Circuit Quantum Circuit Quantum ElectrodynamicsElectrodynamics
Mark David JenkinsMark David Jenkins
““Martes cúantico”, February 25Martes cúantico”, February 25thth, 2014, 2014
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Introduction
● Theory details
– “Cavity quantum electrodynamics for superconducting electrical circuits: An architecture for quantum computation”, A. Blais, R.-S. Huang, A. Wallraff, S.M. Girvin and R.J. Shoelkopf, Physical Review A 69, 062320 (2004)
● Strong coupling experiment
– “Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics”, A. Wallraff, D.I. Schuster, A. Blais, L. Frunzio, R.-S Huang, J. Majer, S. Kumar, S.M. Girvin and R.J. Schoelkopf, Nature 431, p162 (2004)
● General review:
– “Wiring up quantum systems”, R.J. Schoelkopf and S.M. Girvin, Nature 451, p644 (2008)
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Introduction
● Objective:– Quantum Information processing
– Combine quantum mechanics and computers● Superposition and entanglement lead to a kind of
parallel processing● Allows for increased computational power
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Introduction
● Challenges:– Bits must be replaced with qubits
● Quantum 2 level systems
– Mechanism to manipulate qubits● One-qubit operations● Quantum logic gates● Quantum bus
– Reduce decoherence● Quantum states are extremely fragile● Competes with ease of manipulation
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Introduction
● Physical implementations for Qubits– “Natural” candidates
● Atoms, ions, nuclei, spins
– “Synthetic” candidates● Quantum dots● Superconducting circuits
– Voltages and currents exhibit quantum behaviour– Fabricated using techniques from conventional electronics
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Introduction
● The main means to interact with any of these systems is through electromagnetic radiation– Photons are naturally quantum objects
– Can be transmitted over large distances without being lost
● Cavity QED – Prototype of quantum light-matter interaction
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Cavity QED
● Simple case:– Single atom with two energy levels coupled to a
single mode of the EM field● Can be coupled to the electric or magnetic field
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Cavity QED● Resonator / Cavity = Harmonic Osillator
● Quantum equivalent
● Two level system
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Cavity QED
● Jaynes-Cummings Hamiltonian
Cavity Atom Interaction Losses
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Cavity QED
● Vacuum Rabi frequency ( )– Strength of the interaction
– System oscillates between and
– Given by (or )
● Resonance frequencies – Detuning
● Damping– Loss of photons from the cavity ( )
– Decay into undesired modes ( )
● Strong coupling regime -– Quantum information can be exchanged from atom to photon
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Cavity QED
● Solving in absence of damping:
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Cavity QED
● Solving in absence of damping:
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Cavity QED
● Challenge: Maximize g while minimizing ● Theoretical limit (electric coupling)
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Circuit QED
● Circuit QED = Cavity QED on a chip– Cavity is replaced with superconducting coplanar
waveguide resonator (1D cavity)
– Atom is replaced with superconducting qubit
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CPWG resonator
● Relevant parameters:–
– Length ( )
– Dielectric constants
● Easy to fabricate– In a single plane– Standard lithographic
techniques
● Q factors of up to 106
● Microwave frequencies (GHz)
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CPWG resonator
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Superconducting qubits
● Based on Josephson Junctions– Nonlinear inductor – Harmonic oscillator
● Types:– Cooper pair box (d)
● Couples to E field
– Flux qubit (e)● Couples to B field
– Phase qubit (f)
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Superconducting qubits
● Cooper pair box ● Basic hamiltonian:
– Electric energy– Josephson energy
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Circuit QED
● Combined system reduces (under good approximations) to the Jaynes-Cummings hamiltonian.
● At the “charge degeneracy point” ( ):
● At other biases these values are modulated
● Typical losses are
● Number of operations
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Circuit QED
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Circuit QED
● Zero detuning– Transmission at
single photon level
–
–
–
–
– Non-linear effects
● Large detuning– Lifetime enhancement
● From 1 μs to 64 μs
– QND readout
– Coherent control
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Dispersive QND readout
● Large detuning● Cavity frequency is pulled by
● In theses cases, the probability of real transitions is small
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Dispersive QND readout
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Dispersive QND readout
● Driving the cavity induces some dephasing and coherent mixing– Calculations for dephasing yield
– Quantum limit is not reached ( )● Non adiabatic coupling● Reflected wave contains missing information
● Coherent mixing– for given parameters
– Reversible
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Coherent control
● Irradiation at:– Resonator frequency is a measurement
– Qubit frequency is a rotation
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Coherent control
● With given parameters:
● Low photon population– “Virtually populated”– Fast response
● 1 qubit gate
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Quantum bus
● It is possible to place several qubits along the resonator at the nodes of the electric field
● The resonator acts as a quantum bus– Hamiltonian has terms
– Allows entanglement of the different qubits
– operation● 1200 operations with given parameters
– Possible 2 qubit readout● Different detunings on each allows 4 different cavity
pulls
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Strong coupling experiment● Device:
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Strong coupling experiment● Measurement scheme
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Strong coupling experiment● Qubit parameter determination
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Strong coupling experiment● Vacuum rabi splitting
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Further experiments
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Other quantum bits?
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Stronger couplings?
● Magnetic systems have generally weaker couplings but better coherence– Ensambles can be used to achieve strong
coupling● Done with NV centers
– Coupling can be enhanced by moving closer to the currents
● Superconductors have superficial currents and can allow thinner wires
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Stronger couplings?