QAP SP4

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QAP SP4 Quantum Simulation Control
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Quantum Simulation and Control

• Theory
• analyze static and dynamic properties of quantum
  many body systems
• simulate 1-D quantum systems with gt50 qubits.
• Optimal control theory

• Experiment Develop and advance spin systems
  suitable for
• quantum simulations
• creation and analysis of entanglement
• robust and optimised quantum gates
• characterize and control decoherence

3
Quantum Simulation and ControlWP4.1 Objective
and Approach

• Objective
• Several qubit QC based on rare-earth-ion doped
  crystals Testbed for optimum pulses and pulse
  sequences.
• Approach
• Ensemble implementation a few qubits.
• Individual qubits based on single ion readout
  more qubits.

Pr doped yttrium silicate crystal
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Quantum Simulation and Control
lWP4.1 Selected results
The readout ion concept for the single instance
many-qubit implementation.
The qubit 0gt-egt transition turns off the
fluorescence
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Quantum Simulation and Control
lWP4.1 Selected results
Achievements Ce3 as readout ion for single
instance many-qubit implementations

• Ce3 4f-5d transition in Y2SiO5
• identified near 370.6 nm
• inhomogeneous line width 80 GHz
• homogeneous line width 3 MHz (limited by upper
  state lifetime of 50 ns)Importantly, homogeneous
  line width is narrower than expected!!! ?
  qubit-readout ion distance up to several nm
  possible (D4.1.3 and M4.1.3).
• Simulations (M4.1.4) show that interacting
  several qubit structures will be present in
  Y2SiO5 at Pr concentrations of the order of 1
• Experiments to detect single Ce3 ions are now
  starting

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Quantum Simulation and Control
lWP4.1 Deliverables
D4.1.4 Test of pulse sequences for two-qubit
entanglement
Initialized to the 0gt state
Searching for better pulse shapes with optimal
control techniques
1/2 hyperfine state
(8 ms) (4 ms) (2 ms) (2 ms)
Optimal control pulse with 8 MHz
bandwidth Transfer to 1gt state
3/2 hyperfine state
excgt
0gt
1gt
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Quantum Simulation and Control
lWP4.1 Deliverables
D4.1.4 Test of pulse sequences for two-qubit
entanglement

• Single-qubit operations (gt0.9 fidelity) with
  quantum state tomography now in an undergraduate
  lab!!
• Qubit-qubit interaction previously demonstrated.
  However, need faster operations for qubit
  entanglement.
• Shorter duration single-qubit operation pulse
  sequences developed by TU Munich are presently
  tested.
• In order to fulfil the deliverable in time
  attempt two-bit entanglement with pulses (TU
  Munich) that already were implemented
  successfully.

• Experimental quantum state tomography of a
  solid state qubit, L Rippe, B Julsgaard, A
  Walther, Yan Ying, S Kröll, Phys Rev A77, 022307
  (2008). http//lanl.arxiv.org/abs/0708.0764,

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Quantum Simulation and Control
lWP4.2 Selected Results
Goal Use nuclear spins around NV to simulate
properties of multispin cluster with adjustable
interaction.
Free induction decay of NV defect in ultrapure
diamond. This decay is the longest FID for any
solid state system.
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Quantum Simulation and Control
.
D 4.2.4 Entanglement of three qubits in diamond. ?
Generation of GHZ and W states from 1 electron
spin and 2 nuclear spins (13C)
W-state
Neumann et al., Science 320, 1326 (2008)
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Quantum Simulation and Control
lWP4.3 Optimal Control of Quantum Systems
Selected Results
D4.3.3 Extension of MATLAB package to broader
array of experimental settings  ? TEG1-06,
DHK1-07,SDH1-07.
NEW optimal control for generating cluster
states in ion spin molecule
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Quantum Simulation and ControlWP4.4 and WP4.5
Selected Results
Scalable Quantum CISC Compiler by Optimal Control
exploiting 128 parallel nodes on cluster HLRB-II
(9728 n total LINPACK performance of 63.3
TFlops/s)
CISC-Compiler
fast, decoh.-protected

• principle use m-qubit interaction building
  blocks to fight decoherence
• m2 standard universal gate decomposition, RISC
  (restricted instruction set CNOT)
• mgt2 enlarge toolbox to recursively usable
  m-qubit complex instruction sets (CISC)

Schulte-Herbrüggen, Spörl, Glaser
quant-ph/0712.3227
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Quantum Simulation and ControlWP4.4 and WP4.5
Selected Results
Scalable Quantum CISC Compiler for Large-Scale
Q-Computing Example C NOT (generalised
TOFFOLI, multiple-controlled NOT on Ising spin
chain) vast improvement by assembling m-qubit
CISC modules against 2-qubit RISC standard
n
time cost

quality improvement
RISC
estim. limit
CISC
CISC
CISC
estim. limit
RISC
Schulte-Herbrüggen, Spörl, Glaser
quant-ph/0712.3227
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Quantum Simulation and ControlWP4.4 and WP4.5
Selected Results
By-Product Faster General Construction for
Multiply-Controlled Unitary Gates
n
time cost
new general C U
construction
RISC
faster than the classical scheme in Barenco et
al., PRA 52 (1995) 3457
CISC
new
estim. limit
Schulte-Herbrüggen, Spörl, Glaser
quant-ph/0712.3227
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Quantum Simulation and ControlWP4.6 Ion Trap
Quantum Simulation using Ion Spin Molecule
Yb

• Single N-spin designer molecule
• Adjustable coupling constants Jij .
• Individual addressing of spins.
• Insensitive to thermal motion

• Quantum Simulations Phase Transitions.
• Entanglement and Decoherence.
• Neural Network (M. Pons et al., Phys. Rev. Lett.
  98, 023003, 2007)

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Quantum Simulation and ControlWP4.6 Selected
Results
Ion Spin Molecule Spin-Motion Coupling using rf
radiation
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Quantum Simulation and ControlWP4.6
New Trap Set-up for Ion Spin Molecules
M 4.6.3 Laser light sources (369 nm, 935 nm and
638 nm) are ready. Optical components for imaging
of in the uv range have been developed and
built. ?
M 4.6.4 New vacuum recipient with all optical and
electrical interfaces is built, leak tested and
ready to mount ion trap. ?
M 4.6.5 Implement individual addressing in
frequency space ? x
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Quantum Simulation and ControlWP4.7 Selected
Results
M4.7.5 Quantum circuit for 4-qubit Quantum Ising
model ?
Verstraete, Cirac, Latorre, arXiv.org0804.1888
U
Prepare a product state
Obtain the Ising ground state
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Quantum Simulation and ControlWP4.7 Selected
Results
M4.7.6 Entanglement scaling for Matrix Product
States ?
Tagliacozzo, de Oliveira, Iblisdir, Latorre,
Phys. Rev. B 78, 024410 (2008)
Emergence of ?-scaling
Displacement of fixed point Magnetization Ha
lf-chain entropy Correlation length
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Quantum Simulation and ControlWP4.7 Selected
Results

• Density-matrix renormalization group (DMRG) in
  the Heisenberg picture (H-DMRG)
• Efficiency of approximation much better, as only
  the observable of interest but not the entire
  state is considered.
• In some non-trivial cases, H-DMRG can be exact
  for finite bond dimensions.
• Hartmann Plenio, E-print arXiv0808.0666
  quant-ph

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Quantum Simulation and ControlWP4.8 Selected
Results
M 4.8.5 Propose scheme for the experimental
observation of quantum phase
transition in ion traps. ?
Retzker, Thompson, Segal, Plenio, arXiv0801.0623
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Quantum Simulation and ControlWP4.8 Selected
Results
Hopping Hamiltonian
Dissipation
Dephasing
Plenio Huelga, arXiv0807.4902
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Quantum Simulation and ControlWP4.8 Selected
Results
Plenio Huelga, arXiv0807.4902
Coherent coupling strength in Fenner-Matthews-Olso
n chromophore complex
local site loss rate
No decoherence
probability that excitation in site 1 reaches sink
Optimized decoherence rates
probability that excitation in site 1 reaches sink
Simple demonstration proposed in ion trap set-up
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Quantum Simulation and ControlWP4.8 Selected
Results

• Unruh Effect

a
Uniform acceleration

• Need a quantum field with a low speed of light
• Need a detector that is sensitive to very low
  temperatures

• Yields more moderate acceleration requirement

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Quantum Simulation and ControlWP4.8 Selected
Results
Cigar shaped BEC
Narrow optical dipole trap
Retzker, Cirac, Plenio, Reznik, Phys. Rev. Lett.
101, 110402 (2008)
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Quantum Simulation and ControlWP4.8 Selected
Results
l Simulate local relaxation phenomena in quantum
many-body systems
l Consider sudden quenches from one
nearest-neighbor Hamiltonian to another
l Dynamics of quantum phase transitions,
apparent relaxation phenomena
l Quantum simulations with cold atoms in optical
superlattices
Cramer, Dawson, Eisert, Osborne, Phys Rev Lett
100 (2008) Cramer, Flesch, McCulloch,
Schollwoeck, Eisert, Phys Rev Lett 101 (2008)
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Quantum Simulation and ControlWP4.8 Selected
Results
M.J. Hartmann, F.G.S.L. Brandão and M.B.
PlenioComplex dynamics in coupled arrays of
micro-cavitiesInvited review for Laser
Photonics Review 2008 and E-print arXiv0808.2557
quant-ph
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Quantum Simulation and ControlWP4.8 Selected
Results

• Jahn-Teller model in ultra strongly coupled
  circuit QED.

a,a cavity field
ngt, number of Cooper pairs on junction
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Quantum Simulation and ControlWP4.8 Selected
Results

• Derived Hamiltonian

Coupling scales as inverse root of fine
structure constant
Much stronger than cavity QED Cannot make the
rotating wave approx.
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WP4.9 Generation and protection of multi-qudit
entangled states for cluster states and
investigation of phase transitions-Selected
Results

Multimode bosonic system with a total of n bosons
distributed between modes. Prepare modes in Fock
states ? entangled state (occup.
number) Interaction with phase sensitive
reservoir (squeezed vacuum) ? steady state is
multimode entangled. Resource for cluster state
generation, quantum phase transitions
For example, a steady state of a 4-mode system
with two bosons is
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WP4.9 Generation and protection of multi-qudit
entangled states for cluster states and
investigation of phase transitions-Selected
Results

Decay Rate of Cyclotron Modes

• Each mode is represented by one trapped
  electron,
• Two trapped electrons are enclosed in a cavity
  resonant with a transition frequency ?,
• Axial frequency of a trapping potential is ?z,
• Electric field on the electrode frequency is ?c,
• Distance between two traps/electrons is d,