Block Coordinate Descent for Dynamic Portfolio Optimization on Finite-Precision Coherent Ising Machines

Abstract

Coherent Ising machines (CIMs) have emerged as specialized quantum hardware for large-scale combinatorial optimization. However, for large instances that remain challenging for classical methods, some platforms support only finite-precision inputs, and the required scaling and quantization can degrade solution quality. Dynamic portfolio optimization (DPO) can be formulated as a quadratic unconstrained binary optimization (QUBO) problem, but large instances are especially vulnerable to precision loss under global scaling. We propose a block coordinate descent method that decomposes the DPO model along the time dimension and iteratively solves compact time-block subproblems on the device. Experiments on finite-precision CIM hardware show that the method enables these instances to be solved under hardware precision limits, yields portfolios competitive with classical benchmark solvers, and reduces runtime through fast CIM solution of the resulting subproblems. These results demonstrate the promise of finite-precision CIMs as a practical and scalable approach to structured large-scale combinatorial optimization.

Figures (8)

• Figure 1: Illustration of a single BCD update. The QUBO matrix $Q$ exhibits a block-tridiagonal structure across time steps: black diagonal blocks represent intra-block terms, gray first off-diagonal blocks represent inter-block couplings, and white blocks are zero. At block $i$, the corresponding subproblem $(Q_{\mathrm{sub}}, x_{\mathrm{sub}})$ is extracted to construct the local QUBO $\widehat{Q}_i$ according to Eq. \ref{['eq:Q_hat']}. The resulting subproblem is then solved for $x_i^\star$ using either a classical solver or a CIM backend, and the solution is written back to update $x$.
• Figure 2: Comparison of net mean return under the covariance risk model for the dimension-48 DPO instance.
• Figure 3: Comparison of net mean return over time under the covariance risk model for the dimension-144 and dimension-528 DPO instances.
• Figure S1: Normalized closing-price trajectories of five selected assets.
• Figure S2: Comparison of net mean return under the semicovariance risk model for the dimension-48 DPO instance.