Implementing arbitrary quantum operations via quantum walks on a cycle
graph
- URL: http://arxiv.org/abs/2210.14450v2
- Date: Thu, 13 Apr 2023 12:08:26 GMT
- Title: Implementing arbitrary quantum operations via quantum walks on a cycle
graph
- Authors: Jia-Yi Lin, Xin-Yu Li, Yu-Hao Shao, Wei Wang, and Shengjun Wu
- Abstract summary: We use a simple discrete-time quantum walk (DTQW) on a cycle graph to model an arbitrary unitary operation $U(N)$.
Our model is essentially a quantum neural network based on DTQW.
- Score: 8.820803742534677
- License: http://creativecommons.org/licenses/by-nc-sa/4.0/
- Abstract: The quantum circuit model is the most commonly used model for implementing
quantum computers and quantum neural networks whose essential tasks are to
realize certain unitary operations. Here we propose an alternative approach; we
use a simple discrete-time quantum walk (DTQW) on a cycle graph to model an
arbitrary unitary operation $U(N)$ without the need to decompose it into a
sequence of gates of smaller sizes. Our model is essentially a quantum neural
network based on DTQW. Firstly, it is universal as we show that any unitary
operation $U(N)$ can be realized via an appropriate choice of coin operators.
Secondly, our DTQW-based neural network can be updated efficiently via a
learning algorithm, i.e., a modified stochastic gradient descent algorithm
adapted to our network. By training this network, one can promisingly find
approximations to arbitrary desired unitary operations. With an additional
measurement on the output, the DTQW-based neural network can also implement
general measurements described by positive-operator-valued measures (POVMs). We
show its capacity in implementing arbitrary 2-outcome POVM measurements via
numeric simulation. We further demonstrate that the network can be simplified
and can overcome device noises during the training so that it becomes more
friendly for laboratory implementations. Our work shows the capability of the
DTQW-based neural network in quantum computation and its potential in
laboratory implementations.
Related papers
- Challenges and opportunities in the supervised learning of quantum
circuit outputs [0.0]
Deep neural networks have proven capable of predicting some output properties of relevant random quantum circuits.
We investigate if and to what extent neural networks can learn to predict the output expectation values of circuits often employed in variational quantum algorithms.
arXiv Detail & Related papers (2024-02-07T16:10:13Z) - Projected Stochastic Gradient Descent with Quantum Annealed Binary Gradients [51.82488018573326]
We present QP-SBGD, a novel layer-wise optimiser tailored towards training neural networks with binary weights.
BNNs reduce the computational requirements and energy consumption of deep learning models with minimal loss in accuracy.
Our algorithm is implemented layer-wise, making it suitable to train larger networks on resource-limited quantum hardware.
arXiv Detail & Related papers (2023-10-23T17:32:38Z) - Implementing arbitrary quantum operations via quantum walks on a cycle
graph [9.463363607207679]
We use a simple discrete-time quantum walk (DTQW) on a cycle graph to model an arbitrary unitary operation.
Our model is essentially a quantum neural network based on DTQW.
Our work shows the capability of the DTQW-based neural network in quantum computation and its potential in laboratory implementations.
arXiv Detail & Related papers (2023-04-12T07:48:51Z) - Quantum neural networks [0.0]
This thesis combines two of the most exciting research areas of the last decades: quantum computing and machine learning.
We introduce dissipative quantum neural networks (DQNNs), which are capable of universal quantum computation and have low memory requirements while training.
arXiv Detail & Related papers (2022-05-17T07:47:00Z) - Pretraining Graph Neural Networks for few-shot Analog Circuit Modeling
and Design [68.1682448368636]
We present a supervised pretraining approach to learn circuit representations that can be adapted to new unseen topologies or unseen prediction tasks.
To cope with the variable topological structure of different circuits we describe each circuit as a graph and use graph neural networks (GNNs) to learn node embeddings.
We show that pretraining GNNs on prediction of output node voltages can encourage learning representations that can be adapted to new unseen topologies or prediction of new circuit level properties.
arXiv Detail & Related papers (2022-03-29T21:18:47Z) - A quantum algorithm for training wide and deep classical neural networks [72.2614468437919]
We show that conditions amenable to classical trainability via gradient descent coincide with those necessary for efficiently solving quantum linear systems.
We numerically demonstrate that the MNIST image dataset satisfies such conditions.
We provide empirical evidence for $O(log n)$ training of a convolutional neural network with pooling.
arXiv Detail & Related papers (2021-07-19T23:41:03Z) - Preparation of excited states for nuclear dynamics on a quantum computer [117.44028458220427]
We study two different methods to prepare excited states on a quantum computer.
We benchmark these techniques on emulated and real quantum devices.
These findings show that quantum techniques designed to achieve good scaling on fault tolerant devices might also provide practical benefits on devices with limited connectivity and gate fidelity.
arXiv Detail & Related papers (2020-09-28T17:21:25Z) - On the learnability of quantum neural networks [132.1981461292324]
We consider the learnability of the quantum neural network (QNN) built on the variational hybrid quantum-classical scheme.
We show that if a concept can be efficiently learned by QNN, then it can also be effectively learned by QNN even with gate noise.
arXiv Detail & Related papers (2020-07-24T06:34:34Z) - Recurrent Quantum Neural Networks [7.6146285961466]
Recurrent neural networks are the foundation of many sequence-to-sequence models in machine learning.
We construct a quantum recurrent neural network (QRNN) with demonstrable performance on non-trivial tasks.
We evaluate the QRNN on MNIST classification, both by feeding the QRNN each image pixel-by-pixel; and by utilising modern data augmentation as preprocessing step.
arXiv Detail & Related papers (2020-06-25T17:59:44Z) - Machine learning transfer efficiencies for noisy quantum walks [62.997667081978825]
We show that the process of finding requirements on both a graph type and a quantum system coherence can be automated.
The automation is done by using a convolutional neural network of a particular type that learns to understand with which network and under which coherence requirements quantum advantage is possible.
Our results are of importance for demonstration of advantage in quantum experiments and pave the way towards automating scientific research and discoveries.
arXiv Detail & Related papers (2020-01-15T18:36:53Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.