In the realm of computational science, the fusion of quantum computing processing with various methodologies and frameworks represents a groundbreaking evolution in information science. This article delves into the essence of quantum methodologies and frameworks, exploring their structure, operational mechanisms, potential applications, benefits, and the challenges they present.

Please note that this article generally refers to methodologies and frameworks that are packaged, selected, tweaked, and adapted to provide what is currently being positioned as different 'Operating Systems.' We are still a very long way from a 'Windows' for quantum computing.

Diving into the world of quantum data science is like stepping into a sci-fi reality, where the computational rules we've grown accustomed to are turned on their heads. Here, in the quantum realm, our traditional ways of processing data, which have already worked wonders in understanding complex patterns and making predictions, are given a dose of quantum steroids, expanding their capabilities beyond the wildest dreams of classical computing.

The notion of quantum computing is akin to having a supercharged mathematics brain at our disposal, one that operates not just on the on-and-off switches of classical bits but on the probabilistic, multi-dimensional dance of qubits. This brain doesn't just think; it thinks in dimensions we're just beginning to understand, and for certain types of mathematical problems, quantum computing offers a magical can opener to solve some of the most complex optimisation and calculation problems of our time.

Yet, as with all great adventures into the unknown, the path to quantum supremacy is lined with challenges as daunting as they are exciting. The fragility of quantum states, the nascent state of our quantum hardware, and the intricate ballet of error correction are but a few hurdles in the race to realize the full potential of accurate and scalable quantum computation. We are certainly not there yet, but teams around the world are working to make scalable quantum computation a reality. There is full momentum developing in investment circles to back quantum technology, with government funds writing big checks and investing heavily in both building capabilities and deploying infrastructure, hoping to benefit from the economic outcomes associated with solving previously unsolvable problems for enterprises, governments, and science alike.

The promise—the sheer computational power, the ability to solve hitherto intractable problems, and the potential to revolutionise industries—keeps the dream alive and the capital flowing.

As we forge ahead, the narrative of Quantum Computing methodologies will undoubtedly be one of trial and error, of breathtaking breakthroughs and head-scratching conundrums. But in this narrative lies the future of computing, a future teeming with possibilities that stretch the very fabric of our computational cosmos. Research teams are furiously working away to create new algorithms that cannot even be benchmarked yet, just waiting for the promised processing power to be delivered and myriad current blockers to be removed in order to unleash quantum supremacy. Underpinning these algorithms are specific methodologies for implementing quantum computing solutions, whether for optimisation, simulation, or other computational tasks. Most (not all) are applied at the processing stage of a quantum computational process. For context and those not scientifically inclined, we are going to imagine that process as a Formula One race, where those fast cars race around the track.

Preparation: This is the initial stage where the quantum system is initialised, and data is encoded into qubits. It sets up the essential conditions necessary for the quantum computation to proceed. This stage is akin to calibrating, checking, and preparing your car before a race. You adjust the car's tires, engine, and onboard computer specifically for the quantum race you will participate in.

Processing: After preparation, the quantum system undergoes various computational processes. This stage is where quantum algorithms are executed, involving quantum gates and other operations that manipulate the state of the qubits to perform the intended computations. Essentially, this is the race itself—this is where the computing happens.

Control and Feedback: Integrated throughout the processing phase, this stage can be considered a distinct third phase. It involves monitoring the computation as it occurs, applying error correction, and making real-time adjustments based on feedback from quantum measurements to maintain the integrity and accuracy of the quantum computation. As your car races around the track, imagine how wind forces, failures, errors, suspension issues, noise, and environmental factors impact your ability to navigate the race. Similarly, decoherence and quantum noise affect the processing stage of a quantum computation, necessitating corrections.

During the race, if your car starts to fall apart, consider the Control stage as your car's onboard software, ensuring that any noise or vibration affecting your car is rectified by your onboard computer. Quantum Error Correction (QEC) is typically involved in the control process. QEC is essential for the practical implementation of reliable quantum computers, involving the creation of fault-tolerant procedures to protect quantum information against errors from decoherence and quantum noise.

Feedback can be likened to the pit team speaking to the driver via headset, giving instructions and making real-time adjustments to the onboard computer (ECC) to cope with changing environmental conditions.

Reading: Typically occurring after processing, this stage involves measuring the quantum system to extract information from the quantum state. The results of these measurements are then decoded into classical data that can be understood and utilised for further applications. Think of this as the computing finish line, where you receive your final race position and your trophy.

Storage: This final stage involves storing the quantum information, either by maintaining the quantum state of the system for future use or by converting and storing the results in a classical system. This stage is crucial for scenarios where quantum data needs to be reused or kept secure. Effectively, you put your trophy on the shelf to display it later.

Imagine quantum computing as entering not just one car in a race but a whole team of cars simultaneously. Each car takes a different path around the track, exploring various routes to find the fastest way to the finish line. In quantum computing, each 'car' represents a different possibility, and they all race at the same time. The goal isn't just to see which car wins, but to learn from all the cars' routes to determine the best overall strategy for winning future races. This parallel approach allows quantum computers to handle complex problems much faster than traditional computing, which would be akin to entering one car at a time.

Frameworks for Quantum Computing

Let's break down some of the quantum frameworks used in the creation of Quantum Algorithms. I apologise in advance to any technical readers wanting an explanation of why certain methodologies are chosen for specific problems; the aim of this article is to provide an overview for investors to understand key concepts. The selection of specific methodologies for particular problems involves a significant amount of mathematical explanation, which is outside the scope of this article.

The terms like Full-Quantum Neural Network (FQNN) and QFT / QPE / Quantum Annealing / VQA primarily refer to the structure, framework, or methodology used to construct algorithms, not the algorithm itself.

This distinction is important for understanding how methodologies fit into the broader landscape of quantum computing and machine learning. If we adapt our race car analogy in an incredibly simplified way, you can think of these quantum methodologies as the engine housing, the algorithms that facilitate the compute can be thought of as the engine, and the qubits can be considered the fuel in the tank that powers the computation.

There is somewhat misleading positioning of the "Quantum Operating System" in marketing and communications materials; generally, for the scope of this article, we will refer to these methodologies, frameworks, SDKS, and operating systems collectively as "Frameworks." So, let's look at our first framework, FQNN of Full Quantum Neural Networks. (Apologies, but the world of quantum is peppered with acronyms.)

Full-Quantum Neural Networks

At its core, a Full-Quantum Neural Network (FQNN) is a quantum analog of the classical neural network used in machine learning. Whereas classical neural networks operate on binary data (ones and zeros), processing information through layers of interconnected nodes (neurons) using classical bits, FQNNs operate on quantum data, using quantum bits (qubits) and quantum gates to process information. This quantum-based approach allows for the exploitation of superposition and entanglement, two cornerstone phenomena of quantum mechanics, thereby enabling a quantum neural network to analyse and process information in ways that are fundamentally unattainable by classical neural networks.

The FQNN is the underlying structure or architecture that supports quantum computing operations within the framework of a neural network, and the algorithms are the specific processes or methods implemented within this structure to solve particular problems. FQNNs potentially perform tasks more efficiently than classical neural networks, especially for problems that are naturally suited to quantum computation. The architecture of an FQNN closely mirrors that of its classical counterpart, comprising an input layer, one or more hidden layers, and an output layer. However, the neurons in these layers are not mere software constructs but are represented by qubits or systems of qubits. The connections between these quantum neurons, akin to synapses in biological neural networks, are modelled using quantum gates and operations that govern the interactions and transformations of quantum states.

Quantum Gates as Neurons: In FQNNs, the quantum gates function analogously to neurons in classical neural networks. These gates manipulate the quantum state of the qubits through various quantum operations, effectively performing the computational tasks typically handled by neurons in classical networks.

Implementation of Computational Tasks: While the structure provides the framework, the specific tasks that FQNNs perform, such as classification, regression, or pattern recognition, are defined by the algorithms that run on this structure. These algorithms determine how the quantum gates are arranged, how data is encoded into the qubits, how processing is conducted, and how outputs (measurements) are interpreted. Although FQNNs are theoretically possible and powerful, they may not universally be the fastest for all types of quantum data processing and exist largely in the realm of theoretical discussion rather than fully usable software architecture as of 2024. Here are a few other quantum computing methods that might be faster in certain scenarios:

Quantum Fourier Transform (QFT)

QFT is generally regarded as better for signals types computation, including modulation or demodulation in communications and for Quantum Radar Signal Analysis to interpret the radar signals that return from objects to determine their distance and speed relative to the radar source.

In classical computing, the Fourier transform is a mathematical tool that transforms a sequence of data points (usually in the time domain) into a representation in the frequency domain. It breaks down a waveform or function into its constituent frequencies, just like decomposing a musical chord into notes that make it up. This is particularly useful in signal processing, where understanding the frequency components of a signal can help in tasks like filtering noise or compressing data. It also has applications in music, radio and seismology.

Quantum Phase Estimation (QPE)

This is crucial for problems like finding eigenvalues of a unitary operator and can be significantly faster than classical or even some quantum neural network approaches for specific tasks. QPE seems to be used quite heavily in finance to evaluate complex financial derivatives and risk assessment models.

Quantum Annealing and Adiabatic Quantum Computing

For optimisation problems, quantum annealing can sometimes find solutions faster by exploiting quantum tunneling, especially in cases where the energy landscape of the problem is complex. This characteristic makes this approach particularly well-suited for complex optimization challenges.

Adiabatic Quantum Computing (AQC) is a form of quantum computing that operates on the principle of adiabatic evolution. This method is used to solve optimisation and sampling problems by gradually evolving an initial Hamiltonian into a final Hamiltonian, whose ground state encodes the solution to the problem. You can think of the Hamiltonian as a program loaded onto your quantum race car’s onboard computer.

Variational Quantum Algorithms (VQAs)

For certain types of problems like finding the ground state of a quantum system, VQAs can be faster because they are designed to run on noisy intermediate-scale quantum (NISQ) computers and are robust against certain types of errors. This may mean that they are more accurate for certain types of problem related to quantum chemistry or materials research, especially where electron correlation plays a significant role.

VQAs are designed to be feasible on todays devices, making them a practical choice even with the current limitations of quantum technology.

As quantum hardware improves, VQAs can scale to handle more complex molecules and interactions, potentially speeding up the drug discovery process significantly.

Quantum Walks

Quantum walks are the quantum counterpart of classical random walks and can be used to develop quantum algorithms. They are crucial for algorithms that explore large search spaces more efficiently than classical approaches and are useful for solving graph-based problems, searching databases, and quantum simulation.

Quantum walks are particularly useful in the design of search algorithms and for solving graph theory problems. For example, they are applied in the quantum search algorithm where they can provide a quadratic speedup over classical search algorithms in certain structured search spaces.

Quantum Simulation

Quantum simulation involves using a quantum system to simulate another quantum system. This methodology is particularly important in physics and chemistry for studying systems that are too complex to simulate accurately with classical computers.

Quantum Dynamics:

The simulation of quantum dynamics involves evolving the quantum state according to a Hamiltonian that models the energy and interactions within the quantum system. This can involve complex sequences of quantum gates that mimic these interactions over time.

If you want to simulate a quantum system, the Hamiltonian tells the quantum computer how to mimic the real quantum system’s behavior. Hamiltonians provide the detailed steps and ingredients needed to ensure the quantum computer performs as expected.

While Hamiltonians are integral to many quantum algorithms, particularly those simulating physical systems or solving optimisation problems, (Annealing, Adiabatic,Variational Quantum Algorithms) they are not universally necessary for all quantum algorithms. Some algorithms, especially those based on quantum information processing principles or specific quantum computing techniques, function without directly invoking a Hamiltonian. (QFT)

Gate-based Quantum Computing

This is the most common form of quantum computing, where algorithms are implemented using sequences of quantum gates, which manipulate qubits. This model forms the basis for implementing various quantum algorithms and is a fundamental methodology in developing quantum software.

As most people are generally aware of Gate based quantum computing we left it there, but you may be interested to read our article The Difference Between Quantum Gates, Walks and Annealing.

Measurement-based Quantum Computing (MBQC):

Also known as one-way quantum computing, this methodology uses a highly entangled initial state (like a cluster state) and performs computation through a sequence of adaptive measurements. MBQC represents an alternative to the circuit model of quantum computing.

While traditionally MBQC is seen as a general computation model rather than a simulation-specific framework, it is theoretically possible to use MBQC to perform quantum simulations.

It operates fundamentally differently from the typical gate-based quantum computing model. In MBQC, computations are carried out through a sequence of measurements on a pre-prepared highly entangled state (often a cluster state).

In conclusion, while MBQC can theoretically be adapted for quantum simulations, it is not commonly used for this purpose due to practical challenges and the efficiency of the gate-based models in handling the typical tasks associated with quantum simulations. Therefore, MBQC remains primarily a powerful alternative model for general quantum computing, and gate-based methods are more commonly employed for conducting quantum simulations.

Topological Quantum Computing:

This approach uses anyons and braiding for quantum computation. It is theoretically robust against local noise and errors because the qubits are stored in the topology of the quantum system, making it inherently fault-tolerant.

The concept of braiding is almost exclusively related to topological quantum computing. This form of computing leverages the topological properties of anyons, which are particularly well-suited for this type of manipulation due to their unique statistical characteristics and how they respond to being exchanged or braided.

Anyons are types of particles that can only exist in two-dimensional spaces and have unique properties that differ from the more familiar particles like electrons or photons. Unlike electrons which are fermions and photons which are bosons, anyons do not adhere to the conventional rules of particle statistics used in three dimensions.

In simpler terms, when two fermions are swapped, their quantum state acquires a negative sign, and when two bosons are swapped, their quantum state remains the same. Anyons, however, exhibit something in between: when two anyons are swapped, the quantum state of the system changes by a certain phase, which can be something other than just +1 or -1. This phase change depends on the type of anyon and how they are moved around each other, leading to their unique behavior and potential applications in quantum computing.

The reason topological quantum computing is so intriguing is its theoretical robustness to noise and errors. Since the computational operations are based on the topology (the global geometric features) of the particle paths, they are less susceptible to small local disturbances that can cause errors in other types of quantum computers.

In summary, quantum braiding is a fascinating and crucial component of topological quantum computing, providing a potentially powerful and fault-tolerant way to process information at the quantum level.

As one of the largest accepted problems in quantum computing is decoherence and error correction, advances in topological quantum computing methodologies could unlock significant value.

So what is the difference?

Algorithmic Focus: QFT and QPE are more algorithmic, focusing on specific computational tasks (Fourier transforms and phase estimations) which are great for signals use and quantum chemistry.

In contrast, quantum annealing and adiabatic quantum computing are more heuristic, aimed at solving broader optimisation problems or search.

Hardware Suitability: Quantum annealing has been particularly associated with specific types of quantum hardware (like those produced by D-Wave Systems), whereas VQAs and QPE can be implemented on a broader range of quantum computers.

Error Tolerance: VQAs are explicitly designed to be robust against certain types of errors, which is not inherently the case with QPE or QFT.

What is the best Quantum Architecture:

There is no one best quantum architecture. Using our race car analogy, you use the car that best fits the track. Different types of architectures are being worked on in labs and universities the world, many, one may even say most, of these algorithms have not yet been successfully benchmarked to provide any statistical advantage or "Quantum Supremacy" when compared to classical computing environments. Quantum Supremacy relates to a quantum computer solving a problem that no classical computer can solve in a feasible amount of time.

Teams are furiously building these architecture frameworks and the algorithms and burning the midnight oil in the expectation that the quantum processing power will increase and that innovation in key areas such as Quantum Error Correction, Feedback and the other significant problems limiting the scalability of quantum computing systems will indeed, one day eventually be solved.

Innovation in Quantum Architectures:

The architectures we are getting excited about are VQA's and Topological Quantum Computing because they may offer significant advantages, especially in molecular science and drugs discovery.

Both brand new and combinations of existing hybrid solutions containing sub components or combinations of many component parts of different architectures will undoubtably be where most of the innovation occurs.

For example, theoretically, the Hybrid Topological-Photonic Quantum Computing System (HTPQCS) is possible and could offer several significant advantages over other quantum computing methodologies

1. Topological Qubits: These are theoretically robust against local perturbations due to their reliance on braiding anyons, which are quasi-particles that encode information in their topological properties rather than their specific states. This makes the topological approach inherently fault-tolerant.

2. Photonic Links: Photonic technology is well-established for transmitting information with high speed and low loss, even over long distances. It's used in classical computing for optical data transmission and has been successfully demonstrated in basic quantum communication experiments.

3. Integration of Topological and Photonic Systems: While challenging, integrating these systems is theoretically possible. Photons can be used to interlink qubits stored in different quantum states or locations, facilitating quantum entanglement and state transfer across a quantum computing platform
   
   

The benefits of this type of combined / hybrid methodology and the many others that will follow are expected to allow for increased fault tolerance, scalability, speed of computation and hybridisation that could perform a wide range of quantum computations, from quantum simulations and cryptography to complex optimisation problems, leveraging the strengths of both technologies. However, and for the foreseeable future these developments and innovations are some years in the distance and would also require breakthroughs in both theoretical understanding and practical engineering to realise.

The Quantum Operating System?

There are indeed companies now working on packaging frameworks and software into Quantum Operating Systems, although it should be noted that the word "Operating System" is somewhat too liberally used and normally applied to help non practitioners that understand classical computing terminology to position and compartmentalise the technology.

Quantum operating systems are probably better termed as Quantum Architectures, they are software packages or single methodologies used to facilitate the Quantum Computation cycle, in some instances a more suitable terminology is probably SDK (Software Development Kit) for the majority of software applications using the Operating System Positioning. .

Interesting innovations and promising developments here come from companies including:

Parityqc.com - An Austrian company providing a quantum annealing architecture that offers to reduce the complexity and scalability in quantum calculations. Quantum Operating System

colibritd.com - Is a Quantum Innovative Computing Kit (QUICK) and Multiple Platform Quantum Programming (MPQP) language that offers cost efficient and hardware agnostic software to facilitate easier to run quantum computing computations. Quantum SDK

Well known SDKs include, for instance, IBM's Qiskit and AWS's Braket quantum computing service.

There are in fact an over-abundance of existing SDKs designed for platform specific purposes, but few that offer platform independent solutions. MicroSoft, Nvidia, Google, Ali Baba and BaiDu all have SDK's and their own SDK's and Operating Systems in the works. BaiDu have launched QIAN, aiming to bridge the gap between quantum hardware and practical applications.

Hardware companies like Alice & Bob and Dwave also offer a variety of solutions to facilitate ease of use of their platforms.

Challenges and Considerations:

• Technical Complexity: The technical complexity in building new architectures and methodologies should not be understated, the level of complexity and the skills required to ideate, define and then code new architectures and the benchmarking and testing are gargantuan efforts requiring highly skilled multi disciplinary teams in Quantum Physics, Mathematics and Data Science .

• Theoretical and Experimental Maturity: Many architectures and methodologies are still very much in experimental stages, with many still largely unexplored.

• Cost and Infrastructure: Developing such an advanced systems require substantial investment in research and development, specialised facilities, and materials.

• Hardware availability: Queue times for computational resources are already backing out of the door like your supermarket on a Friday night, there is more demand for compute on platforms like IBM than there is compute capacity.

• Hype & Market Confusion: There is a lot of mislabeling, unclear positioning and categorisation of quantum computing architectures.

The Future​ and The Return

Despite these challenges, the potential​ оf new quantum computing methodologies and architectures continues​ tо drive research and experimentation.​ As quantum hardware advances and more sophisticated algorithms are developed, the limitations facing the architectures of today may gradually​ be overcome.

This progress will likely lead​ tо practical applications​ оf specific architectures іn specialised fields, serving​ as​ a stepping stone towards more generalised quantum computing applications.

These architectures / methodologies and lets say very loosely "Quantum Operating Systems" will likely all find their specific niche, and at that point big players that need to have both a wide and deep offering in order to maximise the revenue and value they can provide will undoubtably move into acquire and consolidate many of the smaller players, resulting in potentially huge payers to the Savvy investment firms that back innovation in this area.