Dynex: The Neuromorphic Quantum Computing Platform

Despite the incredible power of today’s supercomputers, many complex computing problems cannot be addressed by conventional systems. The huge growth of data and our need to better understand everything from the universe to our own DNA leads us to seek new tools that can help provide answers. Quantum computing and Neuromorphic computing are the next frontiers in computing, providing an entirely new approach to solving the world’s most difficult challenges.

Neuromorphic quantum computing is a special type of computing that combines ideas from brain-like computing with quantum technology to solve problems. It works differently from regular quantum computing by using a network of connected components that can quickly react to changes, helping the system to swiftly find the best solutions.

Dynex is applying a Digital Twin of a physical neuromorphic quantum computing machine, which is operated on thousands of GPUs in parallel, delivering unparalleled quantum computing performance at scale for real-world applications.

Quantum computing employs some quantum phenomena to process information. It has been hailed as the future of computing but it is plagued by serious hurdles when it comes to its practical realization. Neuromorphic quantum computing is a paradigm that instead employs non-quantum dynamical systems and exploits time non-locality (memory) to compute. It can be efficiently emulated as Digital Twin in software and its path towards hardware is more straightforward. In essence, n.quantum computing is leveraging memory and physics to compute efficiently, a concept studied intensively by a number of researchers and institutions, including a $2M CORDIS funded project by the European Union amongst others.

This technology is exciting because it leads to computer systems that are faster and capable of handling complex tasks more efficiently than traditional computers.

Harnessing Quantum Advantage Today, a Decade Ahead of Projections

Market researchers are forecasting that full quantum advantage, characterized by effective error correction and scalability, will be achieved by 2040. However, Dynex's n.quantum computing technology enables customers to leverage this quantum advantage today, effectively providing a technological leap of more than a decade. By integrating advanced neuromorphic quantum computing capabilities, Dynex empowers users with unprecedented computational power and efficiency, positioning itself at the forefront of technological innovation well ahead of the projected timeline.

Neuromorphic Quantum Computing: A Milestone in Quantum History

Neuromorphic quantum computing, made publicly available in 2023, represents one of the most significant milestones in the history of quantum computing. As depicted in the timeline of key algorithm development, various breakthroughs have been made since the 1980s, including the Deutsch algorithm, Grover's algorithm, and quantum machine learning algorithms. The introduction of neuromorphic quantum computing builds upon these advancements by utilizing neuromorphic circuits that emulate the brain's architecture to perform quantum computations. This breakthrough technology enhances the efficiency and scalability of quantum computing, addressing limitations of traditional quantum hardware. By leveraging neuromorphic systems, we are now able to tackle complex computational problems with unprecedented speed and accuracy, marking a revolutionary leap forward in the field of quantum computing.

The Dynex Quantum Advantage

Dynex achieves quantum advantage by efficiently computing a Digital Twin of a physical system through the following steps:

1. A n.quantum computing problem is being submitted to the Dynex cloud with the Dynex SDK;
2. The problem is then converted into a circuit layout consisting of memristor-based logic gates. This circuit seeks the optimal energy ground state based on voltages and current;
3. Next, the circuit layout is transformed into a system of ordinary differential equations (ODEs) by applying their equations of motion, effectively creating a "Digital Twin" of the physical system. We have published the specific equations of motion used in this process;
4. This system of ODEs is solved on our distributed network of GPUs, similar to how the trajectory of the moon landing was simulated by considering the equations of motion for the Earth and the moon.
5. Once the desired number of integration steps (simulated time) is reached, the voltages on the circuit are read and passed back as the result of the computation.

Utilising Digital Twins of physical systems for computation has been demonstrated to exhibit similar characteristics to quantum superposition, quantum entanglement and quantum tunnelling effects. This is evidenced in works such as "Topological Field Theory and Computing with Instantons"[11] or "Superconducting Quantum Many-Body Circuits for Quantum Simulation and Computing"[10] amongst others.

These inherent physical mechanisms enable both, n.quantum computing circuits and quantum computing to navigate towards the best possible solution out of a vast array of potential configurations, by effectively mapping the solution into their system.

The NSF San Diego Supercomputer Center performed a stress-test to measure the capability of a similar memristor based simulated system on finding approximate solutions to hard combinatorial optimization problems. These fall into a class which is known to require exponentially growing resources in the worst cases, even to generate approximations. They showed that in a region where state of the art algorithms demonstrate this exponential growth, simulations of a memristor based system only require time and memory resources that scale linearly. Up to 64 × 10^6 variables (corresponding to about 1 billion literals), namely the largest case that they could fit on a single node with 128 GB of DRAM where simulated, supporting the theory of Dynex' n.quantum computing. They also measured the memory requirement to perform the simulations. Usage scaled linearly with increasing problem size, whereas traditional methods require exponentially growing memory. This stress test shows the considerable advantage of non-combinatorial, physics inspired approaches over standard combinatorial ones.

• Dynex Publications
• Dynex Benchmarks

Practical n.Quantum Computing with Dynex

Dynex's platform supports a variety of tools for creating and working with both n.quantum gate circuits and n.quantum annealing models. Quantum programs are mapped onto a Dynex n.quantum circuit and then computed by the contributing workers. This ensures that both traditional quantum algorithms and quantum gate circuits can be computed without modifications on the Dynex platform using the Python-based Dynex SDK. It also provides libraries compatible with Google TensorFlow, IBM Qiskit, PyTorch, Scikit-Learn, and others. All source codes are publicly available.

• Dynex n.Quantum Computing

Dynex: Native Support for Quantum Gate Circuits

Dynex's platform natively supports quantum gate circuits, which are integral to many well-known quantum algorithms. Programmers familiar with quantum gate circuit languages such as Qiskit, Cirq, Pennylane, and OpenQASM will find it straightforward to run their computations on the Dynex neuromorphic computing platform. These tools allow for the creation of quantum circuits, enabling the execution of famous algorithms like Shor's algorithm (for efficient problem-solving in number theory), Grover's search algorithm (for unstructured search), Simon's algorithm (for finding hidden periods), and the Deutsch-Jozsa algorithm (for determining the parity of a function).

Quantum gate circuits are a fundamental aspect of quantum computing, employing quantum bits (qubits) to perform computations. Unlike classical bits, qubits can exist in multiple states simultaneously due to quantum superposition, and can be entangled, allowing for the representation and manipulation of complex data structures. Quantum gate circuits manipulate these qubits using a series of quantum gates, analogous to classical logic gates, to perform specific operations.

The versatility of quantum gate circuits allows them to implement a wide range of quantum algorithms. Shor's algorithm, for instance, leverages quantum parallelism for efficient problem-solving in number theory. Grover's algorithm offers a quadratic speedup for unstructured search problems, showcasing the potential of quantum computing in database searches and optimization tasks. Simon's algorithm and the Deutsch-Jozsa algorithm further demonstrate the power of quantum computing in solving problems that are infeasible for classical systems, highlighting the unique advantages of quantum superposition and entanglement.

The support for these quantum gate circuits on the Dynex platform means that researchers and developers can seamlessly transition their existing quantum algorithms and applications to leverage Dynex's neuromorphic quantum computing capabilities. This integration facilitates the exploration of new computational paradigms and the development of advanced quantum applications, pushing the boundaries of what is possible with quantum computing.

Dynex: Native Support for Quantum Annealing

The Dynex platform also excels in computing Ising and QUBO problems, which 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 minimize an energy function describing the interactions between spins. Similarly, the QUBO framework represents optimization problems with binary variables, where the objective is to minimize 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 standardization also facilitates the development of quantum algorithms and the benchmarking of quantum hardware, accelerating progress in the quantum computing field.

Dynex SDK

The Dynex SDK natively supports both n.quantum gate-based circuits and n.quantum annealing-based sampling, seamlessly integrating with any Python code. Programmers who are familiar with quantum gate circuit languages such as Qiskit, Cirq, Pennylane, OpenQASM, or quantum annealing tools like the Dimod framework, PyQUBO, and other QUBO frameworks, will find it easy to run computations on the Dynex neuromorphic computing platform. The Dynex SDK supports both quantum circuits and quantum annealing, but without the typical constraints associated with conventional quantum machines. The Dynex SDK is a suite of open-source Python tools for solving hard problems with neuromorphic computing which helps reformulate your application’s problem for solution by the Dynex computing platform. It also handles communication between your application code and the Dynex neuromorphic computing platform automatically.

Next:

• Workflow: Formulation and Sampling