CoTenN: Constrained Optimization with Tensor Networks

Simulation of physics problems is one of the most important use cases of quantum computing. For this class of problems, the goal is typically to find the minimum energy state, or the ground state, of a physical system’s Hamiltonian. These problems frequently have constraints, such as symmetry conditions, which must also be satisfied. To solve such problems, researchers in computational physics use quantum-inspired algorithms that execute on classical computers. In particular, tensor network-based eigensolvers such as DMRG have become popular. However, to use these eigensolvers, the constrained optimization problem must first be encoded as a tensor network that implements a low-rank decomposition of the system’s Hamiltonian and state vector. These tensor network encodings are highly flexible, allowing for variables with ≥ 2 quantum states and supporting efficient constraint encodings that directly constrain the state vector. A critical challenge to developing tensor network-based encodings is that, currently, the encoding process is manual; significant effort is required to identify an efficient encoding for a new physics problem. In this work, we introduce a quantum constrained optimization problem (QCOP), a general abstraction for describing minimization problems over quantum variables that are subject to hard constraints. We present Masq, the first constraint programming language for QCOPs implementable with tensor networks, and CoTenN, a compiler that automatically maps QCOPs specified with Masq programs to tensor networks. To demonstrate the utility of Masq and CoTenN, we formulate two physics problems in Masq and then use CoTenN to find their ground states. We find the CoTenN-generated tensor networks generally outperform SOTA problem formulations, providing between 2.05×–53.32× total speedups across runs for QCOPs and yielding up to 2.49 · 10 7 × lower truncation errors for otherwise unconstrained problems.