Caltech MURI Center

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Caltech MURI Center for Quantum
Networks with Lee Center for Advanced
Networking (CIT) University of Calgary University
of Colorado Los Alamos National Laboratory HP
Laboratories IBM Research Microsoft Research
storage and processing
Interconnection of quantum nodes ...
of quantum information
robust transmission over
... by quantum wires
large distances
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Outline

• Motivation and intro to quantum communication
• Indications of the range of potential
  applications
• Primary technical requirements and timeline
• Overview of the Caltech program

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Quantum information science
We can exploit quantum resources to enhance
information processing

• is a unit of irreducible uncertainty,
• manifest at nanometer scales

• Models of quantum computation define new
  run-time complexity classes factoring is QBP.
• Quantum networks would enable novel
  cryptographic protocols and reduce communication
  complexity for some distributed computations.

• Quantum phenomena give rise to essentially-new
  forms of complexity at the quantumclassical
  interface, e.g., in nanoscale device physics.
• General principles for managing quantum
  uncertainty would enable robust feedback control
  in quantum components and systems.

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Quantum information science
We can exploit quantum resources to enhance
information processing

• is a unit of irreducible uncertainty,
• manifest at nanometer scales

• Models of quantum computation define new
  run-time complexity classes factoring is QBP.
• Quantum networks would enable novel
  cryptographic protocols and reduce communication
  complexity for some distributed computations.

• Quantum phenomena give rise to essentially-new
  forms of complexity at the quantumclassical
  interface, e.g., in nanoscale device physics.
• General principles for managing quantum
  uncertainty would enable robust feedback control
  in quantum components and systems.

The quantum nature of reality has an intriguing
tendency to become most evident when we
investigate the physical limits of technology.
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Quantum information science at Caltech
Physics Jeff Kimble Hideo Mabuchi John
Preskill Michael Roukes
MURI Center For Quantum Networks (DDRE/DARPA)
Institute for Quantum Information (IQI) (pending,
NSF)
Engineering and Applied Science John
Doyle Michelle Effros Richard Murray Axel
Scherer Leonard Schulman Erik Winfree
Lee Center for Advanced Networking (Caltech)
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Academic rebuttal

• QIS as a fundamental paradigm shift, vs. new
  devices
• proper understanding now leverages future
  research direction
• relies on platform development of the most
  audacious kind
• DoD can play a crucial role in shaping early
  phases of research
• key to focus on robustness, e.g. TCP/IP for
  todays Internet
• forcing concreteness is good, forcing .com
  timescales is bad

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Quantum vs. classical information
Classical bit single binary digit, b (0
or 1) Quantum bit state of a two-level
quantum system, ?? ? ? span ?0 ?,?1 ?
Quantum register joint state of N
qubits, ??ab ? c0?1a 0b ? c1?1a 1b ?
c0?2ab ? c1?3ab ?

• Superposition ?? ? c0?0 ? c1?1 ?
• Entanglement ??ab ? c0?0a 0b ? c1?1a 1b ?

Entanglement is stronger than any form of
statistical correlation between classical
variables
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Quantum communication
B
A

• C Photon polarization can encode one bit of
  information ?H ? ? 0, ?V ? ? 1
• Q Polarizations at arbitrary angle encode a
  single qubit ??? ? c0?H ? c1?V ?
• Q usage, with local processing and memory,
  enables quantum comm. protocols
• C/Q resource equivalence underlies quantum
  communication complexity model
• In practice, Q transmission is very fragile
  need error correction, repeaters

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Quantum information with atoms and photons
Qubit representations
s
s -
Internal states of atoms / ions
Atomic / ionic center-of-mass
Photon number or polarization

• Long coherence times
• Easy single-qubit gates
• Trapped atoms / ions
• Difficult to transmit

• Easy single-qubit gates
• Easy to transmit
• Difficult to store

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Quantum state transfer via cavity QED
Map state from atom to cavity field
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W1( t )
Cavity field flows out through optical channel
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Received field is transferred into state of atom
3
W2( t )
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Entanglement distribution in a quantum network
Qubit transmission converts local entanglement to
distributed entanglement
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Using entanglement to establish cryptographic key
Entangled pairs can be stored until needed
Local measurements convert them into key bits
0
0
Security can be checked via CSHS inequalities
1
1
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Using entanglement for quantum state transfer
losses may be too high for direct quantum transfer
Suppose A and B share prior entanglement
A performs a joint measurement
A must communicate the result to B
B can then reconstruct the original state
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Distributed quantum computation
Robust quantum state transfer enables distributed
database search (Grover, Cleve et al)
Query intersection of A, B databases (appointment
scheduling) fab(x) fa(x) ? fb(x)
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Timeline for quantum communication
Robust teleportation over 100 km

• quantum memory for local storage
• local quantum logic gates
• quantum state transfer between nodes
• error correction for quantum state transfer
• demonstration of quantum repeater architecture

1-3
3-4
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optical losses compromise fidelity of raw
quantum state transfer exponential (with
distance) losses necessitate use of repeaters
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Overview of Caltech program, I.
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Overview of Caltech program, II.

• Error correction in-place entanglement
  purification of EPR pairs
• easier to purify a known state than an unknown
  state
• use quantum state teleportation to send data
  after establishing entanglement resource

Q. repeaters entanglement swapping to connect
end stations
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Laser cooling and trapping with cavity QED
x
104 Cesium Atoms
y
Mirror Surface
z
Detector
Probe Laser
Mirror Substrate
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Spherical-mirror, Fabry-Perot optical cavity
Record finesse - F 1.9 x106, R 0.9999984 CIT
R. Lalezari, REO, Opt. Lett. 17, 363 (1992)

• High Reflectivity Surfaces - Finesse 470,000
• Length actively stabilized to 10-15 m

1mm
BK7 Substrate
Length l 10 - 50 mm Mode waist w0 15mm
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Single atom transits the atom-cavity microscope
(a)
(b)
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Real-time tracking and trapping of single atoms
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Lifetime for single atoms trapped in a cavity

• Limits?
• Current - fluctuations in FORT beam
• Savard et al., Phys. Rev. A56, R1095 (1997),
• C. Gardiner (1999)
• Ultimate - 102 sec set by background gas

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Enhanced atom-photon coupling via cavity QED
Critical photon number
Critical atom number
g
k
Cs
Nonlinear optics with one photon per mode
Single-atom switching of optical cavity response
g
H. J. Kimble (Caltech)
A. Scherer (Caltech)
m0 ? 10?4 N0 ? 10?3
m0 ? 10?8 N0 ? 10?2
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Planar photonic bandgap structures
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Cavity QED with photonic bandgap cavities
Finite-difference time domain calculations (J.
Vuckovic and A. Scherer) Slab thickness 163
nm Normal hole radius 81 nm Closest distance
between holes 271 nm Defect hole radius 54
nm Theoretical limiting Q 16389 Effective mode
volume 0.092 l3 (f.s.) Critical photon number
5.4 x 10-8 Critical atom number 1.8 x 10-3
Magnetic micro traps Designs of Weinstein
Libbrecht (1995) 10 mm Ioffe coil radius Dx
approx. 10 nm. Small dimensions lead to high
curvatures, but small trap depth and loading
volume.
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Caltech MURI center for Quantum Networks

• Objectives
• Entanglement between distant atoms
• Fault-tolerant quantum state teleportation
• Demonstrate quantum repeater architecture
• Analyze quantum communication networks
• Investigate quantum network algorithms

• Technical approach
• Dipole and micromagnetic atom trapping
• Fabry-Perot, photonic bandgap cavities
• Raman cavity QED with special pump pulses
• In-place entanglement purification
• Entanglement-swapping quantum repeaters

• Current status
• Single atoms optically trapped in F-P cavity
• m magnetic traps, PBG cavities fabricated
• Fault-tolerant protocols designed/analyzed

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Caltech MURI senior personnel and expertise

• Mabuchi, Kimble cavity QED and atom trapping
• Preskill, Van Enk quantum error correction and
  fault tolerance
• Scherer, Roukes nanofabrication, photonic
  devices and MEMs
• Cleve, Watrous distributed quantum computing,
  complexity theory
• Ye laser stabilization and precision
  measurement
• Habib decoherence, high-performance numerical
  simulation
• Bennett, DiVincenzo, Smolin quantum
  information/entanglement theory
• Freedman, Gottesman, Kitaev quantum algorithms
  and fault-tolerance