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

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?

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?

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?

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?

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)

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

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