Solving Large‐Scale Linear Systems of Equations by a Quantum Hybrid Algorithm

Today's intermediate-scale quantum computers, although imperfect, already perform computational tasks that are manifestly beyond the capabilities of modern classical supercomputers. However, so far, quantum-enabled large-scale solutions have been realized only for limited set problems. Here a hybrid algorithm based on phase estimation and optimization circuit width depth is employed solving specific class large linear systems equations ubiquitous to many areas science engineering. A classification entanglement properties associated phase-estimation unitary operation introduced, enabling highly efficient search facilitated by straightforward matrix-to-circuit map. 217-dimensional problem implemented several IBM computer superconducting processors, record-breaking result system solved computer. Demonstrated realisation sets clear benchmark in quest future speedup solution.