Theory - qudev.phys.ethz.ch · JPA: Josephson parametric amplifier • Qubits Q1/Q3 couple to...

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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

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

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:

Four entangled Bell States

State to be teleported:

Bell-State:

After CNOT:

Hadamardgate gives:

Measurement: AND

Thats the reason we need to feed-forward classical information!

Feed-forward

Nothing to do

Apply X

Apply Z

Apply X than Z

Experimental Challenges

• Entanglement in macroscopic system

• Distinguish bell-states in single shot

• Feed-forward of classical information in real time

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

Cj, Ej φ

Reminder: Transmon

Frequency is tunable by

applying flux

Cj, Ej φ

Reminder: Transmon

Frequency is tunable by

applying flux

Resilient to charge noise

Cj, Ej φ

Circuit implementation

Circuit implementation Q1, Q2, Q3: Qubits

R1, R2, R3: Resonators

Red: Resonator input/output lines

Green: Microwave charge gate lines

Blue: flux-bias lines

Process

Read-out

JPA: Josephson parametric amplifier

Read-out

HEMT: High electron mobility transistor

(amplifier)

Read-out

RT: room temperature amplifier

(amplifier)

Read-out IF: Converts signal to intermediate frequency

(amplifier)

• Qubits Q1/Q3 couple to resonators R1/R3.

(amplifier)

• Qubits Q1/Q3 couple to resonators R1/R3.

• Measure amplitude and phase of the transmitted signal.

Single-shot measurement

Single-shot measurement • Single-shot measurement yields 1

data point.

• Ideally cluster size << cluster

separation

data point.

• Ideally cluster size << cluster

separation

• Achieved fidelity of 81.8%

Feed-forward • Implemented with a field-

programmable gate array (FPGA)

• Total time delay for feed-forward

is 505 ns

• Total time delay for feed-forward

is 505 ns

• To avoid decoherence of Q3

during this, apply series of

dynamical decoupling pulses

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

• Determine whether result is or not

Post-selection

• Can post-select on other states by pre-rotating qubits (rotate other state to , , then measure it)

Post-selection

• Can post-select on other states by pre-rotating qubits

• Time scale: 400 ns

Post-selection

• Can post-select on other states by pre-rotating qubits

→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 %

Simultaneous deterministic measurement

• Distinguish between all 4 Bell states in real time.

→ 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%)

Full scheme

• Distinguish between all 4 Bell states in real time

Full scheme

• Apply single-qubit rotation to Q3 if necessary

Full scheme

• Apply single-qubit rotation to Q3 if necessary

Full scheme process tomography

Average process fidelity: 62.2 ± 0.3 % (65.5%) Average state transfer fidelity: 77.4 ± 0.2 % (77.1%)

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?

• Demonstrated a feed-forward implementation

– Application in error correction schemes

What was achieved?

• 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

Blue: flux-bias lines

Post-selection

Full scheme

Theory - qudev.phys.ethz.ch · JPA: Josephson parametric amplifier • Qubits Q1/Q3 couple to...

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