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 c0 or c1?: c0|01> + c1|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