Quantum Devices or How to Build Your Own

Quantum Devices (or, How to Build Your Own Quantum Computer)

Pop Quiz: Question 1: What is Q? 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

Pop Quiz: Question 2: What is a fiducial state? 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

Pop Quiz: Question 3: What is the Fabry-Perot cavity? 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

Pop Quiz: Question 4: What are Rabi oscillations? 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

Necessary Conditions for Quantum Computation • • Representation of quantum information Universal family of unitary transformations Fiducial initial state Measurement of output result

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

Decoherence and Operation Times What is the difference between decoherence and quantum noise?

Physical Qubit Representations • Photon – Polarization – Spatial mode • Spin – Atomic nucleus – Electron • Charge – Quantum dot

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

Fiducial Initial State • Need only to produce a single known state • Need high fidelity to avoid decoherence • Need low entropy to make measurements accessible

Measurement • Strong measurements are difficult • Weak measurements can suffice using ensembles of qubits • Figure of merit: SNR (signal to noise ratio)

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>

Optical Photon: Unitary evolution: • Mirrors • Phase shifters • Beamsplitters • Kerr media

Optical Photon: Initial state preparation: • Attenuating laser light Readout: • Photodetector (photomultiplier tube)

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

Optical Cavity Quantum Electrodynamics (QED)

Optical Cavity Quantum Electrodynamics (QED) Qubit representation: • polarization or location of single photon between two modes • atomic spin mediated by photons Unitary evoluation: • phase shifters • beamsplitters • cavity QED system

Optical Cavity Quantum Electrodynamics (QED) Initial state: • attenuating laser light Readout: • photomuliplier tube

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

Ion Trap

Ion Trap 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

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.

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.

NMR Schematic

Initial State Preparation (NMR) • Refocusing • Temporal Labeling • Spatial Labeling

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

Unitary Transformations (NMR) • Single spin – can affect arbitrary single bit rotations using RF • CNOT – use refocusing and single qubit pulses