# Quantum Computer Implementations

## Presentation on theme: "Quantum Computer Implementations"— Presentation transcript:

Quantum Computer Implementations
Christopher Monroe University of Michigan Department of Physics US Advanced Research and Development Activity US Army Research Office US National Security Agency National Science Foundation

ENIAC (1946)

The first solid-state transistor (Bardeen, Brattain & Shockley, 1947)

Moore’s Law # Transistors 109 108 Pentium III 107 Pentium Pro 106 Pentium i486 i386 1. The “real” Moore’s law is coming to a close. Molecular transistors, beyond that? 105 80286 104 8086 103 1975 1980 1985 1990 1995 2000 2005 2010 2015 Projected Source: Intel

“There's Plenty of Room at the Bottom”
(1959 APS annual meeting) Richard Feynman “When we get to the very, very small world – say circuits of seven atoms - we have a lot of new things that would happen that represent completely new opportunities for design. Atoms on a small scale behave like nothing on a large scale, for they satisfy the laws of quantum mechanics…”

“qubit” = two-level system
A quantum computer hosts quantum bits which can store superpositions of 0 and 1 classical bit: or 1 quantum bit: |0 + |1 |1 “qubit” = two-level system |1 |0 |0 Benioff (1980) Feynman (1982)

N qubits can store 2N numbers simultaneously
GOOD NEWS… N qubits can store 2N numbers simultaneously Example: N=3 qubits  = a 0 |000 + a 1 |001 + a 2 |010 + a 3 |011 a 4 |100 + a 5 |101 + a 6 |110 + a 7 |111 …BAD NEWS… Measurement gives random result e.g.,   |011 Good-bad-good. Exponential storage. X2 example of parallelism.

quantum interference before measurement
…GOOD NEWS! quantum interference before measurement quantum gates depends on all inputs |0 |0  |0 |0 |0 |1  |0 |1 |1 |0  |1 |1 |1 |1  |1 |0 e.g., (|0 + |1)|0  |0|0 + |1|1 quantum XOR gate: superposition  entanglement Shor started it all Deutsch (1985) Shor (1994) Grover (1996) fast number factoring

Quantum Entanglement: Einstein’s “Spooky action-at-a-distance”
“superposition” “entangled superposition” or or

Quantum computer hardware requirements
Must make states like |000…0 + |111…1 x + strong coupling between qubits weak coupling to environment 2. Must measure state with high efficiency strong coupling to environment

Physical Implementations
1. Individual atoms and photons a. ion traps b. atoms in optical lattices c. photon downconversion and cavity-QED 2. Superconductors a. Cooper-pair boxes (charge qubits) b. rf-SQUIDS (flux qubits) 3. Semiconductors quantum dots 4. Other condensed-matter a. NMR b. electrons floating on liquid helium c. single phosphorus atoms in silicon

0.3 mm

Trick: apply sinusoidal electric field (rotate saddle)
Ion Trap Primer + E(r) NO! E = 0 saddle point z E(r) ? + Trick: apply sinusoidal electric field (rotate saddle) RF (PAUL) TRAP

Dynamics of a single ion in a rf trap
e = ion charge m = ion mass V0 = rf voltage amplitude d = trapsize x + [k2 cosWt]x = 0 k2 = eV0/md2 time position x “secular” motion at frequency wtrap  k2/W  MHz “micromotion” at frequency W  100 MHz Mathieu Equation: x(t) bounded for k << W

3D ion trap geometry endcap d V ring endcap

Michigan Ion Trap 2 mm

0.2 mm |0 |1

“Perfect” quantum measurement of a single atom
state |0 state |1 # photons collected in 200ms Probability 30 20 10 0.2 ion fluoresces 108 photons/sec laser laser ion remains dark 30 20 10 1 # photons collected in 200ms >99% detection efficiency!

Atomic Cd+ energy levels
or Be+, Mg+, Sr+, Ca+, Ba+, Cd+, Hg+,…. P3/2 215nm ~108 photons/sec S1/2 |1 15GHz |0

Coherent transitions between |0 and |1
P3/2 2-photon “stimulated Raman” transitions S1/2 |1 |0 Coherent transitions between |0 and |1

Mapping: (|0 + |1) |0m  |0 (|0m + |1m) S1/2 |1
2-photon “stimulated Raman” transitions Mapping: (|0 + |1) |0m  |0 (|0m + |1m) 2 1 S1/2 |1 2 1 |0

Pulse Raman beams for time t Pulse Detection beams for 200 ms step t
Prepare in |0|rest  Pulse Raman beams for time t Pulse Detection beams for 200 ms step t Single ion transitions between |0|rest  and |1 |moving  20 40 60 80 100 1 t (ms) Prob(|0) CM, et. al., Phys. Rev. Lett. 75, 4714 (1995)

Trapped Ion Quantum Computer
laser cool to rest laser j k map jth qubit to collective motion laser j k flip kth qubit if collective motion laser j k map collective motion back to jth qubit Cirac and Zoller, Phys. Rev. Lett. 74, 4091 (1995)

State-of-the-art: Four-qubit quantum logic gate
|0000  |0000 + eif|1111 Sackett, et al., Nature 404, 256 (2000)

fluctuating electric patch potentials on surface
Why only 4 ? More ions: difficult (& slow) to isolate single mode of motion Decoherence of motion: fluctuating electric patch potentials on surface 0.5 mm technical, not fundamental limitation

Scaling proposal 1: the “quantum CCD”
(Kielpinski, Monroe, Wineland, submitted to Nature) “refrigerator” ions suppress motional decoherence few mm quantum memory

“accumulator”

target quantum bits entangled laser pulse

Scaling proposal 2: ion trap array and head Cirac and Zoller, Nature 404, (2000). motion head target pushing laser

Physical Implementations
1. Individual atoms and photons a. ion traps b. atoms in optical lattices c. photon downconversion and cavity-QED 2. Superconductors a. Cooper-pair boxes (charge qubits) b. rf-SQUIDS (flux qubits) 3. Semiconductors quantum dots 4. Other condensed-matter a. NMR b. electrons floating on liquid helium c. single phosphorus atoms in silicon

Optical Lattices (trapped neutral atoms)
m = -aE U = -m•E = -a|E|2 U(x) = -a|E(x)|2 a = polarizability lasers induce electric dipole that interacts with laser itself! l/2

moving neutral atoms qubits together for entanglement

Physical Implementations
1. Individual atoms and photons a. ion traps b. atoms in optical lattices c. photon downconversion and cavity-QED 2. Superconductors a. Cooper-pair boxes (charge qubits) b. rf-SQUIDS (flux qubits) 3. Semiconductors quantum dots 4. Other condensed-matter a. NMR b. electrons floating on liquid helium c. single phosphorus atoms in silicon

A B Individual photons Quantum Entanglement! qubit: |0 = zero photons
|1 = one photon 50/50 A weak laser B |1 = |0A|1B + |1A|0B Quantum Entanglement! send single photons

single photon source: optical parametric downconversion
X visible (or infrared) (l/2) ultraviolet (l) c(2) nonlinear crystal (e.g., ADP, BBO,…) BUT… not scalable! Prob(downconversion)~10-8

cavity-QED: deterministically creating and storing
single photons in a resonator qubit: |0 = zero photons in cavity |1 = one photon in cavity L Interaction strength between atom & photon U = -matom•E1  (Vol)1/2 L = 1 mm, t > 10-3sec requires Reflectivity > % M1 M2 atom

Quantum Network Cirac, Zoller, Kimble, Mabuchi, Phys. Rev. Lett
W(t) W(-t)

H.J. Kimble (CalTech) M. Chapman (Georgia Tech) G. Rempe (Max Planck Inst., Garching)

H. J. Kimble, CalTech

Physical Implementations
1. Individual atoms and photons a. ion traps b. atoms in optical lattices c. photon downconversion and cavity-QED 2. Superconductors a. Cooper-pair boxes (charge qubits) b. rf-SQUIDS (flux qubits) 3. Semiconductors quantum dots 4. Other condensed-matter a. NMR b. electrons floating on liquid helium c. single phosphorus atoms in silicon

Superconducting charges
Nakamura (NEC-Japan) Schoelkopf (Yale) Devoret (Yale)

Single-qubit rotations on a Cooper-pair Box
|N  |N+1 (N=# Cooper pairs) Nakamura, et. al., Nature 398, 786 (1999)

Physical Implementations
1. Individual atoms and photons a. ion traps b. atoms in optical lattices c. photon downconversion and cavity-QED 2. Superconductors a. Cooper-pair boxes (charge qubits) b. rf-SQUIDS (flux qubits) 3. Semiconductors quantum dots 4. Other condensed-matter a. NMR b. electrons floating on liquid helium c. single phosphorus atoms in silicon

Superconducting currents
J.E. Mooij,… Science 285, 1036 (1999). quantized flux qubit states

Physical Implementations
1. Individual atoms and photons a. ion traps b. atoms in optical lattices c. photon downconversion and cavity-QED 2. Superconductors a. Cooper-pair boxes (charge qubits) b. rf-SQUIDS (flux qubits) 3. Semiconductors quantum dots 4. Other condensed-matter a. NMR b. electrons floating on liquid helium c. single phosphorus atoms in silicon

Semiconductor Quantum Dots
e.g., Duncan Steel (University of Michigan) Optical Field AlGaAs GaAs AlGaAs

Excitonic Rabi oscillations
~10.5 ps ~18.5 ps Exciton Population Pulse Area T. Stievater, et al. (submitted)

Optical Field AlGaAs GaAs AlGaAs GaAs AlGaAs

Physical Implementations
1. Individual atoms and photons a. ion traps b. atoms in optical lattices c. photon downconversion and cavity-QED 2. Superconductors a. Cooper-pair boxes (charge qubits) b. rf-SQUIDS (flux qubits) 3. Semiconductors quantum dots 4. Other condensed-matter a. NMR b. electrons floating on liquid helium c. single phosphorus atoms in silicon

Nuclear Magnetic Resonance
Gershenfeld and Chuang, Science 275, 350 (1997) liquid state, room temperature NMR several “qubit operations” demonstrated, BUT: no entanglement not scalable (signal decreases exponentially with # qubits) (not quantum computing?)

Physical Implementations
1. Individual atoms and photons a. ion traps b. atoms in optical lattices c. photon downconversion and cavity-QED 2. Superconductors a. Cooper-pair boxes (charge qubits) b. rf-SQUIDS (flux qubits) 3. Semiconductors quantum dots 4. Other condensed-matter a. NMR b. electrons floating on liquid helium c. single phosphorus atoms in silicon

Electrons floating on liquid helium
Platzman and Dykman, Science 284 (1999) 1-dimensional “atom”

geometry

readout positive bias applied imaging channel plate
… electrons tunnel out only if in state 2

Fabrication of submerged electrodes
(J. Goodkind, UCSD)

Physical Implementations
1. Individual atoms and photons a. ion traps b. atoms in optical lattices c. photon downconversion and cavity-QED 2. Superconductors a. Cooper-pair boxes (charge qubits) b. rf-SQUIDS (flux qubits) 3. Semiconductors quantum dots 4. Other condensed-matter a. NMR b. electrons floating on liquid helium c. single phosphorus atoms in silicon

Phosphorus atoms in Silicon
Kane, Nature 393, 133 (1998) U. Maryland, Los Alamos, Australia NOTE: Bruce Kane will give Physics Dept. colloquium Wed., Nov. 7, 4PM qubit stored in phosphorus nuclear spin (P: spin-1/2) (Si: spin 0)

Single-qubit rotations:
electron/nuclear spin-spin interaction (hyperfine interaction) Two-qubit entangling gates: bring adjacent donor electrons together (exchange interaction)

Physical Implementations
1. Individual atoms and photons a. ion traps b. atoms in optical lattices c. photon downconversion and cavity-QED 2. Superconductors a. Cooper-pair boxes (charge qubits) b. rf-SQUIDS (flux qubits) 3. Semiconductors quantum dots 4. Other condensed-matter a. NMR b. electrons floating on liquid helium c. single phosphorus atoms in silicon works scales

Quantum Computing Abyss
state-of-the-art experiments theoretical requirements for “useful” QC  5 # quantum bits >1000 # quantum bits <100 # logic gates >109 noise reduction error correction ? new technology efficient algorithms