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LEESBURG, Va., Jan. 18, 2024 /PRNewswire/ -- Quantum Computing Inc. ("QCi", "we", "our" or the "Company") (Nasdaq: QUBT), an innovative quantum optics andnanophotonics technology company,today proudly announces that two of its engineers have been honored with the esteemed 44th Edison Patent Award for their pathbreaking contributions to quantum-secured privacy-preserving computations. This recognition underscores their exceptional work in addressing cybersecurity threats and developing innovative solutions, including a revolutionary method of quantum authenticationand private-data computing that can process and verify information withoutsharingthat information.

The Edison Patent Award, a symbol of innovation and excellence, is a testament to the commitment, expertise, and innovation demonstrated by Dr. Yuping Huang, OCi's Chief Quantum Officer and Dr. Lac Thi Thanh Nguyen, the Quantum Technology Lead for QCi's Cybersecurity platform. Their critical work has significantly advanced Quantum Computing Inc's mission to harness the power of quantum technologies for real-world applications.

The patent underlying the award represents a milestone in the field of quantum information networks, a critical domain in the ongoing battle against cybersecurity threats facing industry, government, and individuals. The patent, which was granted approval in the United States and over 40 other countries during 2023, addresses a method for quantum authentication and zero-knowledge proof for network security that uses fundamental quantum physics to protect passwords, private information, and online assets. The patented technology describes a method of generating pairs of so-called "entangled" photons that can share certain properties, measurement results and security checks with each other sharing joint communications without ever disclosing in any way that private data in the process, either with each other or with external parties or computing processes. Distinct to any other protocol, the private information is coded on the measurement bases and never shared with any party, either directly or via encryption. Thus, it provides the ultimate protection and unconditional security.

In contrast to quantum key distribution which only protects encryption, this breakthrough patent fills a critical security breach vulnerability by offering a way to effectively secure identity authentication, data mining, and digital assetsin an untrusted environment. Designed to be compatible with existing fiber-based communication infrastructure and satellite-based networks, the patent is a broad-use award based on a fundamental methodology for secure networking among multiple parties, uniquely combining quantum authentication and encryption in a single step and thereby safeguarding an entire network at all points of slippage.

The patent was exclusively licensed to QCi with perpetual terms. For rapid commercialization, QCi has recently built a two-node quantum authentication system, leveraging the engineering skills that Huang and Nguyen acquired when they and team built a pilot three-node quantum network system over a university campus in 2018.

"Quantum Computing Inc. salutes our esteemed engineers. In an era where digital security is paramount, Drs. Huang and Nguyen have played a pivotal role in developing a method of quantum authentication that promises to revolutionize data protection and privacy. Until now, there was no end-to-end quantum solution to defend the security of our digital assets against AI or quantum computer attacks in the coming future. The integration of this comprehensive quantum protocol with quantum key distribution holds the promise of establishing a robust quantum-secured communication system that safeguards the internet for everyone," commented Robert Liscouski, CEO of Quantum Computing Inc. "The company is proud to be at the forefront of quantum technology advancements, providing solutions that address the evolving challenges of cybersecurity, and we remain committed to pushing the boundaries of quantum technology and providing innovative solutions to complex global challenges."

For additional information on the Company's suite of solutions, please visit our websiteor contact our team directly.

About Quantum Computing Inc. (QCi)

Quantum Computing Inc. (QCi) (Nasdaq: QUBT) is an innovative, quantum optics and nanophotonics technology company on a mission to accelerate the value of quantum computing for real-world business solutions, delivering the future of quantum computing, today. The company provides accessible and affordable solutions with real-world industrial applications, using nanophotonic-based quantum entropy that can be used anywhere and with little to no training, operates at normal room temperatures, low power and is not burdened with unique environmental requirements. QCi is competitively advantaged delivering its quantum solutions at greater speed, accuracy, and security at less cost. QCi's core nanophotonic-based technology is applicable to both quantum computing as well as quantum intelligence, cybersecurity, sensing and imaging solutions, providing QCi with a unique position in the marketplace. QCi's core entropy computing capability, the Dirac series, delivers solutions for both binary and integer-based optimization problems using over 11,000 qubits for binary problems and over 1000 (n=64) qubits for integer-based problems, each of which are the highest number of variables and problem size available in quantum computing today.Using the Company's core quantum methodologies, QCi has developed specific quantum applications for AI, cybersecurity and remote sensing, including its Reservoir Photonic Computer series (intelligence), reprogrammable and non-repeatable Quantum Random Number Generator (cybersecurity) and LiDAR and Vibrometer (sensing) products. For more information about QCi, visitwww.quantumcomputinginc.com.

The Edison Patent Awards

For more than 40 years, the Research & Development Council of New Jerseyhas recognized and highlighted the broad array of research conducted in the state and celebrated its exceptional inventors in an annual award ceremony named for Thomas Alva Edison, New Jersey's most famous inventor. Winners are selected by a team of Research & Development Council researchers who evaluate nominated patents based on the significance of the problem addressed, its utility/socioeconomic value, novelty and commercial impact.The Research & Development Council is a nonprofit 501(c)(3) organization whose membership includes representatives from academia, government, and industry, including several Fortune 500 companies. More information can be found at the Research & Development Council's website:www.rdnj.org.

Important Cautions Regarding Forward-Looking Statements

This press release contains forward-looking statements as defined within Section 27A of the Securities Act of 1933, as amended, and Section 21E of the Securities Exchange Act of 1934, as amended. By their nature, forward-looking statements and forecasts involve risks and uncertainties because they relate to events and depend on circumstances that will occur in the near future. Those statements include statements regarding the intent, belief or current expectations of QCi and members of its management as well as the assumptions on which such statements are based. Prospective investors are cautioned that any such forward-looking statements are not guarantees of future performance and involve risks and uncertainties, and that actual results may differ materially from those contemplated by such forward-looking statements.

QCi undertakes no obligation to update or revise forward-looking statements to reflect changed conditions. Statements in this press release that are not descriptions of historical facts are forward-looking statements relating to future events, and as such all forward-looking statements are made pursuant to the Securities Litigation Reform Act of 1995. Statements may contain certain forward-looking statements pertaining to future anticipated or projected plans, performance and developments, as well as other statements relating to future operations and results. Words such as "may," "will," "expect," "believe," "anticipate," "estimate," "intends," "goal," "objective," "seek," "attempt," "aim to," or variations of these or similar words, identify forward-looking statements. These risks and uncertainties include, but are not limited to, those described in Item 1A in QCi's Annual Report on Form 10-K and other factors as may periodically be described in QCi's filings with the U.S. Securities and Exchange Commission.

SOURCE Quantum Computing Inc.

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Quantum Computing Inc. Congratulates Achievement as its Engineers Receive Prestigious Edison Patent Award for ... - PR Newswire

The advent of quantum computers carries a potent threat to data encryption, potentially leading to catastrophic impacts on mission-critical infrastructure. With power utilities, hospitals, banks, and transit systems becoming increasingly digitalized, the menace of quantum hacking looms large. The U.S. Cybersecurity and Infrastructure Security Agency has issued an alert, underscoring the urgency to prepare for quantum threats. It is vital for organizations to assess their current security posture, develop a quantum roadmap, and implement quantum-safe solutions to defend against these threats.

Quantum computers differ significantly from conventional computers. They possess exponential speed and power, enabling them to break traditional encryption methods in a fraction of the time it would take a regular computer. This immense potential makes quantum computers a significant threat to critical infrastructure, especially for smaller companies and municipal infrastructure operations that might lack the resources to counter such advanced threats.

Preparing for the day when quantum computers can compromise traditional encryption methods, often referred to as Q-Day, is crucial. Organizations must prioritize the protection of high-impact assets. Developing a quantum roadmap and assessing the current security posture are essential steps in preparing for this threat. Utilizing encryption methods and key distribution techniques that ensure data integrity can provide protection against quantum attacks.

The World Economic Forum (WEF) has raised concerns about the potential impact of quantum computing on critical infrastructure. It could pose radical global risks with the ability to break public key encryption, potentially leading to the paralysis of national or global critical infrastructure. The report also warns about the acceleration of risks presented by other emerging technologies and the potential for cyberattacks. Criminal actors are already launching attacks on encrypted data in anticipation of cryptographically relevant quantum computers being available.

Quantum computing is also posing significant challenges to corporate security and privacy compliance. Its potential to revolutionize various industries and threaten traditional encryption methods is a cause for concern. Post-quantum cryptography is seen as a potential solution to protect against quantum computing threats. Regulatory bodies in the EU and Canada are assessing the potential impacts of quantum computing on various sectors, underlining the need for quantum-resistant algorithms to safeguard data against the threat of quantum computers.

Quantum computing presents both opportunities and challenges for the modern enterprise. It is expected to help solve complex problems but also poses a risk to traditional cryptographic systems. The National Institute of Standards and Technology (NIST) has selected four quantum-resistant algorithms for standardization, three of which were contributed by IBM researchers and partners. Organizations are advised to create a quantum readiness roadmap for transitioning to these standards. Becoming quantum-safe involves three critical steps: discovering, observing, and transforming the cryptography infrastructure.

Large Language Models (LLM) are redefining cybersecurity operations. The cybersecurity workforce is expected to grow, reaching its highest number ever with 5.5 million people in cybersecurity jobs. However, cybersecurity teams should be aware of the hidden risks associated with them. The year 2023 had unexpected twists in cybersecurity, driving organizations to plan their security strategies for 2024 and beyond. As quantum computing continues to evolve, its clear that the cybersecurity landscape must adapt to meet the challenges of this new era.

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Quantum Computing: An Emerging Threat to Cybersecurity - Medriva

Quantum computing, the next frontier in information technology, is not just bringing new opportunities, but also posing significant challenges in corporate security and privacy compliance. Its arrival has been marked with a wave of excitement and concern in equal measure due to its potential to revolutionize various industries, including healthcare, and its ability to threaten traditional encryption methods. This article delves into the implications of quantum computing and the need for post-quantum cryptography to protect against its threats.

Unlike classical computers which use bits representing either 0 or 1, quantum computers use qubits that can represent 0 and 1 simultaneously. This characteristic allows quantum computers to process information at an exponentially faster rate than classical computers. The increased processing power, while advantageous in many fields, poses a significant threat to traditional encryption methods and calls for a re-evaluation of data protection and security compliance.

Post-quantum cryptography is seen as a potential solution to protect against quantum computing threats. It involves the creation of cryptographic systems that can withstand attacks from both classical and quantum computers. To address this, organizations are encouraged to create a quantum readiness roadmap, and follow three critical steps: discover, observe, and transform their cryptography. As artificial intelligence continues to evolve, organizations are urged to consider the impact of Generative Artificial Intelligence (GenAI) and adopt a holistic approach to IT and OT cybersecurity.

Regulation plays an essential role in managing the impact of quantum computing. In the EU and Canada, regulatory bodies are assessing the potential impacts of quantum computing on various sectors, including the insurance industry. Financial institutions are being encouraged to assess their quantum-readiness, with the development of rules, interpretation of legislation and regulation, and provision of regulatory approvals for certain types of transactions being key areas of focus.

Quantum computing has the potential to revolutionize various fields, from healthcare to financial services. Managed Service Providers (MSPs) have a critical role in helping small and medium-sized enterprises manage their cybersecurity needs effectively in this new era. They offer insights, strategies, and comprehensive IT and security services to mitigate risks and protect against cyber threats.

The rise of quantum computing calls for a paradigm shift in cybersecurity. Quantum-resistant algorithms are being developed to safeguard data against the threat of quantum computers. Groundbreaking inventions in the field, like the quantum authentication and private data computing method patented by Quantum Computing Inc (QCi), offer promising solutions. This technology allows for processing and verifying information without sharing that information, effectively securing identity authentication, data mining, and digital assets in an untrusted environment.

In conclusion, while quantum computing offers unprecedented opportunities, it also raises concerns about corporate security and privacy compliance. Organizations need to adopt a proactive approach to quantum readiness, embracing the potential of post-quantum cryptography, and leveraging the expertise of MSPs. Regulation will play a key role in managing the impact of this technology, and quantum-resistant algorithms could be the future of cybersecurity.

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Quantum Computing and Its Impact on Corporate Security and Privacy Compliance - Medriva

With help from Christine Mui and Steven Overly

Participants waiting for a session at the 2024 meeting of the World Economic Forum. | Fabrice Coffrini/AFP via Getty Images

Davos wants you to plan to have a plan on quantum technology.

The World Economic Forum that sponsors the annual Switzerland confab released a Quantum Economy Blueprint today its first major paper on how a global economy centered around quantum technology might develop, even as many skeptics say the technology isnt yet ready for prime time.

Its authors, a trio of researchers from the WEF, AI and quantum startup SandboxAQ, and IBM, lay out a set of recommendations and examples for how countries can find their fit in the global development of quantum computing, sensing, and communications technologies especially as China invests billions into the technology largely in isolation from the West.

If youve been reading DFDs past coverage of quantum developments, you might be wondering: Isnt it a bit early for this? Thats what the reports authors are counting on, writing that seizing on an early adopter advantage will allow governments to get infrastructure in place to ensure all countries are able to benefit from the gradual replacement of zeroes and ones by superposition and entanglement.

Notably, the report, with the full backing of the WEF, makes assumptions about quantum that are decidedly up for debate in the wider research community. Those include: it will be possible to build a useful, fully programmable universal fault-tolerant quantum computer; quantum computing will make the computation of specific problems more efficient or precise, and that quantum utility, the ability for existing quantum computers to solve problems beyond classical computings reach, has been demonstrated.

(Some in the commercial sector even say the WEF isnt bullish enough Allison Schwartz, government relations lead for commercial quantum company D-Wave, told DFD in a statement that the report narrowly focuses on a single approach that is far from market readiness in a manner that skews the timelines for adoption and near-term application development.)

With that in mind I pinged Sergio Gago Huerta, head of quantum at Moodys and someone who does not hesitate to call out quantum hype as the author of the Quantum Pirates Substack newsletter. Huerta was all in favor of the blueprint, saying that by focusing on governance and infrastructure it provides helpful pointers to pretty much anyone hoping to compete or even participate in the quantum economy.

Every country should have their own quantum program, either as part of a coalition or by themselves, Huerta wrote in an email. He noted that while many countries tend to focus on quantum as a cyber threat the ability of quantum computers to bust traditional cryptography is one of the most well-established findings in the field the report provides welcome focus on other technologies like quantum sensing and metrology, something governments will need to provide enough support, governance and training [for]... in order to stay relevant and keep a competitive advantage.

Celia Merzbacher, executive director of the Quantum Economic Development Consortium that aims to grow quantum in the U.S., was a consultant on the report. She praised its analysis of the complex landscape facing nations on quantum and said it would be useful to anyone working right now in the quantum technology stack.

The report takes a granular dive into nations quantum building blocks, from national research funding to politics to worker training, and finds not surprisingly that the most successful innovation efforts come from deeply interconnected and collaborative ecosystems.

One example they cite is the United Kingdoms National Quantum Strategy: In that case, pumping a billion-plus British pounds into the U.K.s research infrastructure led to a successful effort to develop commercial applications for quantum in fields like the automotive industry, telecom, and defense.

At a smaller scale, that virtuous-cycle collaboration tends to cross national boundaries, like in the case of the Quantum Leap Africa program that saw five nations team up to gather top students from across the continent and educate them about quantum.

The U.S. National Quantum Initiative, authorized by a $1.2 billion bill passed in 2018, has placed Washington at the center of this global conversation even as its re-authorization lingers in Congressional limbo. The report contains plenty of detail about the U.S. quantum push and its ripples throughout the global economy, as well as the importance of maintaining a quantum advantage to defense and national security. Where its decidedly more circumspect, however, is on exactly what those geopolitical threats are: State Department official Rick Switzer is quoted saying its critical that the United States and our allies retain access to key components in the quantum supply chain, requiring policy-makers to account for the geopolitics surrounding this access.

By geopolitics, he means China and the repercussions for quantum in what the New York Times called Americas silicon blockade against Beijing. The WEF report notes that China has spent $15 billion on quantum, more than the U.S., U.K., France and Germany combined.

The number of times China itself is referenced in the report? Exactly two, a far cry from the in-depth treatment other nations quantum strategies get. Anyone who tracks quantum development (or any other technology, for that matter) in the West knows that potential threat from Beijing is a huge political motivator for quantum policy, especially when it comes to cybersecurity. Davos plan might be a globally collaborative one, but as with so many other tech policy issues, theres a large elephant in the room thats central to its analysis while remaining oddly silent.

Also in Davos, India made its case as a democratic alternative source for electronics manufacturing to China.

The worlds fifth-largest economy for years lagged on making microchips, lacking the specialized hardware and skilled talent needed to grow the industry. Then in late 2021, the Modi government offered up $10 billion in incentives, luring companies like Micron and Tata Group to invest in new fabs. With nine semiconductor manufacturing proposals on the table, India is eager for more.

Speaking at the WEF, Chip War author Chris Miller drew parallels between India and past success stories: Taiwan, South Korea started a half century ago developing their chip industries, and today theyre the world leaders. And so I think theres no doubt that India is beginning to follow that path.

But the country wont dive into the competition around cutting-edge chips thats captured governments around the world yet choosing to first focus on legacy chips for telecommunications and cars, Indian Cabinet Minister Ashwini Vaishnaw told the panel. Asked about future pressure to take sides between China and the West, Vaishnaw dodged, saying we dont think that its a battle and that circumstances are too complex and too dynamic to imagine what could happen in a decade.

Indias semiconductor moves piqued the interest of the Netherlands, a chipmaking equipment powerhouse thats all too familiar with getting caught in the U.S.-China faceoff. Dutch Minister of Economic Affairs and Climate Micky Adriaansens called India a different story from China and reiterated its plan to join forces with like-minded countries. Christine Mui

A fundamental question hangs over the global debate over how to regulate artificial intelligence: open or closed?

That is, should the most powerful AI systems be widely available to any interested developer or under the tight control of just a few players? Top politicos and tech minds grappled with that topic in Davos, including at POLITICO Lives own AI debate on Tuesday.

In the U.S., Assistant Secretary of Commerce Alan Davidson said the answer may not be so binary.

Weve learned that theres a real gradient of openness, and that we may be able to find ways, we have to be able to find ways, to support innovation and competition, but also protect safety and security as we open up these systems, Davidson told the POLITICO Tech podcast.

Davidson heads the National Telecommunications and Information Administration, which has been tasked by the White House with studying the open vs. closed question. He made the case that while closed systems are seemingly easier to close off to bad actors, they also concentrate power in the hands of a small number of tech companies, many of which already exert significant influence over our daily lives.

We know that its very powerful if you can democratize access to these technologies, Davidson said. Its good for innovation. It actually can be good for safety and security. Steven Overly

Listen to the full interview with Davidson on todays POLITICO Tech.

Stay in touch with the whole team: Ben Schreckinger ([emailprotected]); Derek Robertson ([emailprotected]); Mohar Chatterjee ([emailprotected]); Steve Heuser ([emailprotected]); Nate Robson ([emailprotected]); Daniella Cheslow ([emailprotected]); and Christine Mui ([emailprotected]).

If youve had this newsletter forwarded to you, you can sign up and read our mission statement at the links provided.

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Davos and the global state of quantum - POLITICO

An overview of the challenges and opportunities Photo by Anton Maksimov 5642.su on Unsplash

Today, were diving into the intersection of quantum computing and machine learning, exploring quantum machine learning. Our main goal is to compare the performance of a quantum neural network for stock price time series forecasting with a simple single-layer MLP.

To facilitate this project, well be utilizing the Historical API endpoint offered by Financial Modeling Prep (FMP) for reliable and accurate data which is very critical. With that being said, lets dive into the article.

Lets start by importing the necessary libraries for our analysis. These libraries will provide the basic tools required to explore and implement our project.

Weve set up our environment by installing the Qiskit library for working with quantum computing networks, along with other essential libraries. To extract the data, well use the historical data API endpoint provided by Financial Modeling Prep.

FMPs historical data API offers a conveniently accessible endpoint, providing a diverse and extensive collection of historical stock data that proves invaluable at every step of our project. This resource enables us to access a wide range of financial information, enhancing the depth and accuracy of our analysis. Its user-friendly interface and comprehensive dataset contribute significantly to the success and efficiency of our research and implementation.

Now we are going to extract historical data as follows:

Replace YOUR API KEYwith your secret API key which you can obtain by creating an FMP account. The output is a JSON response which looks as follows:

In regular computers, we have tiny switches called digital gates. These switches control how information moves around. They work with basic units of data called bits, which can be either 0 or 1. The gates help computers do calculations and process stuff. Now, in quantum computers, we use something called qubits instead of bits. Qubits are special because they can be both 0 and 1 at the same time. Its like having a coin thats spinning and showing both heads and tails until you catch it, and then it picks one side.

When we say the wave function collapses, its just a fancy way of saying the qubit decides to be either 0 or 1 when we check it. We make these qubits using different things like light particles (photons), tiny particles that make up stuff (atoms), or even small electrical circuits (Josephson junctions). These are like the building blocks for our special qubits.

These quantum systems (particles or circuits) do some interesting things. They can be in different states at the same time (superposition), connect in a special way (entanglement), and even go through barriers they shouldnt (tunneling).

Whats cool is that quantum computers, with their qubits and special behaviors, use certain algorithms to solve some problems faster than regular computers. Its like having a new tool that might help us solve tough puzzles more efficiently in the future.

In traditional computing, we perform operations using basic logic gates like AND, NOT, and OR. These gates work with 0s and 1s, and their rules are based on a simple mathematical system called:

which essentially deals with counting modulo 2.

Now, imagine a quantum computer it also has gates, but these are like supercharged versions. Instead of dealing with simple bits, quantum gates work with quantum bits or qubits. The math behind these quantum gates involves complex numbers and Matrix operations.

Lets take the quantum NOT gate, called:

as an example. Apply it to a qubit initially in the state 0, and the operator flips it to 1 , and if you apply it again, it goes back to 0. Its a bit like flipping a coin.

Theres also the Hadamard gate (H) that does something really cool. Applying it to a qubit initially in the state 0 puts it in this special mix of 0 and 1 states at the same time to show mathematically H operates on |0 and converts it into the standard superposition of the basis states:

Its like having a coin spinning in the air, showing both heads and tails until it lands.

Now, lets talk about the Controlled-NOT (CNOT) gate. This one works on two qubits. If the first qubit is 1, it flips the second qubit from 0 to 1 or vice versa. Its like a quantum switch that depends on the state of the first qubit.

In the quantum world, things get more interesting. If you have two qubits in a special state, the CNOT gate uniquely rearranges their combinations, creating what we call entanglement. This entanglement is like a special connection between the qubits, making them behave in a coordinated manner.

So, in a nutshell, while regular computers use basic rules with 0s and 1s, quantum computers have these fascinating gates that play with probabilities, mix states, and create connections between qubits, opening up a world of possibilities for solving complex problems more efficiently.

In our project, we place special emphasis on a category of gates known as parameterized gates. These gates exhibit behavior that is contingent on specific input parameters, denoted by the symbol . Notably, we focus on rotation gates such as:

each characterized by a unitary matrix as described in the below figure:

Lets delve a bit deeper into these rotation gates. Consider:

envision it as a quantum gate resembling a rotating door that allows for the rotation of a qubit by a specific angle . The

and,

gates function similarly, introducing rotations around different axes.

The significance of these gates lies in their parameterized nature. By adjusting the input parameter , we essentially introduce a customizable element into our quantum algorithms. These gates serve as the foundational components for constructing the quantum neural network integral to our Project.

In essence, acts as a tuning parameter, akin to a knob, enabling us to finely adjust and tailor the behavior of our quantum algorithms within the framework of the quantum neural network. This flexibility becomes pivotal in optimizing and customizing the performance of our quantum algorithms for specific tasks.

Quantum algorithms can be thought of as a series of operations performed on a quantum state, represented by expressions like:

These algorithms are translated into quantum circuits, as illustrated in Figure below. In this depiction, the algorithm starts from the initial state |q_0 q_1 = |00 and concludes with a measurement resulting in either |00 or |11 with an equal probability of 0.5, recorded into classical bits (line c).

In a quantum circuit, each horizontal line corresponds to a single qubit, and gates are applied sequentially until measurement. Its important to note that loops are not allowed in a quantum program. A specific type of quantum circuit is the Variational Quantum Circuit (VQC). Notably, VQC incorporates parameterized gates like the aforementioned R_x(), R_y(), R_z().

In simpler terms, quantum algorithms are like step-by-step instructions for a quantum computer, and quantum circuits visually represent these steps. The Variational Quantum Circuit introduces a special kind of flexibility with parameterized gates, allowing for customization based on specific values, denoted by .

The primary objective of QML is to devise and deploy methods capable of running on quantum computers to address conventional supervised, unsupervised, and reinforcement learning tasks encountered in classical Machine Learning.

What makes QML distinct is its utilization of quantum operations, leveraging unique features like superposition, tunneling, entanglement, and quantum parallelism inherent to Quantum Computing (QC). In our study, we specifically concentrate on Quantum Neural Network (QNN) design. A QNN serves as the quantum counterpart of a classical neural network.

Breaking it down, each layer in a QNN is a Variational Quantum Circuit (VQC) comprising parameterized gates. These parameters act as the quantum equivalents of the weights in a classical neural network. Additionally, the QNN incorporates a mechanism to exchange information among existing qubits, resembling the connections between neurons in different layers of a classical network. Typically, this information exchange is achieved through entanglements, employing operators such as the CNOT gate.

Creating a Quantum Machine Learning (QML) model typically involves several steps, as illustrated in Figure above. First, we load and preprocess the dataset on a classical CPU. Next, we use a quantum embedding technique to encode this classical data into quantum states on a Quantum Processing Unit (QPU) or quantum hardware. Once the classic data is represented in quantum states, the core model, implemented in the ansatz, is executed, and the results are measured using classical bits. Finally, if needed, we post-process these results on the CPU to obtain the expected model output. In our study, we follow this overall process to investigate the application of a Quantum Neural Network for time series forecasting.

A Quantum Neural Network (QNN) typically consists of three main layers:

1. Input Layer: This layer transforms classical input data into a quantum state. It uses a parameterized variational circuit with rotation and controlled-rotation gates to prepare the desired quantum state for a given input. This step, known as quantum embedding, employs techniques like basis encoding, amplitude encoding, Hamiltonian encoding, or tensor product encoding.

2. Ansatz Layer: The heart of the QNN, this layer contains a Variational Quantum Circuit, repeated L times to simulate L network layers classically. Its responsible for processing and manipulating quantum information.

3. Output Layer: This layer performs measurements on qubits, providing the final expected outcome.

For the input layer, we use a tensor product encoding technique. It involves a simple X-rotation gate for each qubit, where the gate parameter is set by scaling the classic data to the range [-, ]. Although its a quick and straightforward encoding method (O(1) operations), it has limitations. The number of qubits needed scales linearly with the input classic data. To address this, we introduce learnable parameters for scaling and bias in the input data, enhancing the flexibility of the quantum embedding. In Figure 3, you can see an example of the input layer for a network with 3 qubits, where classic data features:

, input scale parameters:

, and bias parameters:

come into play.

Regarding the ansatz, its interesting to note that, unlike classical neural networks, there isnt a fixed set of quantum layer structures commonly found in the literature (such as fully connected or recurrent layers). The realm of possible gates for quantum information transfer between qubits is extensive, and the optimal organization of these gates for effective data transfer is an area that hasnt been thoroughly explored yet.

In our Project, we adopt the Real Amplitudes ansatz, a choice inspired by its success in various domains like policy estimation for quantum reinforcement learning and classification. This ansatz initiates with full rotation X/Y/Z parameterized gates, akin to the quantum version of connection weights. It is then followed by a series of CNOT gates arranged in a ring structure to facilitate qubit information transfer. Figure 4 provides a visual representation of how this ansatz is implemented, serving as the quantum equivalent of a network layer for a 3-qubit network.

To break it down, a quantum network layer in our work involves a set of parameters totaling 3 times the number of qubits (3*n), where n represents the number of qubits in the quantum network.

Now, lets talk about the output layer, which is a critical part of our quantum model. In quantum computing, when we want to extract information from our quantum state, we often perform measurements using a chosen observable. One such commonly used observable is represented by the _z operator over the computational basis. To understand this, think of it as a way to extract information from our quantum state.

The network output is determined by calculating the expectation of this observable over our quantum state. This is expressed as |_z|, where | denotes the complex conjugate of |. The result falls within the range of [-1, 1].

No need to stress over those complex mathematical equations our trusty library, Qiskit, has got it covered! Qiskit will handle all the intricate quantum calculations seamlessly, making the quantum computing process much more accessible for us. So, you can focus on exploring the quantum world without getting bogged down by the nitty-gritty math

Now, to make our network output less sensitive to biases and scales inherent in the dataset, we introduce a final scale parameter and bias to be learned. This step adds a layer of adaptability to our model, allowing it to fine-tune and adjust the output based on the specific characteristics of our data. The entire model architecture is visually represented in the figure below.

The training of our proposed Quantum Neural Network (QNN) happens on a regular CPU using classical algorithms like the Adam optimizer. The CPU handles the gradient computation through traditional propagation rules, while on the Quantum Processing Unit (QPU), we calculate the gradient using the parameter-shift rule. Its a bit like having a dual system where the CPU manages the main training, and the QPU comes into play for specific quantum computations.

Visualize the training process pipeline in Figure 6, where represents the scale/bias parameters in the input layer, corresponds to the parameters of the layers containing the ansatz, and are the scale/bias parameters for the network outputs. This orchestration ensures a cohesive training approach, leveraging both classical and quantum computing resources.

As a Quantum Neural Network (QNN) operates as a feedforward model, our initial step involves defining a time horizon, denoted as T. To adapt the time series data for the QNN, we transform it into a tabular format. Here, the target is the time series value at time t, denoted as x(t), while the inputs encompass the values x(t-1), x(t-2), , x(t-T). This restructuring facilitates the models understanding of the temporal relationships in the data, allowing it to make predictions based on past values.

First, we fetch the data using the historical Data API endpoint provided by Financial Modeling Prep as follows:

The output is a Pandas dataframe which looks something like this (before that, make sure to replace YOUR API KEY with your secret API key):

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Stock Price Prediction with Quantum Machine Learning in Python - DataDrivenInvestor