Computing n-time correlation functions without ancilla qubits

n-time correlation function plays a central role in connecting theoretical predictions with experimental observations of a quantum system. Traditional approaches for computing n-time correlation functions on quantum computers, such as the Hadamard test, require an ancilla qubit. This ancilla should control the entire quantum system, posing significant challenges for digital quantum devices with limited qubit connectivity and for analog quantum platforms. Here, we propose a method for computing n-time correlation functions without the need for ancilla qubits, applicable to arbitrary fermionic and bosonic operators. We demonstrate the method by measuring bosonic and fermionic single-particle spectra and out-of-time-ordered correlators on near-term quantum computers.