Dual-GSE: Resource-efficient Generalized Quantum Subspace Expansion

Quantum error mitigation (QEM) is a class of hardware-efficient error reduction methods through additional modest quantum operations and classical postprocessing on measurement outcomes. The generalized quantum subspace expansion (GSE) has been recently proposed as a unified framework of two distinct QEM methods: quantum subspace expansion (QSE) and purification-based QEM. GSE takes over the advantages of these two methods, achieving the mitigation of both coherent and stochastic errors. However, GSE still requires multiple copies of quantum states and entangled measurements between the copies, as required in purification-based QEM. This is a significant drawback under the current situation of the restricted number and connectivity of qubits. In this work, we propose a resource-efficient implementation of GSE, which we name "Dual-GSE", circumventing significant overheads of state copies by constructing an ansatz of error-mitigated quantum states via dual-state purification. Remarkably, Dual-GSE can further simulate larger quantum systems beyond the size of available quantum hardware with a suitable ansatz construction inspired by those divide-and-conquer methods that forge entanglement classically. This also contributes to a significant reduction of the measurement overhead because we only need to measure subsystems' Pauli operators. The proposed method is demonstrated by numerical simulation of the eight-qubit transverse field Ising model, showing that our method estimates the ground state energy in high precision under gate noise with low mitigation overhead and practical sampling cost.