Periodical modulation of longitudinal coupling strength for quantum non-demolition qubit readout
Method and circuit for reading a value {circumflex over (σ)} z stored in a quantum information unit (qubit) memory having a qubit frequency ω a , with a resonator defined by a resonator damping rate κ, a resonator frequency ω r , a resonator electromagnetic field characterized by â † and â, a longitudinal coupling strength g z , an output â out and a longitudinal coupling g z {circumflex over (σ)} z (â † +â). At a quantum non-demolition (QND) longitudinal modulator, periodically modulating the longitudinal coupling strength g z with a signal of amplitude {tilde over (g)} z at least three (3) times greater than the resonator damping rate κ and of frequency ω m with ω m +κ resonant with ω r , wherein the longitudinal coupling strength g z varies over time (t) in accordance with g z (t)= g z +{tilde over (g)} z cos(ω m t) with g z representing an average value of g z 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 .
1. A circuit quantum electrodynamics (circuit QED) implementation of a quantum information unit (qubit) memory having a qubit frequency ω a 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 ω r ;
a resonator electromagnetic field characterized by â † and â;
a longitudinal coupling strength g z ;
an output â out ;
a quantum non-demolition (QND) longitudinal coupling g z {circumflex over (σ)} z (â † +â); and
a modulator periodically modulating the longitudinal coupling strength g z with a signal of amplitude {tilde over (g)} z greater than or equal to the resonator damping rate κ and of frequency ω m with ω m ±κ resonant with ω r ±a correction factor, wherein the correction factor is smaller than |ω r /10| and the longitudinal coupling strength g z varies over time (t) in accordance with:
g z ( t )= g z +{tilde over (g)} z cos(ω m t ) with g z representing an average value of g z ; and
a homodyne detector for measuring the value {circumflex over (σ)} z of the qubit memory from a reading of the output â out .
2. The circuit QED implementation of claim 1 , wherein the correction factor is between 0 and |ω r /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 â out .
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 â out is reduced while noise is left to augment on one or more interrelated characteristics of the output â out .
6. The circuit QED implementation of claim 3 , wherein the average value of g z , g z =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 Φ x 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 Φ 0 , Josephson energy asymmetry of the transmon is below 0.02 and Φ x varies by ±0.05Φ 0 around Φ x =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 ω a 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 ω a , with a resonator defined by a resonator damping rate κ, a resonator frequency ω r , a resonator electromagnetic field characterized by â † and â, a longitudinal coupling strength g z , an output â out and a quantum non-demolition (QND) longitudinal coupling g z {circumflex over (σ)} z (â † +â), the method comprising:
at a modulator, periodically modulating the longitudinal coupling strength g z with a signal of amplitude {tilde over (g)} z greater than or equal to the resonator damping rate κ and of frequency ω m with ω m ±κ resonant with ω r ±a correction factor, wherein the correction factor is smaller than |ω r /10| and the longitudinal coupling strength g z varies over time (t) in accordance with:
g z ( t )= g z +{tilde over (g)} z cos(ω m t ) with g z representing an average value of g z ; and
at a homodyne detector, measuring the value {circumflex over (σ)} z of the qubit memory from a reading of the output â out .
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 â out is reduced while noise is left to augment on one or more interrelated characteristics of the output â out .
15. The method of claim 14 , wherein the average value of g z , g z =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 Φ x 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 Φ 0 , Josephson energy asymmetry of the transmon is below 0.02 and Φ x varies by ±0.050Φ 0 around Φ x =0.
18. The method of claim 16 , further comprising detuning the resonator from the qubit frequency ω a 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 Q 1 and the resonator R a .
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).