Experimental one-way quantum computing

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Experimental one-way quantum computing
Student presentation by Andreas Reinhard
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Outline

1. Introduction
2. Theory about OWQC
3. Experimental realization
4. Outlook

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Introduction

• Standard model
• Computation is an unitary (reversible) evolution
  on the input qubits
• Balance between closed system and accessibility
  of qubitsgt decoherence, errors
• Scalability is a problem

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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 gt one-way,
  irreversible

1R. Raussendorf, H. J. Briegel, A One-Way Quantum
Computer, PhysRevLett.86.5188, 2001 2R.
Raussendorf, et al., A fault-tolerant one-way
quantum computer, ph/050135v1, 2005
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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?

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Entanglement of qubits with CPhase operations

• Computational basis
• Notation
• Prepare "physical" 2-qubit state (not entangled)
• CPhase operation gthighly entangled state

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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!

Cluster state
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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.
• Thats the way a OWQC works!

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A Rotation

• Disentangle qubit 1 from qubits 2, 3, 4
• and project the state on gt
  post selection

Single qubit rotation
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SU(2) rotation gates

• A general SU(2) rotation and 2-qubit gates
• CPhase operations single qubit rotations
  universal quantum computer!

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A one-way Quantum Computer

• Initial cluster structure ltgt 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.
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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)
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Experimental setup

• Parametric down-conversion with a nonlinear
  crystal
• PBS transmits H photons and reflects V photons
• 4-photon events
• gt Highly entangled state
• Entanglement achieved through post-selection
• Equivalent to proposed cluster state under
  unitary transformations on single qubits

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State tomography

• Prove successful generation of cluster state gt
  density matrix
• Measure expectation valuesin order to
  determine all elements
• Fidelity

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Realization of a rotationand a 2-qubit gate

• Output characterized by state tomography
• Rotation
• 2-qubit CPhase gate

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Problems of this experiment

• Noise due to imperfect phase stability in the
  setup (and other reasons). gt low fidelity
• Scalability probability of n-photon coincidence
  decreases exponentially with n
• No feedforward
• No storage
• Post selection
• gt proof of principle experiment

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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)