Quantum Computing with
Entangled Ions and Photons
Boris Blinov
University of Washington
http://depts.washington.edu/qcomp/
28 June 2010
Seattle
Outline
• Quantum computing
• Ion traps and trapped ion qubits
• Ion-photon entangled system
• Putting 2 and 2 together: a hybrid system
• Trapped ion QC at Washington
What is a qubit (Qbit, q-bit)?
Quantum two-level system
|1
State of the qubit is
described by its wavefunction
| = |0 + |1
|0
|1
“Bloch sphere”
|0
Classical vs. Quantum
• In a classical computer, the data is
represented in series of bits, each taking a
value of either 0 or 1.
0 1 1 0 0 1 0 0 1 1 1 0 ….
• Classical computation consists of
operations on single bits (NOT) and
multiple bits (e.g. NAND).
• In a quantum computer, the data is
represented in series of quantum bits, or
qubits, each taking a value of |0, |1 or any
superposition of |0 and |1.
|0 + |1
• Quantum computation consists of
operations on single qubits (called rotations)
and multiple bits (e.g. CNOT - the
Controlled-NOT gate).
Quantum CNOT gate
control qubit target qubit
result
|0
|0
|0 |0
|0
|1
|0 |1
|1
|0
|1 |1
|1
|1
|1 |0
|0 + |1
|0
|0|0 + |1|1
Entangled state!
Quantum computing revealed
• The power of quantum computing is twofold:
- parallelism and
- entanglement
massive entanglement
input
• Example: Shor’s factoring algorithm
|0
H
|0
H
...
|0
H
|0
H
output
|0
|0
QFT
...
U(x)
(axmodb)
|0
|0
...
...
...
evaluating f(x) for 2n inputs
Outline
• Quantum computing
• Ion traps and trapped ion qubits
• Ion-photon entangled system
• Putting 2 and 2 together: a hybrid system
• Trapped ion QC at Washington
RF (Paul) ion trap
ring
end
cap
RF
Potential
end
cap
3-d RF quadrupole
Position
Position
The UW trap: linear RF quadrupole
4 Ba ions
Chip-scale ion traps
NIST racetrack trap
NIST X-trap
European microtrap
137Ba+
qubit
• Qubit: the hyperfine levels of the
ground state
• Initialization by optical pumping
• Detection by state-selective shelving
and resonance fluorescence
• Single-qubit operations with
microwaves or optical Raman
transitions
|1
|0
• Multi-qubit quantum logic gates
via Coulomb interaction or via
photon coupling
Cirac-Zoller CNOT gate – the classic trapped ion gate
Ions are too far apart, so their spins do
not talk to each other directly.
~4 microns
To create an effective spin-spin coupling, “control” spin
state is mapped on to the motional “bus” state, the target
spin is flipped according to its motion state, then motion is
remapped onto the control qubit.
|
|
control
target
Raman
beams
Cirac and Zoller, Phys. Rev. Lett. 74, 4091 (1995)
Outline
• Quantum computing
• Ion traps and trapped ion qubits
• Ion-photon entangled system
• Putting 2 and 2 together: a hybrid system
• Trapped ion QC at Washington
Ion-photon entanglement via spontaneous emission
| mj=-1/2 
| mj=+1/2 
s+ = H
P1/2
p =V
S1/2
|
|
| = |H| + |V|
Remote Ion Entanglement
using entangled ion-photon pairs
D2
D1
Coincidence only if photons in state:
| - = |H1 |V2 - |V1 |H2
This projects the ions into …
|1 |2 - |1 |2 = | -ions
BS
The ions are now entangled!
|i = |H| + |V|
2 distant ions
Simon and Irvine, PRL, 91, 110405 (2003)
Outline
• Quantum computing
• Ion traps and trapped ion qubits
• Ion-photon entangled system
• Putting 2 and 2 together: a hybrid system
• Trapped ion QC at Washington
“Hybrid” System:
Small(ish) Ion Trap and Optical Interconnects
We want to combine a number of “small” (10 – 100 qubits) ion
traps in a network trough ion-photon entanglement interface.
• novel trap designs (anharmonic, ring, …)
• use of multiple vibrational modes and ultrafast pulses
• fast optical switching
Anharmonic Linear Ion Trap
By using a combination of electrodes make a “flat-bottom” axial
trap; transverse trapping still harmonic.
• ion-ion spacing nearly uniform even for large ion crystals
• transverse vibrational modes tightly bunched (“band”)
• sympathetic cooling on the fringes of the trap
"Large Scale Quantum Computation in an Anharmonic Linear Ion Trap," G.-D. Lin, S.-L. Zhu, R. Islam, K. Kim, M.-S.
Chang, S. Korenblit, C. Monroe, and L.-M. Duan, Europhys. Lett. 86, 60004 (2009).
Anharmonic Ring Ion Trap
Removing the end cap electrodes of a linear trap and connecting
the quadrupole rods onto themselves makes a (storage) ring ion
trap
• ion-ion spacing perfectly uniform
• transverse vibrational modes tightly bunched (“band”)
• sympathetic cooling on one side of the ring
Anharmonic Ring Ion Trap
Outline
• Quantum computing
• Ion traps and trapped ion qubits
• Ion-photon entangled system
• Putting 2 and 2 together: a hybrid system
• Trapped ion QC at Washington
Optical pumping: qubit initialization
p-polarized light pumps
the population into the
F=2, mf=0 state. When
pumped,
ion
stops
fluorescing. We adjust the
pump light polarization by
tuning the magnetic field
direction instead.
6P1/2
650nm
5D5/2
493nm
5D3/2
1762nm
F=2
mF=0
6S1/2
8.037 GHz
F=1
mF=0
Rabi flops on the S – D transition
Hyperfine qubit Rabi flopping
Femtosecond optical Rabi flopping
Ion excitation with unit probability
“Integrated optics”: ion trap with
a spherical mirror
N.A. = 0.9
Putting things in prospective…
Ion imaging using the mirror
– Resolve multiple (2) ions
infinity-corrected microscope lens
• x`
spherical mirror
Aspherical Schmidt-type corrector
fixes aberration (somewhat)
• Made from acrylic, in the machine shop
– Cut the to precision of 25 μm
– Hand-polish to ~0.1μm
• Results:
– Far from ideal due to misalignment and
mirror imperfection, but…
“Tack” Trap: Almost Zero Obstruction
“Tack” trap at work
Final remarks...
“Computers in the future may weigh no more than 1.5 tons.”
- Popular Mechanics (1949)
“I think there is a world market for maybe five computers.”
- Thomas Watson, chairman of IBM (1943)
UW ion trappers