Computing n-Time Correlation Functions without Ancilla Qubits

A research team led by Xiaoyang Wang (Postdoctoral Researcher, Quantum Mathematical Science Team, iTHEMS) has proposed a new method for computing n-time correlation functions, which play a central role in understanding the dynamics of quantum many-body systems. The proposed approach requires neither ancilla qubits nor controlled operations, and evaluates correlation functions using only the unitary time evolution of the system of interest.

Conventional methods, such as the Hadamard test, rely on ancilla qubits that control the entire system, posing significant challenges for digital quantum processors with limited qubit connectivity and for analog quantum simulators where controlled operations are difficult or impossible to implement. The present work overcomes these limitations and broadens the range of quantum platforms on which multi-time correlation functions can be experimentally accessed.

The protocol was demonstrated on IBM quantum hardware with up to 12 qubits, where the team successfully measured the single-particle spectrum of the Schwinger model and the out-of-time-order correlator (OTOC) in the transverse-field Ising model. In addition, an error-mitigation strategy based on signal processing—combining signal filtering and correlation analysis—was introduced, enabling the recovery of ideal noiseless simulation results from noisy experimental data.

This work provides a new foundation for experimentally probing complex quantum many-body correlation functions under realistic hardware constraints, thereby strengthening the connection between theoretical predictions and quantum experiments.