![Page 1: Quantum Computation using Circuit Cavity QEDcourses.washington.edu/bbbteach/576/CCQED.pdfCavity QED Optical CQED Microwave CQED Drive cavity with laser Monitor changes in transmission](https://reader035.vdocuments.mx/reader035/viewer/2022081522/5fb99feb53cbef235c1b0120/html5/thumbnails/1.jpg)
Quantum Computation using Circuit Cavity QED
Phys 576, Winter 2007.
Joaquín E. Drut
![Page 2: Quantum Computation using Circuit Cavity QEDcourses.washington.edu/bbbteach/576/CCQED.pdfCavity QED Optical CQED Microwave CQED Drive cavity with laser Monitor changes in transmission](https://reader035.vdocuments.mx/reader035/viewer/2022081522/5fb99feb53cbef235c1b0120/html5/thumbnails/2.jpg)
Outline
• Cavity QED: optical and microwave.
• Zero and large detuning
• Proposed architecture: TLRs & CPBs
• Qubit readout, control & entanglement
• Summary & epilogue
![Page 3: Quantum Computation using Circuit Cavity QEDcourses.washington.edu/bbbteach/576/CCQED.pdfCavity QED Optical CQED Microwave CQED Drive cavity with laser Monitor changes in transmission](https://reader035.vdocuments.mx/reader035/viewer/2022081522/5fb99feb53cbef235c1b0120/html5/thumbnails/3.jpg)
Cavity QED
Optical CQED
Microwave CQED
Drive cavity with laserMonitor changes in transmission due to atoms falling through cavity
Determine state of atoms after passingGet information about photons inside the cavity
Blais et al.PRA 69, 062320 (2004)
![Page 4: Quantum Computation using Circuit Cavity QEDcourses.washington.edu/bbbteach/576/CCQED.pdfCavity QED Optical CQED Microwave CQED Drive cavity with laser Monitor changes in transmission](https://reader035.vdocuments.mx/reader035/viewer/2022081522/5fb99feb53cbef235c1b0120/html5/thumbnails/4.jpg)
Cavity QED
Jaynes-Cummings Hamiltonian
Blais et al.PRA 69, 062320 (2004)
![Page 5: Quantum Computation using Circuit Cavity QEDcourses.washington.edu/bbbteach/576/CCQED.pdfCavity QED Optical CQED Microwave CQED Drive cavity with laser Monitor changes in transmission](https://reader035.vdocuments.mx/reader035/viewer/2022081522/5fb99feb53cbef235c1b0120/html5/thumbnails/5.jpg)
Jaynes-Cummings Hamiltonian
cavity frequency
atomictransitionfrequency
atom-cavity coupling
coupling tocontinuum
coupling toother decay
modes
![Page 6: Quantum Computation using Circuit Cavity QEDcourses.washington.edu/bbbteach/576/CCQED.pdfCavity QED Optical CQED Microwave CQED Drive cavity with laser Monitor changes in transmission](https://reader035.vdocuments.mx/reader035/viewer/2022081522/5fb99feb53cbef235c1b0120/html5/thumbnails/6.jpg)
SolutionEigenstates
Energies
Resonant &Non-resonant regimes
![Page 7: Quantum Computation using Circuit Cavity QEDcourses.washington.edu/bbbteach/576/CCQED.pdfCavity QED Optical CQED Microwave CQED Drive cavity with laser Monitor changes in transmission](https://reader035.vdocuments.mx/reader035/viewer/2022081522/5fb99feb53cbef235c1b0120/html5/thumbnails/7.jpg)
Zero detuning (resonance)Rabi frequency
Decay rate (width)
strong coupling :
Coupling
Transition dipole
Resolution of the states requires
![Page 8: Quantum Computation using Circuit Cavity QEDcourses.washington.edu/bbbteach/576/CCQED.pdfCavity QED Optical CQED Microwave CQED Drive cavity with laser Monitor changes in transmission](https://reader035.vdocuments.mx/reader035/viewer/2022081522/5fb99feb53cbef235c1b0120/html5/thumbnails/8.jpg)
Large detuning
Atom ‘modifies’ cavity frequency ! Qubit readout
![Page 9: Quantum Computation using Circuit Cavity QEDcourses.washington.edu/bbbteach/576/CCQED.pdfCavity QED Optical CQED Microwave CQED Drive cavity with laser Monitor changes in transmission](https://reader035.vdocuments.mx/reader035/viewer/2022081522/5fb99feb53cbef235c1b0120/html5/thumbnails/9.jpg)
Circuit implementation
Cavity: Transmission line resonator (TLR)
Atom: Cooper pair box (CPB)
![Page 10: Quantum Computation using Circuit Cavity QEDcourses.washington.edu/bbbteach/576/CCQED.pdfCavity QED Optical CQED Microwave CQED Drive cavity with laser Monitor changes in transmission](https://reader035.vdocuments.mx/reader035/viewer/2022081522/5fb99feb53cbef235c1b0120/html5/thumbnails/10.jpg)
Circuit implementation
Wallraff et al.Nature 431, 162 (2004)
![Page 11: Quantum Computation using Circuit Cavity QEDcourses.washington.edu/bbbteach/576/CCQED.pdfCavity QED Optical CQED Microwave CQED Drive cavity with laser Monitor changes in transmission](https://reader035.vdocuments.mx/reader035/viewer/2022081522/5fb99feb53cbef235c1b0120/html5/thumbnails/11.jpg)
Superconducting Island
The ‘atom’Josephson junction (x2)
Gate voltage
SC Island Hamiltonian
# Cooper pairs(only degree of freedom if
the gap is large enough)
total charge injected into the island by the
source
Charging energy Josephson energy
![Page 12: Quantum Computation using Circuit Cavity QEDcourses.washington.edu/bbbteach/576/CCQED.pdfCavity QED Optical CQED Microwave CQED Drive cavity with laser Monitor changes in transmission](https://reader035.vdocuments.mx/reader035/viewer/2022081522/5fb99feb53cbef235c1b0120/html5/thumbnails/12.jpg)
The ‘atom’
Advantage: large effective dipole moment, can be 10
times larger than in a Rydberg atom.
Effective HamiltonianCharge regime
One can show that the resonator modes are quantized just like the cavity modes of CQED.The whole TLR-CPB system is described effectively by the Jaynes-Cummings Hamiltonian.
![Page 13: Quantum Computation using Circuit Cavity QEDcourses.washington.edu/bbbteach/576/CCQED.pdfCavity QED Optical CQED Microwave CQED Drive cavity with laser Monitor changes in transmission](https://reader035.vdocuments.mx/reader035/viewer/2022081522/5fb99feb53cbef235c1b0120/html5/thumbnails/13.jpg)
Qubit readoutDrive the qubit-resonator system in the far-detuned regime, but close to the cavity resonance frequency.Measure amplitude and phase.Small shifts in the resonator frequency are sensitively measured as a phase shift.In this regime the mixing with the photon is minimized.
![Page 14: Quantum Computation using Circuit Cavity QEDcourses.washington.edu/bbbteach/576/CCQED.pdfCavity QED Optical CQED Microwave CQED Drive cavity with laser Monitor changes in transmission](https://reader035.vdocuments.mx/reader035/viewer/2022081522/5fb99feb53cbef235c1b0120/html5/thumbnails/14.jpg)
Qubit readoutThis measurement is the complement of the microwave CQED measurement, where the state of the cavity is inferred from the phase shift in the atomic beam.Most sensitive at charge degeneracy of the CPB,where dephasing is minimized.
![Page 15: Quantum Computation using Circuit Cavity QEDcourses.washington.edu/bbbteach/576/CCQED.pdfCavity QED Optical CQED Microwave CQED Drive cavity with laser Monitor changes in transmission](https://reader035.vdocuments.mx/reader035/viewer/2022081522/5fb99feb53cbef235c1b0120/html5/thumbnails/15.jpg)
Qubit control
Little entanglement with photon
High fidelity rotation
Drive the qubit-resonator system in the far-detuned regime, but close to the qubit resonance frequency.
Large detuning little dependence of the phase on the state of the qubit.
![Page 16: Quantum Computation using Circuit Cavity QEDcourses.washington.edu/bbbteach/576/CCQED.pdfCavity QED Optical CQED Microwave CQED Drive cavity with laser Monitor changes in transmission](https://reader035.vdocuments.mx/reader035/viewer/2022081522/5fb99feb53cbef235c1b0120/html5/thumbnails/16.jpg)
Qubit controlDetuning between resonator and drive
Small cavity photon number
Fast qubit response to drive
There is a speed limit set by the cavity-qubit detuning
If the drive is turned on or off faster than then the frequency spread of the drive may dephase the qubit
Δ Δ-l
![Page 17: Quantum Computation using Circuit Cavity QEDcourses.washington.edu/bbbteach/576/CCQED.pdfCavity QED Optical CQED Microwave CQED Drive cavity with laser Monitor changes in transmission](https://reader035.vdocuments.mx/reader035/viewer/2022081522/5fb99feb53cbef235c1b0120/html5/thumbnails/17.jpg)
Multiple qubits
It should be possible to place multiple qubits along the length of the TLR and entangle them together.
Two qubits coupled to and in resonance with each other but detuned from the cavity can provide a CNOT gate.
![Page 18: Quantum Computation using Circuit Cavity QEDcourses.washington.edu/bbbteach/576/CCQED.pdfCavity QED Optical CQED Microwave CQED Drive cavity with laser Monitor changes in transmission](https://reader035.vdocuments.mx/reader035/viewer/2022081522/5fb99feb53cbef235c1b0120/html5/thumbnails/18.jpg)
Summary & conclusionsIt is possible to construct a circuit implementation of cavity QED based on TLRs and CPBs, with many attractive features:
Strong coupling is achieved
Coherent superpositions of a single qubit state and a single photon can be generatedThe properties of the qubit can be determined in a transmission measurementFull in-situ control over the qubit parameters is achievedTwo-qubit entanglement over cm distances ‘should be possible’
![Page 19: Quantum Computation using Circuit Cavity QEDcourses.washington.edu/bbbteach/576/CCQED.pdfCavity QED Optical CQED Microwave CQED Drive cavity with laser Monitor changes in transmission](https://reader035.vdocuments.mx/reader035/viewer/2022081522/5fb99feb53cbef235c1b0120/html5/thumbnails/19.jpg)
Some numbers...