Quantum expectation value estimation by doubling the number of qubits

Estimating the expectation values of operators is crucial in many hybrid quantum-classical algorithms designed for near-term noisy devices. Its practical applications to quantum chemistry, however, are hampered by too many measurements required to suppress the statistical fluctuation. This is mainly because the expectation value of an operator, represented as a linear combination of multi-qubit Pauli operators (Pauli strings) on qubits, is estimated based on separate measurements of the individual Pauli strings, whose number grows with the system size. Here, to reduce the measurement cost, we utilize the fact that the expectation values of all the Pauli strings, albeit their absolute values alone, can be simultaneously ``measured'' by performing Bell basis measurements on two copies of the quantum state of interest. Taking molecular Hamiltonians for illustration, we numerically examine the efficiency of our method in terms of the measurement cost in comparison with the conventional methods adopted in near-term calculations.