Session: Quantum Computing and continuous optimization
Chair: David Bernal Neira
Cluster: Optimization for Emerging Technologies (LLMs, Quantum Computing, ...)
Talk 1: QHDOPT: A Software for Nonlinear Optimization with Quantum Hamiltonian Descent
Speaker: Yuxiang Peng
Abstract: We develop an open-source, end-to-end software (named QHDOPT), which can solve nonlinear optimization problems using the quantum Hamiltonian descent (QHD) algorithm. QHDOPT offers an accessible interface and automatically maps tasks to various supported quantum backends (i.e., quantum hardware machines). These features enable users, even those without prior knowledge or experience in quantum computing, to utilize the power of existing quantum devices for nonlinear and nonconvex optimization tasks. In its intermediate compilation layer, QHDOPT employs SimuQ, an efficient interface for Hamiltonian-oriented programming, to facilitate multiple algorithmic specifications and ensure compatible cross-hardware deployment. The detailed documentation of QHDOPT is available at https://github.com/jiaqileng/QHDOPT.
Talk 2: Minimization of Multi-variate Polynomials Using Entropy Computing
Speaker: Wesley Dyk
Abstract: The computing paradigm known as entropy quantum computing (EQC) has the capability of minimizing multi-variate polynomials. This paradigm operates by conditioning a quantum reservoir to promote the stabilization of the ground state in a quantum optical system. By mapping a polynomial to a Hamiltonian operator representing the total energy of a quantum system, the polynomial can be minimized using the optical quantum system as an analog computer. In one encoding scheme, variables are mapped to qudits, which exist in the photon number Hilbert space. Qudits are valued using normalized photon counts. This encoding scheme produces an approximation of continuous values for the variables, with an additional restriction that all variables sum to a user-specified total. We demonstrate this paradigm and encoding scheme together to solve QCL (quadratic objective, continuous variables, linear constraints) class problems from QPLIB of up to 500 variables. In many applications of model predictive control, relationships are simplified to accommodate the available solver tools. We demonstrate how EQC can overcome some limitations in solving complex models and then be used in just-in-time optimal control applications.
Talk 3: Non-convex Continuous Optimization Using Coherent Optical Networks
Speaker: Pooya Ronagh
Abstract: Analog computing using photonic integrated circuits (PIC) is a leading approach to surpassing the computational speed and energy limitations of von Neumann architectures. The challenges of manufacturing large-scale PICs have led to hybrid solutions that integrate optical analog and electronic digital components. A notable example is the coherent Ising machine (CIM), initially designed for solving quadratic binary optimization problems. We reinterpret the dynamics of optical pulses in the CIM as solutions to Langevin dynamics, a stochastic differential equation (SDE) that plays a key role in non-convex optimization and generative AI. This interpretation establishes a computational framework for understanding the system’s operation, the critical role of each component, and its performance, strengths, and limitations. Notably, we demonstrate that the CIM is inherently a continuous solver, capable of being extended to solve more general SDEs. Finally, we observe that the iterative digital-to-analog and analog-to-digital conversions within the protocol create a bottleneck for the low power and high speed of optics to shine and envision that fully analog opto-electronic realizations of such experiments can open doors for broader applications, and orders of magnitude improvements in speed and energy consumption.
