Quantum Computing with Quantum Computing with Entangled Ions and Entangled Ions and PhotonsPhotons Boris BlinovBoris Blinov
University of WashingtonUniversity of Washingtonhttp://http://
depts.washington.edu/depts.washington.edu/qcomp/qcomp/
28 June 201028 June 2010SeattleSeattle
OutlineOutline
• 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-What is a qubit (Qbit, q-bit)?bit)?
Quantum two-level system
| 1
|0
“Bloch sphere”
State of the qubit is described by its wavefunction | = |0 + |1
| 1
|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.
• 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.
• Quantum computation consists of operations on single qubits (called rotations) and multiple bits (e.g. CNOT - the Controlled-NOT gate).
0 1 1 0 0 1 0 0 1 1 1 0 ….|0 + |1
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
• Example: Shor’s factoring algorithm
U(x)(axmodb)
H
H
H
H
...
input
ou
tput
|0
|0
|0
|0
|0
...|0
|0|0
...
...
QFT ...
evaluating f(x) for 2n inputs
massive entanglement
OutlineOutline
• 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 trapRF (Paul) ion trap
Pote
nti
al
Position
Position
endcap
endcap
ring
3-d RF quadrupole
RF
The UW trap: linear RF The UW trap: linear RF quadrupolequadrupole
4 Ba ions
Chip-scale ion traps
NIST X-trapNIST X-trap
NIST racetrack trapNIST racetrack trap
European microtrapEuropean microtrap
137137BaBa++ qubit 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
• Multi-qubit quantum logic Multi-qubit quantum logic gates via Coulomb gates via Coulomb interaction or via photon interaction or via photon couplingcoupling
|0
|1
Cirac-Zoller CNOT gate – the classic trapped ion gate
Ions are too far apart, so their spins do not talk to each other directly.
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
Cirac and Zoller, Phys. Rev. Lett. 74, 4091 (1995)
Raman beams
~4 microns
OutlineOutline
• 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
+ = H
S1/2
P1/2
= V
| mj=+1/2
||
| = |H| + |V|
Ion-photon entanglement via spontaneous Ion-photon entanglement via spontaneous emissionemission
| mj=-1/2
D
BS
DD1
D2
Remote Ion Entanglementusing entangled ion-photon pairs
2 distant ions
Coincidence only if photons in state:
| = |H1 |V2 - |V1 |H2
This projects the ions into …
|1 |2 - |1 |2 = | -ions
The ions are now entangled!|i = |H| + |V|
Simon and Irvine, PRL, 91, 110405 (2003)
OutlineOutline
• 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
OutlineOutline
• 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
493nm
650nm
1762nm
6S1/2
6P1/2
5D5/2
5D3/2
8.037 GHz
F=2
F=1
mF=0
mF=0
-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.
Rabi flops on the S – D transition
Hyperfine qubit Rabi flopping
Femtosecond optical Rabi flopping
Ion excitation with unit probability
““Integrated optics”: ion trap Integrated optics”: ion trap with a spherical mirrorwith a spherical mirror
N.A. = N.A. = 0.90.9
UW Physics
Putting things in Putting things in prospective…prospective…
UW Physics
Ion imaging using the mirror
– Resolve multiple (2) ions
• x`
infinity-corrected microscope lens spherical mirror
UW Physics
Aspherical Schmidt-type correctorfixes 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…
UW Physics
“Tack” Trap: Almost Zero Obstruction
UW Physics
“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