Improving Qubit Readout with Autoencoders in Quantum Science Workshop
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Piero Luchi 8 September 2023
1
Quantum Science and Technology in Trento
ECT* workshop:
Many Body Quantum Physics and Machine Learning
Outline
1.
Dispersive qubit readout for superconducting qubits
2.
Standard readout models
3.
Improving qubit readout with autoencoders
2
•
Qubit - readout cavity system described by Jaynes-Cumming model:
Qubit – Cavity system
3
Dispersive Regime
4
•
Dispersive Readout approach
•
Write the equation in the dispersive regime
Dispersive approximation
Dispersive Qubit Readout
•
D
ispersive shift of the resonator frequency based on the state of the
qubit
•
Measurement
: Indirectly measuring the qubit state by measuring the resonator frequency
shift.
5
Dispersive Qubit Readout
6
Input signal
Full Demodulation
Output
signal
Signal manipulation
Results of Readout
•
According to the qubit state, the point
will fall in different part of the I-Q plane.
•
Labelled data:
Prepared in state 0 (or 1) and immediately measured.
7
Qubit Readout:
Classification
How to assign the correct label to each point?
8
?
Unlabelled data
Labelled data
Qubit Readout:
Classification
How to assign the correct label to each point?
•
Dataset
:
Prepare many times each state and measure it immediately
•
Methods :
1.
Gaussian Mixture models
2.
Neural Networks
3.
Neural Network with Autoencoder-type Pre-training
9
Readout Classification:
1. Gaussian Mixture Model (GMM)
10
Sharp edge
Optimize
parameters of a
superposition
of Gaussians
•
Real data
•
GMM labelled data
Problems
:
•
Incorrect
classification of
many points
•
Not good for long
or short
measurements
Qubit Readout:
Demodulation
11
Full Demodulation
Sliced Demodulation
Time average
Input signal
Output
signal
Signal manipulation
Turn to a finer-grained signal
Readout Classification:
2. Feed-Forward Neural Network (FFNN)
12
Lienhard, Benjamin, et al. "Deep-Neural-Network
Discrimination of Multiplexed Superconducting-Qubit
States."
Physical Review Applied
17.1 (2022): 014024.
Try to use all information available
Readout Classification:
Feed-Forward Neural Network (FFNN)
13
•
FFNN labelled data
•
Labelled (real) data
13
gradual
transition
Problems
:
•
Lower
performance for
long
measurements
Readout Classification:
3.
Autoencoder-type Pre-training
Neural Network
(PreTraNN)
14
•
An autoencoder an artificial neural
network that learn a compressed
representation of input data by
encoding it into a lower-dimensional
space and then decoding it back into
its original form.
•
It minimizes the reconstruction
error.
•
Feature extraction, dimensionality
reduction
•
Pre-training of feed-forward neural
network
Unsupervised
approach
14
Encoded/synthetic
representation
encoder
decoder
Input
Input
•
are noisy, difficult to discriminate.
•
h
should retain only the important features
of the readout signals
•
Inner dimension should be optimized.
Readout Classification:
3.
Autoencoder-type Pre-training
Neural Network
(PreTraNN)
•
We
train
the autoencoder on readout data
•
We obtain a low dimensional representation
h
of readout signals
15
Encoded
representation
Qubit Readout:
3.
Autoencoder-type Pre-training
Neural Network
16
•
Train
the
new neural network
on
the
encoded representation
h
of
the readout signals
, rather than on
the
readout signal itself
.
•
This should improve the
classification accuracy.
16
Neural network
LP et al.
Phys. Rev. Applied
20
, 014045 (2023)
Qubit Readout:
3.
Autoencoder-type Pre-training
Neural Network
17
•
Putting it all together...
17
Encoder
Neural network
LP et al.
Phys. Rev. Applied
20
, 014045 (2023)
Qubit Readout:
Summary
18
•
Gaussian
Mixture
•
Neural
Networks
•
PreTraNN
Classification accuracy:
Measurement duration
•
Wide range of measurement times.
•
Autoencoder method (PreTraNN)
has a better classification accuracy.
19
Classification accuracy:
Distributions
•
Neural network-based methods
produce more realistic distributions.
20
GMM
exact
74,4
PreTraNN
20
Conclusions
1.
Dispersive readout in superconducting qubits
2.
Common techniques to classify readout data
3.
Autoecoder-based model to improve the classification accuracy
21
22
Dispersive qubit readout, standard models, and the use of autoencoders for improving qubit readout in quantum science are discussed in the workshop led by Piero Luchi. The workshop covers topics such as qubit-cavity systems, dispersive regime equations, and the classification of qubit states through various methods like Gaussian Mixture Models and Neural Networks with Autoencoder-type Pre-training.
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Presentation Transcript
Improving Qubit Readout Improving Qubit Readout with Autoencoders with Autoencoders Quantum Science and Technology in Trento Piero Luchi 8 September 2023 ECT* workshop: Many Body Quantum Physics and Machine Learning 1
Outline 1. Dispersive qubit readout for superconducting qubits 2. Standard readout models 3. Improving qubit readout with autoencoders 2
Qubit Cavity system Qubit - readout cavity system described by Jaynes-Cumming model: 3
Dispersive Regime Dispersive Readout approach Write the equation in the dispersive regime Dispersive approximation 4
Dispersive Qubit Readout Dispersive shift of the resonator frequency based on the state of the qubit Measurement: Indirectly measuring the qubit state by measuring the resonator frequency shift. 5
Dispersive Qubit Readout Input signal signal ? ? Q Full Demodulation Output signal I 6
Results of Readout According to the qubit state, the point will fall in different part of the I-Q plane. Labelled data: Prepared in state 0 (or 1) and immediately measured. 7
Qubit Readout: Classification How to assign the correct label to each point? Labelled data Unlabelled data ? 8
Qubit Readout: Classification How to assign the correct label to each point? Dataset: Prepare many times each state and measure it immediately Methods : 1. Gaussian Mixture models 2. Neural Networks 3. Neural Network with Autoencoder-type Pre-training 9
Readout Classification: 1. Gaussian Mixture Model (GMM) GMM labelled data Real data Optimize parameters of a superposition of Gaussians Problems: Incorrect classification of many points Not good for long or short measurements Sharp edge 10
Qubit Readout: Demodulation Input signal Sliced Demodulation Turn to a finer-grained signal signal ? ? Full Demodulation Q Output signal I 11
Readout Classification: 2. Feed-Forward Neural Network (FFNN) Try to use all information available Lienhard, Benjamin, et al. "Deep-Neural-Network Discrimination of Multiplexed Superconducting-Qubit States." Physical Review Applied 17.1 (2022): 014024. 12
Readout Classification: Feed-Forward Neural Network (FFNN) FFNN labelled data Labelled (real) data Problems: Lower performance for long measurements gradual transition 13
Readout Classification: 3. Autoencoder-type Pre-trainingNeural Network (PreTraNN) An autoencoder an artificial neural network that learn a compressed representation of input data by encoding it into a lower-dimensional space and then decoding it back into its original form. Unsupervised approach encoder decoder Input Input It minimizes the reconstruction error. Feature extraction, dimensionality reduction Pre-training of feed-forward neural network Encoded/synthetic representation 14 14
Readout Classification: 3. Autoencoder-type Pre-trainingNeural Network (PreTraNN) We train the autoencoder on readout data We obtain a low dimensional representation h of readout signals are noisy, difficult to discriminate. h should retain only the important features of the readout signals Encoded representation Inner dimension should be optimized. 15
Qubit Readout: 3. Autoencoder-type Pre-trainingNeural Network Train the new neural network on the encoded representation h of the readout signals, rather than on the readout signal itself. This should improve the classification accuracy. Neural network LP et al. Phys. Rev. Applied 20, 014045 (2023) 16 16
Qubit Readout: 3. Autoencoder-type Pre-trainingNeural Network Putting it all together... Encoder Neural network LP et al. Phys. Rev. Applied 20, 014045 (2023) 17 17
Qubit Readout: Summary Gaussian Mixture Neural Networks PreTraNN 18
Classification accuracy: Measurement duration Wide range of measurement times. Autoencoder method (PreTraNN) has a better classification accuracy. 19
Classification accuracy: Distributions PreTraNN GMM exact 74,4 Neural network-based methods produce more realistic distributions. Readout 8000 ns 20 20
Conclusions 1. Dispersive readout in superconducting qubits 2. Common techniques to classify readout data 3. Autoecoder-based model to improve the classification accuracy 21
