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Experimental one-way quantum computing. Student presentation by Andreas Reinhard. Outline. Introduction Theory about OWQC Experimental realization Outlook. Introduction. Standard model: Computation is an unitary (reversible) evolution on the input qubits - PowerPoint PPT Presentation
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Experimental one-way quantum computing
Student presentation by
Andreas Reinhard
Outline
1. Introduction
2. Theory about OWQC
3. Experimental realization
4. Outlook
Introduction• Standard model:
– Computation is an unitary (reversible) evolution on the input qubits
– Balance between closed system and accessibility of qubits=> decoherence, errors
– Scalability is a problem
Introduction• A One-Way Quantum Computer1
proposed for a lattice with Ising-type next-neighbour interaction
– Hope that OWQM is more easlily scalable– Error threshold between 0.11% and 1.4% depending
on the source of the error2 (depolarizing, preparation, gate, storage and measurement errors)
– Start computation from initial "cluster" state of a large number of engangled qubits
– Processing = measurements on qubits => one-way, irreversible
1R. Raussendorf, H. J. Briegel, A One-Way Quantum Computer, PhysRevLett.86.5188, 20012R. Raussendorf, et al., A fault-tolerant one-way quantum computer, ph/050135v1, 2005
Cluster states• Start from highly entangled configuration of "physical"
qubits.Information is encoded in the structure: "encoded" qubits
• quantum processing = measurements on physical qubits• Measure "result" in output qubits
• How to entangle the qubits?
Entanglement of qubits with CPhase operations
• Computational basis: • Notation:
• Prepare "physical" 2-qubit state (not entangled)
• CPhase operation =>highly entangled state
1 1 2 2
1 1 10 1 0 1 00 10 01 11
22 2
0 , 1
1 2
100 10 01 11
2 –
Cluster states
• Prepare the 4-qubit state
• and connect "neighbouring" qubits with CPhase operations.The final state is highly entangled:
• Nearest neighbour interaction sufficient for full entanglement!
1+ 0 1
2 where
10 1
2
0 0
0 111 02
1 1
Cluster state
Operations on qubits
• Prepare cluster state
• We can measure the state of qubit j in an arbitrarily chosen basis
• Consecutive measurements on qubits 1, 2, 3 disentangle the state and completely determine the state of qubit 4.
• The state of "output" qubit 4 isdependent on the choses bases.
• That‘s the way a OWQC works!
1+ , where 0 1
2i
j j j j j jB e
A Rotation• Disentangle qubit 1 from qubits 2, 3, 4
• and project the state on => post selection
2 22 3 4
2 22 3 4
2 3 41 1
2 3 4 2 22 3 4
2 22 3 4
cos sin2 2
cos sin2 20
0 01
sin cos2 2
sin cos2 2
i i
i i
i i
i i
e e i
e e i
e i e
e i e
( ) ( )
1 2 3 4 0 R R other 3 termsx z
2 3
Single qubit rotation
SU(2) rotation & gates• A general SU(2) rotation and 2-qubit gates
• CPhase operations + single qubit rotations = universal quantum computer!
A one-way Quantum Computer
• Initial cluster structure <=> algorithm
• The computation is performed with consecutive measurements in the proper bases on the physical qubits.
• Classical feedforward makesa OWQC deterministic
Clusters are subunits of larger clusters.
Experimental realization1
• A OWQC using 4 entangled photons
• Polarization states of photons = physical qubits
• Measurements easily performable. Difficulty: Preperation of the cluster state
1P. Walther, et al, Experimental one-way quantum computing, Nature, 434, 169 (2005)
Experimental setup• Parametric down-conversion with
a nonlinear crystal
• PBS transmits H photons and reflects V photons
• 4-photon events:
• => Highly entangled state
• Entanglement achieved through post-selection
• Equivalent to proposed cluster state under unitary transformations on single qubits
HHHH HHVV VVHH VVVV
State tomography• Prove successful generation of cluster state => density matrix
• Measure expectation values
in order to determine all elements
• Fidelity:
2
H ,
V ,
1A B C D with A , B , C , D H V ,2
1H V
2
Cluster
i
0.63 0.02Cluster ClusterF
Realization of a rotationand a 2-qubit gate
• Output characterized by state tomography
• Rotation:
• 2-qubit CPhase gate:
2 0.86 0.03
0.85 0.044 20.83 0.030
F
0
0.84 0.03F
Problems of this experiment
• Noise due to imperfect phase stability in the setup (and other reasons). => low fidelity
• Scalability: probability of n-photon coincidence decreases exponentially with n
• No feedforward• No storage• Post selection
=> proof of principle experiment
Outlook• 3D optical lattices with Ising-type interacting
atoms
• Realization of cluster states on demand with a large number of qubits
• Cluster states of Rb-atoms realized in an optical lattice1
– Filling factor a problem– Single qubit measurements not realized
(adressability)
1O. Mandel, I. Bloch, et al., Controlled collisions for multi-particle entanglement of optically trapped atoms, Nature 425, 937 (2003)
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