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
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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
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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