Distributed Variational Quantum Linear Solver

How can networked quantum processors solve linear systems larger than a single near-term device can accommodate?

Approach

Partition the matrix into blocks and decompose local blocks into linear combinations of unitaries. Coordinate local objectives using DIGing and collective Adam.

My contribution

• Designed a distributed solver for systems of dimension 2⁵⁰ × 2⁵⁰.
• Derived a distributed least-squares formulation and local quantum cost functions.
• Evaluated expectation values with Hadamard tests and gradients with parameter-shift rules.

Results

PennyLane simulations show that the solvable system dimension grows with the number of agents while accommodating sparse communication graphs. Matrix product state simulations reach 51 qubits.

2026 preprint; submitted to the 2027 American Control Conference.