Quantum Computing with Entangled Ions and Photons Boris Blinov University of Washington 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  |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 

Quantum CNOT gate control qubittarget qubit result |0  |0  |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) (a x modb) H H H H... input output |0 ... |0 ... QFT... evaluating f(x) for 2 n inputs massive entanglement

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 Potential Position end cap ring 3-d RF quadrupole RF

The UW trap: linear RF quadrupole 4 Ba ions

Chip-scale ion traps NIST X-trap NIST racetrack trap European microtrap

137 Ba + 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 gates via Coulomb interaction or via photon coupling Multi-qubit quantum logic gates via Coulomb interaction or via photon coupling |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

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

 + = H S 1/2 P 1/2  = V | m j =+1/2  || || |  = |H  |  + |V  |  Ion-photon entanglement via spontaneous emission | m j =-1/2 

D BS D D1D1 D2D2 Remote Ion Entanglement using entangled ion-photon pairs 2 distant ions Coincidence only if photons in state: |    = |H  1 |V  2 - |V  1 |H  2 This projects the ions into … |  1 |  2 - |  1 |  2 = |  -  ions The ions are now entangled! |  i = |H  |  + |V  |  Simon and Irvine, PRL, 91, (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, (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 493nm 650nm 1762nm 6S 1/2 6P 1/2 5D 5/2 5D 3/ GHz F=2 F=1 m F =0  -polarized light pumps the population into the F=2, m f =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 with a spherical mirror N.A. = 0.9

UW Physics Putting things in prospective…

UW Physics Ion imaging using the mirror –Resolve multiple (2) ions x` infinity-corrected microscope lens spherical mirror

UW Physics Aspherical Schmidt-type corrector fixes aberration (somewhat) Made from acrylic, in the machine shop –Cut the to precision of 25 μ m –Hand-polish to ~0.1 μ m 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