Abstract: A quantum computer executes quantum measurement plural times based on information related to a quantum circuit structure so as to acquire measurement results of the quantum measurement, and transmits the measurement results to a classical computer. The classical computer receives the measurement results and selects R individual measurement values from the measurement results. The classical computer generates an effective Hamiltonian based on a Hamiltonian H of a system to be computed and on the selected R individual measurement values, and computes a ground state of the Hamiltonian H and a ground state energy of the Hamiltonian H by diagonalizing a matrix representing the effective Hamiltonian.

Abstract: A classical computer outputs a Hamiltonian and initial information of a parameter expressing a quantum circuit. The classical computer, according to a parameter expressing a first quantum circuit that was output from a quantum computer and was generated by quantum computation employing a Variational Quantum Eigensolver (VQE) based on the Hamiltonian and the initial information, generates a parameter expressing a second quantum circuit including a rotation gate and outputs the parameter expressing the second quantum circuit. The classical computer, based on measurement results of quantum computation that were output from the quantum computer and computed according to the parameter expressing the second quantum circuit, based on the Hamiltonian, and based on a derivative function of the Hamiltonian, generates a derivative function of energy corresponding to the Hamiltonian and outputs the derivative function of energy.

Abstract: A quantum computer executes quantum measurement of <?1|Pi|?2>, <?1|Uij,+|?2>, <?1|Uij,?|?2>, <?1|Pj|?2>, and <?1|PiPj|?2< below based on a quantum state pair configured by a first quantum state ?1 and a second quantum state ?2, and outputs measurement results of the quantum measurement. A classical computer computes a transition amplitude |<?1|A|?2>|2 based on measurement results for <?1|Pi|?2>, <?1|Uij,+|?2>, <?1|Uij,?|?2>, <?1|Pj|?2>, and <?1|PiPj|?2>, wherein A is a physical quantity for computation of transition amplitude, i and j are indices for identifying a and P, a is a real number, P is a tensor product of a Pauli matrix, U is a unitary gate, and <?1|?2>=0.

Abstract: A quantum computer executes quantum measurement of <?1|Pi|?2>, <?1|Uij,+|?2>, <?1|Uij,?|?2>, <?1|Pj|?2>, and <?1|PiPj|?2< below based on a quantum state pair configured by a first quantum state ?1 and a second quantum state ?2, and outputs measurement results of the quantum measurement. A classical computer computes a transition amplitude |<?1|A|?2>|2 based on measurement results for <?1|Pi|?2>, <?1|Uij,+|?2>, <?1|Uij,?|?2>, <?1|Pj|?2>, and <?1|PiPj|?2>, wherein A is a physical quantity for computation of transition amplitude, i and j are indices for identifying a and P, a is a real number, P is a tensor product of a Pauli matrix, U is a unitary gate, and <?1|?2>=0.

Abstract: A classical computer outputs a Hamiltonian and initial information of a parameter expressing a quantum circuit. The classical computer, according to a parameter expressing a first quantum circuit that was output from a quantum computer and was generated by quantum computation employing a Variational Quantum Eigensolver (VQE) based on the Hamiltonian and the initial information, generates a parameter expressing a second quantum circuit including a rotation gate and outputs the parameter expressing the second quantum circuit. The classical computer, based on measurement results of quantum computation that were output from the quantum computer and computed according to the parameter expressing the second quantum circuit, based on the Hamiltonian, and based on a derivative function of the Hamiltonian, generates a derivative function of energy corresponding to the Hamiltonian and outputs the derivative function of energy.

Abstract: A classical computer decides a set of k+1 mutually orthogonal initial states for a Hamiltonian H of qubit number n, wherein k is an integer from 0 to 2n?1, and n is a positive integer. The classical computer decides a first quantum circuit U (?) that is a unitary quantum circuit of qubit number n. The classical computer decides a first parameter ?i and generating quantum computation information for executing the first quantum circuit U (?i) on a qubit cluster of a quantum computer. The classical computer stores a computation result of respective quantum computations based on the quantum computation information for each of the set of initial states. The classical computer computes an expected value sum L1 (?i) of the Hamiltonian H based on the computation results for the initial states. The classical computer stores a value ?* when a convergence condition has been satisfied.