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Simon Gartmann and Tranquillo Janisch
Theory
Quantum Teleportation: Concept
Definition: Transferring an unknown quantum state without transferring the physical carrier of information itself
Quantum Teleportation: Concept
Definition: Transferring an unknown quantum state without transferring the physical carrier of information itself
Means:
• Using non-local correlation
• Exchange of classical information
Quantum Teleportation: Protocol
1. Creation of an entangled pair shared between Alice and Bob
Quantum Teleportation: Protocol
1. Creation of an entangled pair shared between Alice and Bob
2. Alice does a two-qubit measurement identifying Bell states
Quantum Teleportation: Protocol
1. Creation of an entangled pair shared between Alice and Bob
2. Alice does a two-qubit measurement identifying Bell states
3. Feed-forward of the measurement result via a classical information channel from Alice to Bob
Quantum Teleportation: Circuit A
lice
B
ob
Figures: Steffen et al., Deterministic quantum teleportation with feed-forward in a solid state system, Nature 500, 319–322, 15.8.2013
Quantum Teleportation: Circuit
Hadamard gate:
CNOT:
Alic
e
Bo
b
Quantum Teleportation: Circuit
Four entangled Bell States
AND
Quantum Teleportation: Circuit A
lice
B
ob
Quantum Teleportation: Circuit
State to be teleported:
Bell-State:
Alic
e
Bo
b
Quantum Teleportation: Circuit
State to be teleported:
Bell-State:
Alic
e
Bo
b
Quantum Teleportation: Circuit
State to be teleported:
Bell-State:
After CNOT:
Alic
e
Bo
b
Quantum Teleportation: Circuit A
lice
B
ob
Quantum Teleportation: Circuit
Hadamardgate gives:
Alic
e
Bo
b
Quantum Teleportation: Circuit A
lice
B
ob
Quantum Teleportation: Circuit
Measurement: AND
Alic
e
Bo
b
Quantum Teleportation: Circuit
Measurement: AND
Thats the reason we need to feed-forward classical information!
Alic
e
Bo
b
Feed-forward
Nothing to do
Apply X
Apply Z
Apply X than Z
Mea
sure
men
t
Experimental Challenges
• Entanglement in macroscopic system
Experimental Challenges
• Entanglement in macroscopic system
• Distinguish bell-states in single shot
Experimental Challenges
• Entanglement in macroscopic system
• Distinguish bell-states in single shot
• Feed-forward of classical information in real time
Setup
Reminder: Transmon
Superconducting charge qubit
Figure: Wallraff et al., Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics, Nature 431, 162-167, 9.9.2004
Cg
Cj, Ej φ
Reminder: Transmon
Superconducting charge qubit
Frequency is tunable by
applying flux
Figure: Wallraff et al., Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics, Nature 431, 162-167, 9.9.2004
Cg
Cj, Ej φ
Reminder: Transmon
Superconducting charge qubit
Frequency is tunable by
applying flux
Resilient to charge noise
Figure: Wallraff et al., Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics, Nature 431, 162-167, 9.9.2004
Cg
Cj, Ej φ
Circuit implementation
Figures: Steffen et al., Deterministic quantum teleportation with feed-forward in a solid state system, Nature 500, 319–322, 15.8.2013
Circuit implementation Q1, Q2, Q3: Qubits
Figures: Steffen et al., Deterministic quantum teleportation with feed-forward in a solid state system, Nature 500, 319–322, 15.8.2013
Circuit implementation Q1, Q2, Q3: Qubits
R1, R2, R3: Resonators
Figures: Steffen et al., Deterministic quantum teleportation with feed-forward in a solid state system, Nature 500, 319–322, 15.8.2013
Circuit implementation Q1, Q2, Q3: Qubits
R1, R2, R3: Resonators
Red: Resonator input/output lines
Figures: Steffen et al., Deterministic quantum teleportation with feed-forward in a solid state system, Nature 500, 319–322, 15.8.2013
Circuit implementation Q1, Q2, Q3: Qubits
R1, R2, R3: Resonators
Red: Resonator input/output lines
Green: Microwave charge gate lines
Figures: Steffen et al., Deterministic quantum teleportation with feed-forward in a solid state system, Nature 500, 319–322, 15.8.2013
Circuit implementation Q1, Q2, Q3: Qubits
R1, R2, R3: Resonators
Red: Resonator input/output lines
Green: Microwave charge gate lines
Blue: flux-bias lines
Figures: Steffen et al., Deterministic quantum teleportation with feed-forward in a solid state system, Nature 500, 319–322, 15.8.2013
Process
Figures: Steffen et al., Deterministic quantum teleportation with feed-forward in a solid state system, Nature 500, 319–322, 15.8.2013
Process
Figures: Steffen et al., Deterministic quantum teleportation with feed-forward in a solid state system, Nature 500, 319–322, 15.8.2013
Read-out
JPA: Josephson parametric amplifier
Figures: Steffen et al., Deterministic quantum teleportation with feed-forward in a solid state system, Nature 500, 319–322, 15.8.2013
Read-out
HEMT: High electron mobility transistor
(amplifier)
JPA: Josephson parametric amplifier
Figures: Steffen et al., Deterministic quantum teleportation with feed-forward in a solid state system, Nature 500, 319–322, 15.8.2013
Read-out
RT: room temperature amplifier
HEMT: High electron mobility transistor
(amplifier)
JPA: Josephson parametric amplifier
Figures: Steffen et al., Deterministic quantum teleportation with feed-forward in a solid state system, Nature 500, 319–322, 15.8.2013
Read-out IF: Converts signal to intermediate frequency
RT: room temperature amplifier
HEMT: High electron mobility transistor
(amplifier)
JPA: Josephson parametric amplifier
Figures: Steffen et al., Deterministic quantum teleportation with feed-forward in a solid state system, Nature 500, 319–322, 15.8.2013
Read-out IF: Converts signal to intermediate frequency
RT: room temperature amplifier
HEMT: High electron mobility transistor
(amplifier)
JPA: Josephson parametric amplifier
• Qubits Q1/Q3 couple to resonators R1/R3.
Figures: Steffen et al., Deterministic quantum teleportation with feed-forward in a solid state system, Nature 500, 319–322, 15.8.2013
Read-out IF: Converts signal to intermediate frequency
RT: room temperature amplifier
HEMT: High electron mobility transistor
(amplifier)
JPA: Josephson parametric amplifier
• Qubits Q1/Q3 couple to resonators R1/R3.
• Measure amplitude and phase of the transmitted signal.
Figures: Steffen et al., Deterministic quantum teleportation with feed-forward in a solid state system, Nature 500, 319–322, 15.8.2013
Single-shot measurement
Figures: Steffen et al., Deterministic quantum teleportation with feed-forward in a solid state system, Nature 500, 319–322, 15.8.2013
Single-shot measurement • Single-shot measurement yields 1
data point.
Figures: Steffen et al., Deterministic quantum teleportation with feed-forward in a solid state system, Nature 500, 319–322, 15.8.2013
Single-shot measurement • Single-shot measurement yields 1
data point.
• Ideally cluster size << cluster
separation
Figures: Steffen et al., Deterministic quantum teleportation with feed-forward in a solid state system, Nature 500, 319–322, 15.8.2013
Single-shot measurement • Single-shot measurement yields 1
data point.
• Ideally cluster size << cluster
separation
• Achieved fidelity of 81.8%
Figures: Steffen et al., Deterministic quantum teleportation with feed-forward in a solid state system, Nature 500, 319–322, 15.8.2013
Feed-forward • Implemented with a field-
programmable gate array (FPGA)
Figures: Steffen et al., Deterministic quantum teleportation with feed-forward in a solid state system, Nature 500, 319–322, 15.8.2013
Feed-forward • Implemented with a field-
programmable gate array (FPGA)
• Total time delay for feed-forward
is 505 ns
Figures: Steffen et al., Deterministic quantum teleportation with feed-forward in a solid state system, Nature 500, 319–322, 15.8.2013
Feed-forward • Implemented with a field-
programmable gate array (FPGA)
• Total time delay for feed-forward
is 505 ns
• To avoid decoherence of Q3
during this, apply series of
dynamical decoupling pulses
Figures: Steffen et al., Deterministic quantum teleportation with feed-forward in a solid state system, Nature 500, 319–322, 15.8.2013
Results
Principal scheme
Each step causes fidelity losses.
Any delay can lead to decoherence.
Entangled state
preparation
Projective measurement
in Bell basis
Correction by single-qubit
rotations
Post-selection
• Measurement in Bell basis
Post-selection
• Measurement in Bell basis
• Determine whether result is or not
Figures: Steffen et al., Deterministic quantum teleportation with feed-forward in a solid state system, Nature 500, 319–322, 15.8.2013
Post-selection
• Measurement in Bell basis
• Determine whether result is or not
• Can post-select on other states by pre-rotating qubits (rotate other state to , , then measure it)
Post-selection
• Measurement in Bell basis
• Determine whether result is or not
• Can post-select on other states by pre-rotating qubits
• Time scale: 400 ns
Post-selection
• Measurement in Bell basis
• Determine whether result is or not
• Can post-select on other states by pre-rotating qubits
• Time scale: 400 ns
→No simultaneous distinction of all four Bell states and no feed-forward.
Post-selection process tomography
Average process fidelity: 72.0 ± 1.4 % Average state transfer fidelity: 81.7 ± 1.4 %
Figures: Steffen et al., Deterministic quantum teleportation with feed-forward in a solid state system, Nature 500, 319–322, 15.8.2013
Simultaneous deterministic measurement
• Measurement in Bell basis
Simultaneous deterministic measurement
• Measurement in Bell basis
• Distinguish between all 4 Bell states in real time.
Figures: Steffen et al., Deterministic quantum teleportation with feed-forward in a solid state system, Nature 500, 319–322, 15.8.2013
Simultaneous deterministic measurement
• Measurement in Bell basis
• Distinguish between all 4 Bell states in real time.
• Time scale: 600 ns
Simultaneous deterministic measurement
• Measurement in Bell basis
• Distinguish between all 4 Bell states in real time.
• Time scale: 600 ns
→ No feed forward
Simultaneous deterministic measurement process tomography
Average process fidelity: 65.5 ± 1.1 % (72.0 %) Average state transfer fidelity: 77.1 ± 1.2 % (81.7%)
Figures: Steffen et al., Deterministic quantum teleportation with feed-forward in a solid state system, Nature 500, 319–322, 15.8.2013
Full scheme
• Measurement in Bell basis
Full scheme
• Measurement in Bell basis
• Distinguish between all 4 Bell states in real time
Full scheme
• Measurement in Bell basis
• Distinguish between all 4 Bell states in real time
• Apply single-qubit rotation to Q3 if necessary
Full scheme
• Measurement in Bell basis
• Distinguish between all 4 Bell states in real time
• Apply single-qubit rotation to Q3 if necessary
• Time scale: 700 ns
Full scheme process tomography
Average process fidelity: 62.2 ± 0.3 % (65.5%) Average state transfer fidelity: 77.4 ± 0.2 % (77.1%)
Figures: Steffen et al., Deterministic quantum teleportation with feed-forward in a solid state system, Nature 500, 319–322, 15.8.2013
Results Comparison
Post-selection Simultaneous deterministic measurement
Full Classically expected
Average process fidelity
( 72.0 ± 1.4 ) % ( 65.5 ± 1.1 ) % ( 62.2 ± 0.3 ) % 1/2
Average state-transfer fidelity
( 81.7 ± 1.4 ) % ( 77.1 ± 1.2 ) % ( 77.4 ± 0.2 ) % 2/3
What was achieved?
• Realization of full deterministic quantum teleportation in a macroscopic system
– QM experiments on macroscopic scale
What was achieved?
• Realization of full deterministic quantum teleportation in a macroscopic system
– QM experiments on macroscopic scale
• Demonstrated a feed-forward implementation
– Application in error correction schemes
What was achieved?
• Realization of full deterministic quantum teleportation in a macroscopic system
– QM experiments on macroscopic scale
• Demonstrated a feed-forward implementation
– Application in error correction schemes
• Low transmission loss of superconducting waveguides
– Possibly allowing larger teleportation distances
Circuit implementation R1, R2, R3: Resonators
Q1, Q2, Q3: Qubits
Red: Resonator input/output lines
Green: Microwave charge gate lines
Blue: flux-bias lines
Figures: Steffen et al., Deterministic quantum teleportation with feed-forward in a solid state system, Nature 500, 319–322, 15.8.2013
Post-selection
Simultaneous deterministic measurement
Full scheme
Figures: Steffen et al., Deterministic quantum teleportation with feed-forward in a solid state system, Nature 500, 319–322, 15.8.2013