Navigating the Noisy Quantum Landscape: A Look at Generalization in Quantum Machine Learning

As a quantum machine learning (QML) researcher, I’m constantly fascinated by quantum computers’ potential to revolutionize the way we learn from data. We’re living in a time when quantum computers are starting to become a reality, and their potential to revolutionize machine learning is simply mind-blowing. But there’s a catch, and it’s a big one: noise.

Right now, we’re in the era of Noisy Intermediate-Scale Quantum (NISQ) devices. These early quantum computers are incredibly powerful, but they’re also extremely sensitive to errors. And when it comes to machine learning, these errors can be a real deal-breaker. That’s because a core principle of machine learning is generalization: the ability of a model to perform well on unseen data. If our quantum machine learning models are constantly being tripped up by noise, how can we trust them to make accurate predictions in the real world?

That’s where generalization bounds come into play. These are mathematical guarantees that tell us how well a model is expected to perform on unseen data. In the classical realm, generalization bounds are well-established and have proven invaluable in guiding model development and deployment. However, in the quantum domain, particularly in the context of NISQ devices, these bounds are still being actively explored and refined.

We recently published a systematic mapping study article, “Generalization error bound for quantum machine learning in NISQ era—a survey,” that specifically focuses on the generalization bounds for supervised QML in the NISQ era. Our work meticulously analyzed 37 (out of 544) relevant research articles to understand the current state-of-the-art and identify trends and challenges in this critical area. Their work provides valuable insights that can guide future research and development in QML.

Let’s take a look at some of the key findings of this study.

Quantum Noisy Channel Limits Current Quantum Machine Learning Capabilities

The idea behind QML is to leverage the unique properties of quantum systems, like superposition and entanglement, to develop algorithms that can outperform classical machine learning approaches for certain tasks. And our findings do suggest that this quantum advantage is within reach. For instance, some of the generalization bounds proposed in the considered literature suggest that QML models can achieve better performance with smaller datasets compared to classical models, especially when dealing with high-dimensional data. This is huge! Imagine being able to train powerful machine learning models with a fraction of the data we need today. But there’s a flip side. These same bounds also highlight the delicate interplay between noise, model complexity, and generalization. Deeper quantum circuits, while potentially more expressive, are particularly vulnerable to noise accumulation, leading to degradation in performance. This means that while we might be able to achieve a quantum advantage, we need to be very careful about how we design our QML models. We need to strike a balance between expressiveness and noise resilience, which is no easy feat.

Measurement Does Introduce Error

Here’s another wrinkle: measurement. It turns out that simply extracting information from a quantum system can introduce errors, and these errors can affect the generalization ability of our QML models. This means we can’t just focus on building fancy quantum algorithms; we also need to develop robust measurement strategies that minimize information loss. And this becomes even more critical in the presence of noise.

Dataset Choices in Quantum Machine Learning Reflect a Familiarity Bias

The study highlights an interesting trend in dataset selection for QML research. On the one hand, we see a lot of work using synthetic datasets specifically designed to showcase the potential of QML. This makes sense; we need to understand how these models work in ideal settings before we can tackle real-world problems. On the other hand, there’s also a tendency to use familiar classical datasets like MNIST and IRIS, which are benchmarks in the classical machine-learning world. Now, there’s nothing inherently wrong with using classical datasets, but it does raise a few concerns. First, it creates a temptation to directly compare the performance of QML models with their classical counterparts, which might not be the most meaningful comparison. Remember, we’re not just trying to build quantum versions of classical algorithms; we’re trying to tap into something fundamentally different. Second, these classical datasets might not be the best for highlighting the specific advantages of quantum algorithms. They might not even be solvable more efficiently on a quantum computer! This reliance on familiar datasets, while useful for benchmarking and comparison, can inadvertently lead to what I call “familiarity bias.”

We risk falling into the trap of constantly comparing quantum models to classical counterparts, potentially obscuring the specific advantages quantum algorithms might offer. The question then becomes: Are we prioritizing familiarity over the pursuit of quantum advantage?

The Frequent Use of IBM’s Quantum Platforms May Lead to Research Bias

Another interesting tidbit from our findings is the apparent popularity of the IBM Quantum Platform among researchers. While this platform is certainly a frontrunner in the quantum computing race, this preference could lead to research biases. Different quantum computing platforms have different noise characteristics, gate fidelities, and qubit connectivity, all of which can affect algorithm performance. So, if we’re primarily focusing on one platform, we might be missing out on valuable insights that other platforms could offer.

Classical Optimization Techniques is an Intermediate Stop

Another interesting observation is the widespread use of classical optimization techniques like stochastic gradient descent (SGD) and backpropagation in QML. While these techniques have proven incredibly successful in classical machine learning, their suitability for optimizing quantum circuits, particularly in the presence of noise, is still a topic of active debate. While there have been quite a few works on the ‘Parameter-shift’, ‘finite differential’, and ‘Hadamard test’ gradient approach our study emphasizes that the highly non-convex optimization landscape of quantum models can significantly limit the effectiveness of classical techniques.

This raises the question: Are we limiting the potential of QML by relying on classical optimization techniques? Perhaps exploring and developing quantum-specific optimization algorithms could lead to more efficient and effective training procedures.

Quantum Kernels Offer Advantages But Require Further Exploration

A significant portion of the analyzed research focuses on quantum kernel methods. These methods aim to leverage the mathematical power of kernel theory within a quantum framework, potentially leading to improved generalization capabilities for QML models. The study also points out that quantum kernel methods can often achieve competitive performance with simpler circuit architectures compared to other QML approaches, which is particularly advantageous in the noise-prone NISQ era.

However, as promising as they are, quantum kernels aren’t without their challenges. Research suggests that under certain conditions, the values of quantum kernels can exhibit exponential concentration, leading to poor generalization performance. This phenomenon highlights the need for a deeper understanding of the interplay between kernel design, data embedding, and noise mitigation strategies.

Quantum Machine Learning Research Is Exploring a Variety of Approaches

We found the diversity in research approaches, with a mix of theoretical and empirical work, and a particular focus on kernel methods and ensemble learning. While this diversity is valuable, it also risks fragmenting the field. We need a more unified approach, one that combines the rigor of theoretical analysis with the practicality of experimental validation. While theoretical bounds provide valuable insights into the expected behavior of quantum models, their practical relevance hinges on their validation under realistic, noisy conditions. This calls for a more collaborative and iterative approach to research, where theoretical insights guide experimental design, and experimental findings inform further theoretical development.

The Field of Quantum Machine Learning Needs a Unified Approach

The findings of this study reinforce the idea that QML is a nascent field, full of potential but facing unique challenges in the NISQ era. To effectively navigate these challenges, we, as a community, need to adopt a more unified and collaborative approach. This involves:

Sharing knowledge: Openly sharing insights about generalization bounds, measurement complexities, dataset choices, and optimization techniques will accelerate the overall progress of the field.
Embracing diversity: While standardization can be beneficial, we shouldn’t limit ourselves to a single platform, such as IBM hardware, or a narrow set of techniques. Exploring diverse platforms and approaches will lead to a more robust and adaptable field.
Prioritizing quantum-specific solutions: While borrowing from classical techniques can be helpful, we must actively invest in developing quantum-specific algorithms and optimization strategies to fully unlock the power of quantum computing in machine learning.

Future Quantum Machine Learning Research Must Address Several Challenges

Navigating the noisy quantum landscape is not going to be easy. But the potential rewards are simply too great to ignore. As we move forward, we need to focus on:

Developing generalization bounds and other metrics that accurately reflect the challenges of the NISQ era.
Designing robust QML algorithms that can tolerate noise and efficiently extract information from quantum systems.
Exploring a diverse range of datasets that can showcase the unique advantages of quantum algorithms.
Embracing a multi-platform approach to ensure the reproducibility and generalizability of research findings.

The quest for a quantum advantage in machine learning is just beginning. And while there are many hurdles to overcome, the journey itself is a testament to human ingenuity. I, for one, am excited to see what the future holds for this revolutionary field.

For a detailed exploration of the methodology and findings, read the full paper here.

References

Khanal, B., Rivas, P., Sanjel, A. et al. Generalization error bound for quantum machine learning in NISQ era—a survey. Quantum Mach. Intell. 6, 90 (2024). https://doi.org/10.1007/s42484-024-00204-w

About the Author

Bikram Khanal is a Ph.D. student at Baylor University, specializing in Quantum Machine Learning and Natural Language Processing.

Learning Robust Observable to Address Noise in Quantum Machine Learning

In the rapidly evolving field of Quantum Machine Learning (QML), one of the most pressing challenges is handling noise—the errors that naturally arise in quantum systems, particularly in the Noisy Intermediate-Scale Quantum (NISQ) era. But what if we could teach quantum systems to “learn” and address noise head-on? Our paper “Learning Robust Observable to Address Noise in Quantum Machine Learning” explores an approach to mitigating this issue by focusing on learning robust observables. These observables can withstand the effects of noise, improving the performance of QML models in noisy environments.

Understanding the Problem of Noise in QML

In quantum systems, noise comes from imperfections in quantum gates, interactions with the environment, and decoherence—making quantum computations highly error-prone. When applying QML, this noise leads to inaccuracies in predictions and model training. This research aims to identify observables that remain invariant or change minimally even in the presence of noise, thus offering more reliable outputs from quantum systems.

The Framework: Learning Robust Observables

We propose a machine learning-based framework to find observables that are inherently resistant to various types of noise. To tackle this, we propose training a machine learning model to identify observables that remain invariant or less susceptible to noise. The model learns from the behavior of quantum states passing through noisy channels and adjusts to find robust observables that maintain their integrity despite noise. We illustrate the problem using a Bell state (a well-known quantum state), subjecting it to a depolarization channel to simulate noise.

The process can be formalized as an optimization problem where the goal is to minimize the change in the expectation value of the observable when the quantum state is subject to noise. Mathematically, this can be expressed as minimizing:

$\min⁡_{\mathcal{O}}\mathbb{E}[ \left | \langle{\psi}| \mathcal{O} |{\psi} \rangle - \langle{\psi} | \mathcal{O}_n |{\psi} \rangle ]$

Here, $\mathcal{O}$ is a Pauli-Z observable, and $\mathcal{O}_n$ is an observable we are trying to learn. The expectation value is computed before and after noise is introduced. The goal is to find an observable that minimizes this difference, effectively learning a robust observable.

A Toy Example

In our framework, we train QML models by simulating quantum systems across different noise channels, including depolarization, amplitude damping, phase damping, bit flip, and phase flip channels. The objective is to learn observables for various quantum circuits—such as Bell state circuits, Quantum Fourier Transform circuits, and highly entangled random circuits—that can remain robust across different noise levels. The framework demonstrated that it could identify an observable that better retains the state’s properties under noisy conditions, proving that robust observables can be learned effectively.

Consider the following example:

(1) $\begin{equation*} O_{optimized} = \begin{pmatrix} 0.804 & 0.086 + 0.138i & 0.739 + 0.050i & 0.070 + 0.132i\\ 0.086 - 0.138i & 0.302 & 0.087 - 0.122i & 0.277 + 0.019i \\0.739 - 0.050i & 0.087 + 0.122i & 1.253 & 0.133 + 0.215i \\ 0.070 - 0.132i & 0.277 - 0.019i & 0.133 - 0.215i & 0.470\end{pmatrix}\end{equation*}$

We computed its expectation value for Bell’s states under varying degrees of depolarization, $p \in [0,1)$ . The expectation values of the observable $O_{optimized}$ on the depolarized Bell state as a function of the depolarization rate $p$ are plotted in the following figure.

In this figure, $Z$ is the Pauli-Z matrix, $X$ is the Pauli-X matrix, $H$ is the Hadamard gate, $A$ is an arbitrary observable, and $O_{optimized}$ is a learned single qubit Hermitian measurement operator. This toy example shows that the expectation value of the custom observable $O_{optimized}$ on the depolarized Bell state remains constant as the depolarization rate $p$ increases.

Key Findings

Custom observables designed through this method demonstrated remarkable stability against noise, especially when compared to traditional observables like Pauli matrices.
In noisy channels like depolarization, the learned observables maintained a more consistent expectation value, while traditional observables exhibited greater variance.
The approach can be applied to various types of quantum circuits, making it versatile and broadly applicable in enhancing the reliability of QML models.

Implications for Quantum Machine Learning

This study offers a promising avenue for improving the accuracy and stability of QML in real-world applications. By learning robust observables, QML systems can perform more reliably, even as we contend with the inherent noise in current quantum computers. By using learned observables, the performance of quantum machine learning models can be made more stable, even when operating in the inherently noisy NISQ regime. This has implications for advancing practical applications of quantum computing, especially as we seek to scale up quantum algorithms in the near-term.

Looking Ahead: The Future of Noise-Resistant QML

The results from this paper open up exciting possibilities for future work. Imagine a future where every quantum machine learning algorithm can autonomously adjust to different noisy environments by learning which observables to trust. This would make QML models more resilient and, ultimately, more practical for real-world applications.

One immediate future direction is testing the framework on larger systems and more complex noise models. Additionally, combining this method with error correction techniques could further enhance the stability of QML algorithms.

For a detailed exploration of the methodology and findings, read the full paper at:

https://arxiv.org/pdf/2409.07632

References

Khanal, Bikram, and Pablo Rivas. “Learning Robust Observable to Address Noise in Quantum Machine Learning.” arXiv preprint arXiv:2409.07632 (2024).

About the Author

Bikram Khanal is a Ph.D. student at Baylor University, specializing in Quantum Machine Learning and Natural Language Processing.

Efficient Quantum Machine Learning with a Modified Depolarization Approach

As the quantum computing community navigates the NISQ (Noisy Intermediate-Scale Quantum) era, managing noise poses a prominent challenge, particularly in Quantum Machine Learning (QML). Quantum systems inherently exhibit noise, which can drastically impact computational accuracy. Notably, depolarization noise, a prevalent noise model in quantum computing, presents a formidable obstacle in developing efficient QML models. The paper “A Modified Depolarization Approach for Efficient Quantum Machine Learning” introduces a modified representation of the depolarization channel for a single-qubit. The proposed modified channel uses two Kraus operators based only on X and Z Pauli matrices. The approach reduces the computational complexity from six to four matrix multiplications per channel execution.

What’s Depolarization, and Why Does It Matter?

Depolarization is a noise process where a quantum state collapses, with some probability, into a mixed state, essentially scrambling the information. For example, imagine working with a quantum bit (qubit) represented by a density matrix $\rho$ . In the traditional depolarization model, noise can be introduced by applying the three Pauli matrices — X, Y, and Z to $\rho$ with equal probability. Mathematically, this looks like:

(1) $\begin{equation*} \rho \rightarrow (1 - p) \rho + \frac{p}{3} (X \rho X + Y \rho Y + Z \rho Z)\end{equation*}$

where $p$ is the probability of depolarization. Each of the Pauli operators represents a potential disturbance to the qubit. The more noise we apply, the more the system deteriorates. However, simulating this noise is computationally expensive, especially in large quantum systems, as it requires a substantial number of matrix multiplications. This is where the paper’s novel contribution shines.

The Power of Modified Depolarization Channel and Two Kraus Operators

The central innovation of this paper is an alternative representation of the depolarization channel characterized by reduced matrix multiplication operations that only use the $X$ and $Z$ Pauli matrices.

(2) $\begin{equation*} \rho_{m}' = (1 - \frac{2p}{3}) \rho + \frac{2p}{3} Z((\rho X)^T X) Z\end{equation*}$

Traditionally, depolarization uses three Kraus operators, each corresponding to one of the Pauli matrices. In practical terms, this means that when we’re simulating a quantum system with noise, we need to perform six matrix multiplications per qubit per step—this scales rapidly with the size of the system. The modified depolarization approach in the paper proposes reducing the number of Kraus operators to two by cleverly using only the $X$ and $Z$ Pauli matrices, allowing for more efficient simulation without significantly compromising the accuracy of the noise model. The two Kraus operators are defined as:

$\begin{array}{cc}K_0 = \sqrt{1 -\frac{2p}{3}} \mathbb{I}, &K_1 = i \sqrt{\frac{2p}{3}} ZX .\end{array}$

The author provides meticulous proof to assert the proposed modified expression’s authenticity and Kraus operators’ authenticity. This seemingly small change reduces the number of required matrix multiplications from six to four, a non-trivial improvement in computational cost. This reduction becomes especially significant as quantum circuits grow deeper and larger—common in QML algorithms, where we often have to run complex iterative procedures.

Experimenting with Quantum Machine Learning on the Iris Dataset

To validate their approach, the authors experimented with a well-known machine learning problem: classifying the Iris dataset using the Iris dataset by training a variational quantum circuit under a modified depolarization noise channel. Their results verify that the modified depolarization channel accurately represents channel evolution for different values of $p$ , and these results are consistent with simulation results. Once the Iris dataset was encoded into quantum states, the author trained the QML model under noisy conditions using the modified depolarization method. Thanks to Pennylane Library, the authors claim to implement the modified channel efficiently. The findings were fascinating: the computational load was reduced by 1.5 to 2 times compared to the traditional depolarization method, while classification accuracy remained comparable. This is a big deal for QML. Efficiency in quantum simulations is crucial—especially given the already limited coherence times and high noise levels of NISQ devices. Reducing computational cost allows for quicker experimentation and larger models, accelerating the development of quantum machine learning algorithms. The following figure provides the decision boundaries for readers’ reference. We request that the readers to refer to the original manuscript for in-depth analysis.

An increase in circuit depth may enhance the model’s expressivity, but it also increases its vulnerability to noise, which adversely affects the quality of the decision boundary.

Why This Matters for the NISQ Era

We’re still far from having fault-tolerant quantum computers (except google’s latest work) that can operate indefinitely without errors. For now, we must work with what we’ve got: noisy, small to mid-scale quantum devices. This means any improvement in the efficiency of noise simulation or error mitigation has a direct and significant impact on the feasibility of using quantum systems for practical problems.

The reduction in computational overhead offered by this modified depolarization approach is particularly relevant for QML, where deep quantum circuits and iterative optimization processes require substantial computational resources. This is a step toward making QML more scalable and closer to real-world applications, even within the limitations of today’s quantum technology.

Looking Ahead

As quantum hardware continues to evolve, so too will the need for more efficient noise models and error mitigation techniques. The modified depolarization approach presented in this paper offers a glimpse into how we can make QML more computationally feasible. While the improvement in noise simulation efficiency may seem small, these incremental advancements will enable the quantum systems of the future to handle more complex and meaningful tasks.

I’m excited to see how this approach will be applied to larger quantum systems and more complex QML models. The road to fully realizing quantum machine learning’s potential is long, but innovations like this bring us one step closer.

For a detailed exploration of the methodology and findings, read the full paper at: https://www.mdpi.com/2227-7390/12/9/1385

References

Khanal, Bikram, and Pablo Rivas. “A Modified Depolarization Approach for Efficient Quantum Machine Learning.” Mathematics 12.9 (2024): 1385.

About the Author

Bikram Khanal is a Ph.D. student at Baylor University, specializing in Quantum Machine Learning and Natural Language Processing.

International Conference on Emergent and Quantum Technologies (ICEQT’24)

July 22-25, 2024 — Las Vegas, NV

Dear Esteemed Colleagues,

Quantum computing is an expeditiously evolving field of interdisciplinary research, drawing upon fundamental principles from mathematics, physics, and engineering. To maintain scientific rigor and foster advancement, this domain necessitates a collaborative effort across various STEM disciplines.

We are delighted to announce the International Conference on Emergent and Quantum Technologies (ICEQT’24), scheduled for July 22-25, 2024, in Las Vegas, NV. The conference is designed to serve as a platform for researchers specializing in quantum machine learning and machine learning professionals exploring the application of AI in enhancing quantum computing algorithms. It aims to facilitate the exchange of insights and developments within these dynamic areas of study.

The burgeoning interest among machine learning practitioners in leveraging AI for quantum computing endeavors, and vice versa, underscores the relevance of this conference. Thus, we warmly welcome the submission of original research papers that contribute novel insights and state-of-the-art developments in the following areas of interest:

Foundations of Quantum Computing and Quantum Machine Learning

Quantum computing models and paradigms, e.g., Grover, Shor, and others
Quantum algorithms for Linear Systems of Equations
Quantum Tensor Networks and their Applications in QML

Quantum Machine Learning Algorithms

Quantum Neural Networks
Quantum Hidden Markov Models
Quantum PCA
Quantum SVM
Quantum Autoencoders
Quantum Transfer Learning
Quantum Boltzmann machines
Theory of Quantum-enhanced Machine Learning

AI for Quantum Computing

Machine learning for improved quantum algorithm performance
Machine learning for quantum control
Machine learning for building better quantum hardware

Quantum Algorithms and Applications

Quantum computing: models and paradigms
Quantum algorithms for hyperparameter tuning (Quantum computing for AutoML)
Quantum-enhanced Reinforcement Learning
Quantum Annealing
Quantum Sampling
Applications of Quantum Machine Learning

Fairness and Ethics in Quantum Machine Learning

We look forward to receiving your submissions and to welcoming you to ICEQT’24.

All submissions that are accepted for presentation will be included in the proceedings published by IEEE CPS. To ensure consistency in formatting, authors should follow the general typesetting instructions available on the IEEE’s website, including single-line spacing and a 2-column format. Additionally, authors of accepted papers must agree to the IEEE CPS standard statement regarding copyrights and policies on electronic dissemination.

Prospective authors are encouraged to submit their papers through the conference’s evaluation website at CMT. More information about the conference, including submission guidelines, can be found on our website at https://baylor.ai/iceqt/.

Important Deadlines

March 22, 2024: Submission of papers: https://cmt3.research.microsoft.com/ICEQT2024
– Full/Regular Research Papers (maximum of 8 pages)
– Short Research Papers (maximum of 5 pages)
– Abstract/Poster Papers (maximum of 3 pages)

April 15, 2024: Notification of acceptance (+/- two days)

May 1, 2024: Final papers + Registration

June 21, 2024: Last day for hotel room reservation at a discounted price.

July 22-25, 2024: The 2024 World Congress in Computer Science, Computer Engineering, and Applied Computing (CSCE’24: USA)
Which includes the International Conference on Emergent and Quantum Technologies (ICEQT’24)

Chairs:
Pablo Rivas, PhD, Baylor University
Bikram Khanal, PhD Candidate, Baylor University

Power of Data In Quantum Machine Learning

This week at the lab, we read the following paper, and here is our summary:

Huang, Hsin-Yuan, Michael Broughton, Masoud Mohseni, Ryan Babbush, Sergio Boixo, Hartmut Neven, and Jarrod R. McClean. “Power of data in quantum machine learning.” Nature communications 12, no. 1 (2021): 2631.

Summary

This work focuses on the advancement of quantum technologies and their impact on machine learning. The two paths towards the quantum enhancement of machine learning include using the power of quantum computing to improve the training process of existing classical models and using quantum models to generate correlations between variables that are inefficient to represent through classical computation. The authors show that this picture is incomplete in machine learning problems where some training data are provided, as the provided data can elevate classical models to rival quantum models. The authors present a flowchart for testing potential quantum prediction advantage based on prediction error bounds for training classical and quantum ML methods based on kernel functions. This elevation of classical models through some training samples is illustrative of the power of data. The authors also show that, “training a specific classical ML model on a collection of $N$ training examples $(\mathbf{x}, y = f(\mathbf{x}))$ would give rise to a prediction model $h(\mathbf{x})$ with

(1) $\begin{equation*} \mathbb{E}_\mathbf{x}|h(\mathbf{x})-f(\mathbf{x})|\leq c \sqrt{p^2/N} \end{equation*}$

for a constant $c > 0$ . Hence, with $N \approx p^2/\epsilon^2$ training data, one can train a classical ML model to predict the function $f(\mathbf{x})$ up to an additive prediction error $\epsilon$ .” They also show that a slight geometric difference between kernel functions defined by classical and quantum ML guarantees similar or better performance in prediction by classical ML. On the other hand, a sizeable geometric difference indicates the possibility of a large prediction advantage using the quantum ML model.

Additionally, the authors introduced ”projected quantum kernels” and demonstrated, through empirical results, that these outperformed all tested classical models in prediction error. This work provides a guidebook for generating ML problems that showcase the separation between quantum and classical models.

Intellectual Merit

This work provides a theoretical and computational framework for comparing classical and quantum ML models. The authors develop prediction error bounds for training classical and quantum ML methods based on kernel functions, which provide provable guarantees and are very flexible in the functions they can learn. The authors also develop a flowchart for testing potential quantum prediction advantage, a function-independent prescreening that allows one to evaluate the possibility of better performance. The authors provide a constructive example of a discrete log feature map, which gives a provable separation for their kernel. They rule out many existing models in the literature, providing a powerful sieve for focusing the development of new data encodings.

Broader Impact

The authors’ contributions to the field of quantum technologies and machine learning have significant broader impacts. The development of a flowchart for testing potential quantum prediction advantage provides a tool for researchers and practitioners to determine the possibility of better performance using quantum ML models. The authors’ framework can also be used to compare and construct hard classical models, such as hash functions, which have applications in cryptography and secure communication. The authors’ work has the potential to accelerate the development of new data encodings, leading to more efficient and accurate machine learning models. This has far-reaching implications for various applications, including image recognition, text translation, and even physics applications, where machine learning can revolutionize how we analyze and interpret data. The paper was organized and written by collaborating with three famous quantum institutes: Google Quantum AI, the Institute for Quantum Information and Matter at Caltech, and the Department of Computing and Mathematical Sciences at Caltech.

Quantum Machine Learning: A Case Study of Grover’s Algorithm

Interested in how quantum algorithms work, or what does the quantum circuit looks like? Read our recent paper on Grover’s algorithm covering rudimentary to intermediate quantum computation with machine learning descriptions. [pdf, bib]