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Published byNoreen Holt Modified over 9 years ago
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Quantum Devices (or, How to Build Your Own Quantum Computer)
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Pop Quiz: A) A single mode of electromagnetic radiation B) A cavity quality factor determined by the reflectance of the cavity walls C) An omnipotent being that likes to cause havoc with interplanetary explorers Question 1: What is Q?
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Pop Quiz: A) A quantum state that can be reliably reproduced with low variability B) The physical state of superposition shared by photons in a wavepacket C) A trust fund Question 2: What is a fiducial state?
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Pop Quiz: A) Two partially silvered mirrors that bounce photons back and forth, forcing them to interact with atoms B) A way to trap half integer spin particles, known as fermions C) Something your dentist warns will happen if you don’t brush properly Question 3: What is the Fabry-Perot cavity?
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Pop Quiz: A) The motion of a trapped ion in a harmonic field potential B) An atom-field system in which the atom and field exchange a quantum of energy at a particular frequency C) A Jewish dance Question 4: What are Rabi oscillations?
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Necessary Conditions for Quantum Computation Representation of quantum information Universal family of unitary transformations Fiducial initial state Measurement of output result
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Representation of Quantum Information Need to find a balance –Robustness –Ability to interact qubits –Initial state –Measurement Finite number of states Decoherence and speed of operations
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Decoherence and Operation Times What is the difference between decoherence and quantum noise?
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Physical Qubit Representations Photon –Polarization –Spatial mode Spin –Atomic nucleus –Electron Charge –Quantum dot
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Unitary Transformations Single spin operations and CNOT can produce any unitary transformation Imperfections lead to decoherence Must take into account the back-action of quantum system with the computer
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Fiducial Initial State Need only to produce a single known state Need high fidelity to avoid decoherence Need low entropy to make measurements accessible
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Measurement Strong measurements are difficult Weak measurements can suffice using ensembles of qubits Figure of merit: SNR (signal to noise ratio)
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Optical Photon: Qubit representation: polarization –integer spin state of a photon –sidenote: why do polarized sunglasses work? location of single photon between two modes –dual-rail representation –photon in cavity c 0 or c 1 ?: c 0 |01> + c 1 |10>
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Optical Photon: Unitary evolution: Mirrors Phase shifters Beamsplitters Kerr media
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Optical Photon: Initial state preparation: Attenuating laser light Readout: Photodetector (photomultiplier tube)
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Optical Photon: Advantages: Well isolated Fast transmission of quantum states - great for quantum communication Drawbacks: Difficult to make photons interact Absorption loss with Kerr media
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Optical Cavity Quantum Electrodynamics (QED)
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Qubit representation: polarization or location of single photon between two modes atomic spin mediated by photons Unitary evoluation: phase shifters beamsplitters cavity QED system
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Optical Cavity Quantum Electrodynamics (QED) Initial state: attenuating laser light Readout: photomuliplier tube
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Optical Cavity Quantum Electrodynamics (QED) Drawbacks: Absorption loss in cavity Strengthening atom-field interaction makes coupling photon into and out of cavity difficult. Limited cascadibility
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Ion Trap
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Qubit representation: Hyperfine (nuclear spin) state of an atom and phonons of trapped atoms Unitary evolution: Laser pulses manipulate atomic state Qubits interact via shared phonon state
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Ion Trap Initial state preparation: Cool the atoms to ground state using optical pumping Readout: Measure population of hyperfine states Drawbacks: Phonon lifetimes are short, and ions are difficult to prepare in their ground states.
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Nuclear Magnetic Resonance (NMR) Qubit representation: Spin of an atomic nucleus Unitary evolution: Transforms constructed from magnetic field pulses applied to spins in a strong magnetic field. Couplings between spins provided by chemical bonds between neighboring atoms.
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NMR Schematic
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Initial State Preparation (NMR) Refocusing Temporal Labeling Spatial Labeling
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Hamiltonian of NMR Affect single spin dynamics Spin-spin coupling between nuclei –Direct dipolar coupling –Through bond interactions RF Magnetic field of NMR Decoherence: –inhomogeneity of sample –thermalization of spins to equilibrium
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Unitary Transformations (NMR) Single spin –can affect arbitrary single bit rotations using RF CNOT –use refocusing and single qubit pulses
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