Entropy Computing: A Paradigm for Optimization in an Open Quantum System (2407.04512v2)

Abstract: Modern quantum technologies using matter are designed as closed quantum systems to isolate them from interactions with the environment. This design paradigm greatly constrains the scalability and limits practical implementation of such systems. Here, we introduce a novel computing paradigm, entropy computing, that works by conditioning a quantum reservoir thereby enabling the stabilization of a ground state. In this work, we experimentally demonstrate the feasibility of entropy computing by building a hybrid photonic-electronic computer that uses measurement-based feedback to solve non-convex optimization problems. The system functions by using temporal photonic modes to create qudits in order to encode probability amplitudes in the time-frequency degree of freedom of a photon. This scheme, when coupled with electronic interconnects, allows us to encode an arbitrary Hamiltonian into the system and solve non-convex continuous variables and combinatorial optimization problems. We show that the proposed entropy computing paradigm can act as a scalable and versatile platform for tackling a large range of NP-hard optimization problems.

• The paper introduces entropy computing, a novel hybrid photonic-electronic paradigm using an open quantum system for solving non-convex optimization problems.
• The framework utilizes a hybrid optoelectronic setup (Dirac-3) that encodes arbitrary Hamiltonians and employs engineered dissipation to navigate complex energy landscapes more effectively than traditional methods.
• Experimental results demonstrate that entropy computing provides performance superior to classical algorithms like gradient descent and SDP for problems like maximum cut and k-cut, showcasing scalability and flexibility advantages.

Entropy Computing: A Paradigm for Optimization in an Open Quantum System

The paper "Entropy Computing: A Paradigm for Optimization in an Open Quantum System" introduces a novel computing paradigm known as entropy computing, specifically designed for addressing non-convex optimization problems through a hybrid photonic-electronic computing system. This innovative approach challenges the conventional closed-system quantum computing frameworks by leveraging an open quantum system architecture, allowing interactions with the environment to stabilize the ground state, thus improving scalability and practical applicability.

Background and Motivation

Numerous computational optimization problems, particularly NP-hard ones, pose significant challenges due to their inherent complexity and scale. These include finding high-quality approximations or optimal solutions within practical timeframes, crucial for real-world applications. Traditional computational methods and special-purpose processors, both classical and quantum, often encounter scalability issues and extended solution times because of these complexities. Existing approaches like quantum annealing and coherent Ising machines, although promising, face significant constraints related to connectivity, scalability, and the effective mapping of non-Ising problems.

Entropy Computing Framework

The proposed entropy computing framework advances beyond existing quantum analog approaches by conditioning a quantum reservoir. This is achieved through a hybrid optoelectronic setup that utilizes measurement-based feedback to solve non-convex optimization challenges. The system encodes quantum states within temporal photonic modes, effectively using qudits to manage probability amplitudes in a photon's time-frequency domain.

This paradigm allows encoding arbitrary Hamiltonians, enabling the computation to occur within the photon number Hilbert space. By introducing a designed dissipation mechanism, the system promotes quantum state stabilization towards lower energy configurations, mitigating the common pitfalls of local minima entrapment typical in such optimization problems.

Experimental Implementation and Performance

The hybrid system, termed the Dirac-3, employs coherent photonic qudit time-bins functioning in a feedback loop, moderated by electronic components that configure the optimization problem. It is capable of handling optimization tasks with various variable types (binary, mixed-integer, continuous) across multiple problem constraints. By leveraging a polynomial loss function with programmable weight tensors up to fifth-order terms, the device effectively tackles NP-hard tasks showcasing scalability and flexibility advantages over traditional Ising-type solvers.

The results demonstrate the effectiveness of entropy computing in solving complex optimization problems, providing solutions superior to classical methods such as gradient descent, particularly when extending beyond binary problems to handle richer multidimensional interactions efficiently. The research highlights a performance improvement in maximum cut and maximum k-cut problems over existing state-of-the-art solutions like Semi-Definite Programming (SDP).

Implications and Future Directions

The introduction of entropy computing represents a significant step towards practical, scalable quantum computing for optimization. By reducing dependency on auxiliary variables typically necessary in quadratization for higher-order problem mappings, this paradigm sets a foundation for more efficient high-order problem-solving. The open-system approach not only enhances the solution's quality but offers a sustainable path forward in the energy-intensive field of high-performance computing.

Future developments may focus on refining hybrid and fully optical solutions, optimizing single-photon regimes, expanding the photonic integration on chips for broader application deployment, and further benchmarking against a diverse set of optimization challenge libraries. These advancements could elucidate potential new frontiers within AI and optimization fields, altering how complex computations are approached across various scientific and industrial disciplines.