Dynex

Industries

Compute on Dynex

Dynex

Industries

Compute on Dynex

Dynex

Industries

Compute on Dynex

# Dynex Neuromorphic Chip

### Dynex Neuromorphic Chip

#### Dynex Neuromorphic Chip

A Dynex machine is a class of general-purpose computing machines based on memory systems, where information is processed and stored at the same physical location. We analyze the memory properties of the Dynex machine to demonstrate that they possess universal computing power—they are Turing- complete—, intrinsic parallelism, functional polymorphism, and information overhead, namely that their collective states can support exponential data compression directly in memory through their collective states. Moreover, we show that the Dynex machine is capable of solving NP-complete problems in polynomial time, just like a non-deterministic Turing machine. The Dynex machine, however, requires only a polynomial number of memory cells due to its information overhead. It is important to note that even though these results do not prove NP=P within the Turing paradigm, the concept of Dynex machines represents a paradigm shift from the current von Neumann architecture, bringing us closer to the concept of brain-like neural computation.

**n.quantum Circuit Simulation**

Herein, there will be many references to modern computers and the computation they perform. It is important to realise that computing is fundamentally a **physical process**. The statement may seem obvious when considering the physical processes harnessed by the electronic components of computers (for example, transistors), however, virtually any physical process can be harnessed for some form of computation. Note, that we are speaking of **Alan Turing’s model of computation**, that is, a mapping (transition function) between two sets of finite symbols (input and output) in discrete time.

It is important to distinguish between continuous and discrete time: **Dynex circuits** operate in **continuous time**, though, their **simulations** on modern computers **require** **the** **discretisation** of time. Continuous time is physical time: a fundamental physical quantity. Discrete time is not a physical quantity, and might be best understood as counting time: counting something (function calls, integration steps, etc.) to give an indication (perhaps approximation) of the physical time. In the literature of Physics and other Physical Sciences, physical time has an assigned SI unit of seconds, whereas in Computer Science and related disciplines, counting time is dimensionless.

**The Fourth Missing Circuit Element**

Modern computers rely on the implementation of uni-directional logic gates that represent Boolean functions. Circuits built to simulate Boolean functions are desirable because they are deterministic: A unique input has a unique, reproducible output.

Modern computers relegate the task of logic to central processing units (CPUs). However, the resources required for the task might exhaust the resources present within the CPU, specifically, cache memory. For typical processes on modern computers, random-access memory (RAM) is the memory used for data and machine code, and is external to the CPU. The physical separation of CPU and RAM results in what is known as the **von Neumann bottleneck**, a slow down in computation caused by the transfer of information between physical locations.

To overcome the von Neumann bottleneck, we propose computing with and in memory, utilising **ideal memristors**. Distinct from in-memory computation, it is an efficient computing paradigm that uses memory to process and store information in the same physical location.

A **memristor** is an electrical component that limits or regulates the flow of electrical current in a circuit and remembers the amount of charge that has previously flowed through it. Memristors are important because they are non-volatile, meaning that they **retain memory without power**.

The original concept for memristors, as conceived in 1971 by Professor Leon Chua at the University of California, Berkeley, was a nonlinear, passive two-terminal electrical component that linked electric charge and magnetic flux (**“The missing circuit element“**). Since then, the definition of memristor has been broadened to include any form of non-volatile memory that is based on resistance switching, which increases the flow of current in one direction and decreases the flow of current in the opposite direction.

Memristors, which are considered to be a sub-category of resistive RAM, are one of several storage technologies that have been predicted to replace flash memory. Scientists at HP Labs built the first working memristor in 2008 and since that time, researchers in many large IT companies have explored how memristors can be used to create smaller, faster, low-power computers that do not require data to be transferred between volatile and non-volatile memory.

A **digital Dynex chip** is realised as a **memristor based bi-directional logic circuit**. These circuits differ from traditional logic circuits in that input and output terminals are no longer distinct. In a traditional logic circuit, some input is given and the output is the result of computation performed on the input, via uni-directional logic gates. In contrast, a memristor based bi-directional logic circuit can be operated by **assigning the output** terminals, then **reading the input** terminals.

**Self-organising logic** is a recently-suggested framework that allows the solution of Boolean truth tables “in reverse,” i.e., it is able to satisfy the logical proposition of gates regardless to which terminal(s) the truth value is assigned (“terminal-agnostic logic”). It can be realised if time non-locality (memory) is present. A practical realisation of self-organising logic gates can be done by combining circuit elements with and without memory. By employing one such realisation, it can be shown numerically, that self-organising logic gates **exploit elementary instantons** to reach equilibrium points. Instantons are classical trajectories of the non-linear equations of motion describing self-organising logic gates, and connect topologically distinct critical points in the phase space. By linear analysis at those points it can be shown that these instantons connect the initial critical point of the dynamics, with at least one unstable direction, directly to the final fixed point. It can also be shown that the memory content of these gates only affects the relaxation time to reach the logically consistent solution. By solving the corresponding stochastic differential equations, since instantons connect critical points, noise and perturbations may change the instanton trajectory in the phase space, but not the initial and final critical points. Therefore, **even for extremely large noise levels**, the gates **self-organise to the correct solution**.

Note that the self-organising logic we consider here has no relation to the invertible universal Toffoli gate that is employed, e.g., in quantum computation. Toffoli gates are truly one-to-one invertible, having 3-bit inputs and 3-bit outputs. On the other hand, self-organising logic gates need only to satisfy the correct logical proposition, without a one-to-one relation between any number of input and output terminals. Instead, it is worth mentioning another type of bi-directional logic that has been recently discussed in using stochastic units (called p-bits). These units fluctuate among all possible consistent inputs. However, in contrast to that work, the invertible logic we consider here is **deterministic**.

With time being a fundamental ingredient, a **dynamical systems approach** is most natural to describe such gates. In particular, non-linear electronic (non-quantum) circuit elements with and without memory have been suggested as building blocks to realise self-organising logic gates in practice.

By assembling self-organising logic gates with the appropriate architecture, one then obtains circuits that can **solve complex problems efficiently** by mapping the equilibrium (fixed) points of such circuits to the solution of the problem at hand. Moreover, it has been proved that, if those systems are engineered to be point dissipative, then, if equilibrium points are present, they do not show chaotic behaviour or periodic orbits.

It was subsequently demonstrated, using topological field theory (TFT) applied to dynamical systems, that these circuits are described by a Witten-type TFT, and they support long-range order, mediated by instantons. Instantons are classical trajectories of the non-linear equations of motion describing these circuits.

**n.quantum Computing on Dynex**

The DynexSolve algorithm represents a n.quantum implementation of an efficient sampler to compute **Ising and Quadratic Unconstrained Binary Optimization** (QUBO) problems. Ising/QUBO problems are mapped onto a Dynex circuit and then being computed by the contributing workers. This ensures that traditional quantum algorithms can be computed without modifications on the Dynex platform using the Python based Dynex SDK. It also provides libraries which are compatible with Google TensorFlow, IBM Qiskit, PyTorch, Scikit-Learn and others. DynexSolve’s source codes are publicly available.

Ising and QUBO problems play a pivotal role in the field of quantum computing, establishing themselves as the de-facto standard for mapping complex optimization and machine learning problems onto quantum systems. These frameworks are instrumental in leveraging the unique capabilities of quantum computers to solve problems that are intractable for classical computers.

The Ising model, originally introduced in statistical mechanics, describes a system of spins that can be in one of two states. This model has been adapted to represent optimization problems, where the goal is to minimise an energy function describing the interactions between spins. Similarly, the QUBO framework represents optimization problems with binary variables, where the objective is to minimise a quadratic polynomial. Both models are equivalent and can be transformed into one another, allowing a broad range of problems to be addressed using either formulation.

The significance of Ising and QUBO problems in quantum computing lies in their natural fit with quantum annealing and gate-based quantum algorithms. Quantum annealers, for instance, directly implement the Ising model to find the ground state of a system, which corresponds to the optimal solution of the problem. This method exploits quantum tunnelling and entanglement to escape local minima, offering a potential advantage over classical optimization techniques. Gate-based quantum computers, on the other hand, use quantum algorithms like the Quantum Approximate Optimization Algorithm (QAOA) to solve QUBO problems. These algorithms use quantum superposition and interference to explore the solution space more efficiently than classical algorithms, potentially leading to faster solution times for certain problems.

The adoption of Ising and QUBO as standards in quantum computing is due to their versatility and the direct mapping of various optimization and machine learning tasks onto quantum hardware. From logistics and finance to drug discovery and artificial intelligence, the ability to frame problems within the Ising or QUBO model opens up new avenues for solving complex challenges with quantum computing. This standardisation also facilitates the development of quantum algorithms and the benchmarking of quantum hardware, accelerating progress in the quantum computing field.

The beautiful technical detail of the Dynex Chips is that at every point in time, the entire chip can be represented with a status vector, which means it can be stopped, reversed, exchanged and run in different time steps. This feature allows us to use it in an environment where the nodes can be constantly changing without interfering the effective computation.

**This makes it ideal for operating in a malleable, decentralised environment**.

A Dynex machine is a class of general-purpose computing machines based on memory systems, where information is processed and stored at the same physical location. We analyze the memory properties of the Dynex machine to demonstrate that they possess universal computing power—they are Turing- complete—, intrinsic parallelism, functional polymorphism, and information overhead, namely that their collective states can support exponential data compression directly in memory through their collective states. Moreover, we show that the Dynex machine is capable of solving NP-complete problems in polynomial time, just like a non-deterministic Turing machine. The Dynex machine, however, requires only a polynomial number of memory cells due to its information overhead. It is important to note that even though these results do not prove NP=P within the Turing paradigm, the concept of Dynex machines represents a paradigm shift from the current von Neumann architecture, bringing us closer to the concept of brain-like neural computation.

**n.quantum Circuit Simulation**

Herein, there will be many references to modern computers and the computation they perform. It is important to realise that computing is fundamentally a **physical process**. The statement may seem obvious when considering the physical processes harnessed by the electronic components of computers (for example, transistors), however, virtually any physical process can be harnessed for some form of computation. Note, that we are speaking of **Alan Turing’s model of computation**, that is, a mapping (transition function) between two sets of finite symbols (input and output) in discrete time.

It is important to distinguish between continuous and discrete time: **Dynex circuits** operate in **continuous time**, though, their **simulations** on modern computers **require** **the** **discretisation** of time. Continuous time is physical time: a fundamental physical quantity. Discrete time is not a physical quantity, and might be best understood as counting time: counting something (function calls, integration steps, etc.) to give an indication (perhaps approximation) of the physical time. In the literature of Physics and other Physical Sciences, physical time has an assigned SI unit of seconds, whereas in Computer Science and related disciplines, counting time is dimensionless.

**The Fourth Missing Circuit Element**

Modern computers rely on the implementation of uni-directional logic gates that represent Boolean functions. Circuits built to simulate Boolean functions are desirable because they are deterministic: A unique input has a unique, reproducible output.

Modern computers relegate the task of logic to central processing units (CPUs). However, the resources required for the task might exhaust the resources present within the CPU, specifically, cache memory. For typical processes on modern computers, random-access memory (RAM) is the memory used for data and machine code, and is external to the CPU. The physical separation of CPU and RAM results in what is known as the **von Neumann bottleneck**, a slow down in computation caused by the transfer of information between physical locations.

To overcome the von Neumann bottleneck, we propose computing with and in memory, utilising **ideal memristors**. Distinct from in-memory computation, it is an efficient computing paradigm that uses memory to process and store information in the same physical location.

A **memristor** is an electrical component that limits or regulates the flow of electrical current in a circuit and remembers the amount of charge that has previously flowed through it. Memristors are important because they are non-volatile, meaning that they **retain memory without power**.

The original concept for memristors, as conceived in 1971 by Professor Leon Chua at the University of California, Berkeley, was a nonlinear, passive two-terminal electrical component that linked electric charge and magnetic flux (**“The missing circuit element“**). Since then, the definition of memristor has been broadened to include any form of non-volatile memory that is based on resistance switching, which increases the flow of current in one direction and decreases the flow of current in the opposite direction.

Memristors, which are considered to be a sub-category of resistive RAM, are one of several storage technologies that have been predicted to replace flash memory. Scientists at HP Labs built the first working memristor in 2008 and since that time, researchers in many large IT companies have explored how memristors can be used to create smaller, faster, low-power computers that do not require data to be transferred between volatile and non-volatile memory.

A **digital Dynex chip** is realised as a **memristor based bi-directional logic circuit**. These circuits differ from traditional logic circuits in that input and output terminals are no longer distinct. In a traditional logic circuit, some input is given and the output is the result of computation performed on the input, via uni-directional logic gates. In contrast, a memristor based bi-directional logic circuit can be operated by **assigning the output** terminals, then **reading the input** terminals.

**Self-organising logic** is a recently-suggested framework that allows the solution of Boolean truth tables “in reverse,” i.e., it is able to satisfy the logical proposition of gates regardless to which terminal(s) the truth value is assigned (“terminal-agnostic logic”). It can be realised if time non-locality (memory) is present. A practical realisation of self-organising logic gates can be done by combining circuit elements with and without memory. By employing one such realisation, it can be shown numerically, that self-organising logic gates **exploit elementary instantons** to reach equilibrium points. Instantons are classical trajectories of the non-linear equations of motion describing self-organising logic gates, and connect topologically distinct critical points in the phase space. By linear analysis at those points it can be shown that these instantons connect the initial critical point of the dynamics, with at least one unstable direction, directly to the final fixed point. It can also be shown that the memory content of these gates only affects the relaxation time to reach the logically consistent solution. By solving the corresponding stochastic differential equations, since instantons connect critical points, noise and perturbations may change the instanton trajectory in the phase space, but not the initial and final critical points. Therefore, **even for extremely large noise levels**, the gates **self-organise to the correct solution**.

Note that the self-organising logic we consider here has no relation to the invertible universal Toffoli gate that is employed, e.g., in quantum computation. Toffoli gates are truly one-to-one invertible, having 3-bit inputs and 3-bit outputs. On the other hand, self-organising logic gates need only to satisfy the correct logical proposition, without a one-to-one relation between any number of input and output terminals. Instead, it is worth mentioning another type of bi-directional logic that has been recently discussed in using stochastic units (called p-bits). These units fluctuate among all possible consistent inputs. However, in contrast to that work, the invertible logic we consider here is **deterministic**.

With time being a fundamental ingredient, a **dynamical systems approach** is most natural to describe such gates. In particular, non-linear electronic (non-quantum) circuit elements with and without memory have been suggested as building blocks to realise self-organising logic gates in practice.

By assembling self-organising logic gates with the appropriate architecture, one then obtains circuits that can **solve complex problems efficiently** by mapping the equilibrium (fixed) points of such circuits to the solution of the problem at hand. Moreover, it has been proved that, if those systems are engineered to be point dissipative, then, if equilibrium points are present, they do not show chaotic behaviour or periodic orbits.

It was subsequently demonstrated, using topological field theory (TFT) applied to dynamical systems, that these circuits are described by a Witten-type TFT, and they support long-range order, mediated by instantons. Instantons are classical trajectories of the non-linear equations of motion describing these circuits.

**n.quantum Computing on Dynex**

The DynexSolve algorithm represents a n.quantum implementation of an efficient sampler to compute **Ising and Quadratic Unconstrained Binary Optimization** (QUBO) problems. Ising/QUBO problems are mapped onto a Dynex circuit and then being computed by the contributing workers. This ensures that traditional quantum algorithms can be computed without modifications on the Dynex platform using the Python based Dynex SDK. It also provides libraries which are compatible with Google TensorFlow, IBM Qiskit, PyTorch, Scikit-Learn and others. DynexSolve’s source codes are publicly available.

Ising and QUBO problems play a pivotal role in the field of quantum computing, establishing themselves as the de-facto standard for mapping complex optimization and machine learning problems onto quantum systems. These frameworks are instrumental in leveraging the unique capabilities of quantum computers to solve problems that are intractable for classical computers.

The Ising model, originally introduced in statistical mechanics, describes a system of spins that can be in one of two states. This model has been adapted to represent optimization problems, where the goal is to minimise an energy function describing the interactions between spins. Similarly, the QUBO framework represents optimization problems with binary variables, where the objective is to minimise a quadratic polynomial. Both models are equivalent and can be transformed into one another, allowing a broad range of problems to be addressed using either formulation.

The significance of Ising and QUBO problems in quantum computing lies in their natural fit with quantum annealing and gate-based quantum algorithms. Quantum annealers, for instance, directly implement the Ising model to find the ground state of a system, which corresponds to the optimal solution of the problem. This method exploits quantum tunnelling and entanglement to escape local minima, offering a potential advantage over classical optimization techniques. Gate-based quantum computers, on the other hand, use quantum algorithms like the Quantum Approximate Optimization Algorithm (QAOA) to solve QUBO problems. These algorithms use quantum superposition and interference to explore the solution space more efficiently than classical algorithms, potentially leading to faster solution times for certain problems.

The adoption of Ising and QUBO as standards in quantum computing is due to their versatility and the direct mapping of various optimization and machine learning tasks onto quantum hardware. From logistics and finance to drug discovery and artificial intelligence, the ability to frame problems within the Ising or QUBO model opens up new avenues for solving complex challenges with quantum computing. This standardisation also facilitates the development of quantum algorithms and the benchmarking of quantum hardware, accelerating progress in the quantum computing field.

The beautiful technical detail of the Dynex Chips is that at every point in time, the entire chip can be represented with a status vector, which means it can be stopped, reversed, exchanged and run in different time steps. This feature allows us to use it in an environment where the nodes can be constantly changing without interfering the effective computation.

**This makes it ideal for operating in a malleable, decentralised environment**.

A Dynex machine is a class of general-purpose computing machines based on memory systems, where information is processed and stored at the same physical location. We analyze the memory properties of the Dynex machine to demonstrate that they possess universal computing power—they are Turing- complete—, intrinsic parallelism, functional polymorphism, and information overhead, namely that their collective states can support exponential data compression directly in memory through their collective states. Moreover, we show that the Dynex machine is capable of solving NP-complete problems in polynomial time, just like a non-deterministic Turing machine. The Dynex machine, however, requires only a polynomial number of memory cells due to its information overhead. It is important to note that even though these results do not prove NP=P within the Turing paradigm, the concept of Dynex machines represents a paradigm shift from the current von Neumann architecture, bringing us closer to the concept of brain-like neural computation.

**n.quantum Circuit Simulation**

Herein, there will be many references to modern computers and the computation they perform. It is important to realise that computing is fundamentally a **physical process**. The statement may seem obvious when considering the physical processes harnessed by the electronic components of computers (for example, transistors), however, virtually any physical process can be harnessed for some form of computation. Note, that we are speaking of **Alan Turing’s model of computation**, that is, a mapping (transition function) between two sets of finite symbols (input and output) in discrete time.

It is important to distinguish between continuous and discrete time: **Dynex circuits** operate in **continuous time**, though, their **simulations** on modern computers **require** **the** **discretisation** of time. Continuous time is physical time: a fundamental physical quantity. Discrete time is not a physical quantity, and might be best understood as counting time: counting something (function calls, integration steps, etc.) to give an indication (perhaps approximation) of the physical time. In the literature of Physics and other Physical Sciences, physical time has an assigned SI unit of seconds, whereas in Computer Science and related disciplines, counting time is dimensionless.

**The Fourth Missing Circuit Element**

Modern computers rely on the implementation of uni-directional logic gates that represent Boolean functions. Circuits built to simulate Boolean functions are desirable because they are deterministic: A unique input has a unique, reproducible output.

Modern computers relegate the task of logic to central processing units (CPUs). However, the resources required for the task might exhaust the resources present within the CPU, specifically, cache memory. For typical processes on modern computers, random-access memory (RAM) is the memory used for data and machine code, and is external to the CPU. The physical separation of CPU and RAM results in what is known as the **von Neumann bottleneck**, a slow down in computation caused by the transfer of information between physical locations.

To overcome the von Neumann bottleneck, we propose computing with and in memory, utilising **ideal memristors**. Distinct from in-memory computation, it is an efficient computing paradigm that uses memory to process and store information in the same physical location.

A **memristor** is an electrical component that limits or regulates the flow of electrical current in a circuit and remembers the amount of charge that has previously flowed through it. Memristors are important because they are non-volatile, meaning that they **retain memory without power**.

The original concept for memristors, as conceived in 1971 by Professor Leon Chua at the University of California, Berkeley, was a nonlinear, passive two-terminal electrical component that linked electric charge and magnetic flux (**“The missing circuit element“**). Since then, the definition of memristor has been broadened to include any form of non-volatile memory that is based on resistance switching, which increases the flow of current in one direction and decreases the flow of current in the opposite direction.

Memristors, which are considered to be a sub-category of resistive RAM, are one of several storage technologies that have been predicted to replace flash memory. Scientists at HP Labs built the first working memristor in 2008 and since that time, researchers in many large IT companies have explored how memristors can be used to create smaller, faster, low-power computers that do not require data to be transferred between volatile and non-volatile memory.

A **digital Dynex chip** is realised as a **memristor based bi-directional logic circuit**. These circuits differ from traditional logic circuits in that input and output terminals are no longer distinct. In a traditional logic circuit, some input is given and the output is the result of computation performed on the input, via uni-directional logic gates. In contrast, a memristor based bi-directional logic circuit can be operated by **assigning the output** terminals, then **reading the input** terminals.

**Self-organising logic** is a recently-suggested framework that allows the solution of Boolean truth tables “in reverse,” i.e., it is able to satisfy the logical proposition of gates regardless to which terminal(s) the truth value is assigned (“terminal-agnostic logic”). It can be realised if time non-locality (memory) is present. A practical realisation of self-organising logic gates can be done by combining circuit elements with and without memory. By employing one such realisation, it can be shown numerically, that self-organising logic gates **exploit elementary instantons** to reach equilibrium points. Instantons are classical trajectories of the non-linear equations of motion describing self-organising logic gates, and connect topologically distinct critical points in the phase space. By linear analysis at those points it can be shown that these instantons connect the initial critical point of the dynamics, with at least one unstable direction, directly to the final fixed point. It can also be shown that the memory content of these gates only affects the relaxation time to reach the logically consistent solution. By solving the corresponding stochastic differential equations, since instantons connect critical points, noise and perturbations may change the instanton trajectory in the phase space, but not the initial and final critical points. Therefore, **even for extremely large noise levels**, the gates **self-organise to the correct solution**.

Note that the self-organising logic we consider here has no relation to the invertible universal Toffoli gate that is employed, e.g., in quantum computation. Toffoli gates are truly one-to-one invertible, having 3-bit inputs and 3-bit outputs. On the other hand, self-organising logic gates need only to satisfy the correct logical proposition, without a one-to-one relation between any number of input and output terminals. Instead, it is worth mentioning another type of bi-directional logic that has been recently discussed in using stochastic units (called p-bits). These units fluctuate among all possible consistent inputs. However, in contrast to that work, the invertible logic we consider here is **deterministic**.

With time being a fundamental ingredient, a **dynamical systems approach** is most natural to describe such gates. In particular, non-linear electronic (non-quantum) circuit elements with and without memory have been suggested as building blocks to realise self-organising logic gates in practice.

By assembling self-organising logic gates with the appropriate architecture, one then obtains circuits that can **solve complex problems efficiently** by mapping the equilibrium (fixed) points of such circuits to the solution of the problem at hand. Moreover, it has been proved that, if those systems are engineered to be point dissipative, then, if equilibrium points are present, they do not show chaotic behaviour or periodic orbits.

It was subsequently demonstrated, using topological field theory (TFT) applied to dynamical systems, that these circuits are described by a Witten-type TFT, and they support long-range order, mediated by instantons. Instantons are classical trajectories of the non-linear equations of motion describing these circuits.

**n.quantum Computing on Dynex**

The DynexSolve algorithm represents a n.quantum implementation of an efficient sampler to compute **Ising and Quadratic Unconstrained Binary Optimization** (QUBO) problems. Ising/QUBO problems are mapped onto a Dynex circuit and then being computed by the contributing workers. This ensures that traditional quantum algorithms can be computed without modifications on the Dynex platform using the Python based Dynex SDK. It also provides libraries which are compatible with Google TensorFlow, IBM Qiskit, PyTorch, Scikit-Learn and others. DynexSolve’s source codes are publicly available.

Ising and QUBO problems play a pivotal role in the field of quantum computing, establishing themselves as the de-facto standard for mapping complex optimization and machine learning problems onto quantum systems. These frameworks are instrumental in leveraging the unique capabilities of quantum computers to solve problems that are intractable for classical computers.

The Ising model, originally introduced in statistical mechanics, describes a system of spins that can be in one of two states. This model has been adapted to represent optimization problems, where the goal is to minimise an energy function describing the interactions between spins. Similarly, the QUBO framework represents optimization problems with binary variables, where the objective is to minimise a quadratic polynomial. Both models are equivalent and can be transformed into one another, allowing a broad range of problems to be addressed using either formulation.

The significance of Ising and QUBO problems in quantum computing lies in their natural fit with quantum annealing and gate-based quantum algorithms. Quantum annealers, for instance, directly implement the Ising model to find the ground state of a system, which corresponds to the optimal solution of the problem. This method exploits quantum tunnelling and entanglement to escape local minima, offering a potential advantage over classical optimization techniques. Gate-based quantum computers, on the other hand, use quantum algorithms like the Quantum Approximate Optimization Algorithm (QAOA) to solve QUBO problems. These algorithms use quantum superposition and interference to explore the solution space more efficiently than classical algorithms, potentially leading to faster solution times for certain problems.

The adoption of Ising and QUBO as standards in quantum computing is due to their versatility and the direct mapping of various optimization and machine learning tasks onto quantum hardware. From logistics and finance to drug discovery and artificial intelligence, the ability to frame problems within the Ising or QUBO model opens up new avenues for solving complex challenges with quantum computing. This standardisation also facilitates the development of quantum algorithms and the benchmarking of quantum hardware, accelerating progress in the quantum computing field.

The beautiful technical detail of the Dynex Chips is that at every point in time, the entire chip can be represented with a status vector, which means it can be stopped, reversed, exchanged and run in different time steps. This feature allows us to use it in an environment where the nodes can be constantly changing without interfering the effective computation.

**This makes it ideal for operating in a malleable, decentralised environment**.