σ)}z(â†+â), the method comprising: at a modulator, periodically modulating the longitudinal coupling strength gz with a signal of amplitude {tilde over (g)}z greater than or equal to the resonator damping rate κ and of frequency ωm with ωm±κ resonant with ωr±a correction factor, wherein the correction factor is smaller than |ωr/10| and the longitudinal coupling strength gz varies over time (t) in accordance with: gz(t)=gz+{tilde over (g)}z cos(ωmt) with gz representing an average value of gz; and at a homodyne detector, measuring the value {circumflex over (σ)}z of the qubit memory from a reading of the output âout. 13. The method of claim 12, wherein the signal amplitude {tilde over (g)}z is at least three (3) times greater than the resonator damping rate κ or wherein the signal amplitude {tilde over (g)}z is at least ten (10) times greater than the resonator damping rate κ. 14. The method of claim 12, further comprising, from a signal injector, providing a single-mode squeezed input on the resonator such that noise on the phase reading from the output âout is reduced while noise is left to augment on one or more interrelated characteristics of the output âout. 15. The method of claim 14, wherein the average value of gz, gz=0 and the single-mode squeezed input is QND. 16. The method of claim 12, wherein the qubit memory is a transmon comprising two Josephson junctions with substantially equivalent capacitive values and the longitudinal modulator comprises an inductor-capacitor (LC) oscillator with a phase drop δ across a coupling inductance placed between the two Josephson junctions, the longitudinal coupling resulting from mutual inductance between the oscillator and the transmon, the oscillator varying a flux Φx in the transmon. 17. The method of claim 16, wherein the transmon has a flux sweet spot at integer values of a magnetic flux quantum Φ0, Josephson energy asymmetry of the transmon is below 0.02 and Φx varies by ±0.050Φ0 around Φx=0. 18. The method of claim 16, further comprising detuning the resonator from the qubit frequency ωa by |Δ|≧{tilde over (g)}z. 19. The method of claim 16, wherein a 3-Wave mixing Josephson dipole element is used to couple the qubit Q1 and the resonator Ra. 20. The method of claim 16, wherein the oscillator inductance is provided by an array of Josephson junctions or wherein the oscillator inductance is provided by one or more Superconducting Quantum Interference Device (SQUID).