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1. Basic: Calculation of ground state energy with VQE

A simple procedure to use QURI is explained with an example of a ground state energy calculation of the hydrogen molecule (H2\text{H}_2.)

1-1. How to perform calculation​

1-1-1. Log in​

Click the 'Log In' and enter the email address and password you have registered to log in.

1-1-2. Molecule settings​

Fill the Basic / Molecule section with the information on the target molecule.

  1. Enter the atomic coordinates into the Coordinates field. A line of the input here consists of [element symbol] [x coordinate] [y coordinate] [z coordinate] in units of Å. In this example, the following coordinates are used.
H 0.0 0.0 0.35
H 0.0 0.0 -0.35

Avogadro or Molview (external services) are convenient for creating xyz coordinates for the target molecule.

  1. Enter the basis set to use into the Basis field. In this example, sto-3g is used.

1-1-3. SCF Settings​

Fill the Basic / SCF Settings section with the settings for SCF calculation.

  1. Enter the spin multiplicity of the target state into the Multiplicity field. In this example, the multiplicity is 1.

  2. Enter the charge of the target state into the Charge field. In this example, the charge is 0.

1-1-4. Active space settings​

Fill the Basic / Active space section with the settings for the active space.

  1. Enter the number of electrons in the active space into the Number of electrons field. In this example, the number of electrons is 2.

  2. Enter the number of active orbitals into the Number of orbitals field. In this example, the number of orbitals is 2. When the sto-3g basis set is used for the hydrogen molecule, two molecular orbitals are generated from linear combinations of the 1s orbitals from each hydrogen atom.

1-1-5. Simulation method settings​

Select the method to simulate the quantum circuit from the Advanced / Device field. In this example, state vector simulator, which is selected by default, is used.

1-1-6. Launch the calculation​

Click Launch to launch the calculation. When the calculation job is finished, the result page is shown.

1-2. See the results​

1-2-1. Job Result​

If Job Result / Status is success, the job is successfully finished.

1-2-2. Molecule Results​

See the Molecule Results section for calculation results such as the molecular energy.

  1. The calculated energy is shown in the VQE & classical CASCI results field. VQE is the results from quantum circuit simulator and CASCI is the eigenvalues from diagonalization of the CASCI Hamiltoian.

  2. A graphical representation of the input molecule is shown in the Structure field.

  3. A plot of the Cost function as a function of the number of iterations is shown in the Cost function history field. In this example, the value of the cost function is equal to the molecular energy.

1-2-3. Quantum Resources​

See the Quantum Resources field for information on the quantum circuit and the resources used by its simulator during the execution of this job.

  1. Information on the quantum circuit is shown in the Quantum Circuit field.
  • Number of qubits: The number of qubits required for the circuit. In this example, the value is 4, which is equal to the number of the spin-orbitals in the active space.
  • Number of params: The number of parameters in the circuit.
  • Number of gates: The total number of quantum gates in the circuit.
  • Number of 1-qubit gates: The number of 1-qubit gates in the circuit.
  • Number of 2-qubit gates: The number of 2-qubit gates in the circuit.
  1. Information on the sampling simulation is shown in the Sampling field.
  • Observable groups: The number of operator groups that can be simultaneously measured in the cost function.
  • Total shots: The total number of measurements performed, i.e. the number of samples.

In this calculation, Total shots is equal to 0 , because state vector simulator is used and no sampling is performed.

  1. The estimated execution time to perform the calculation with a real quantum computer is shown in the Estimated execution time field.
  • Superconductor (s): The estimated execution time with a superconducting quantum computer.
  • Trapped ion (s): The estimated execution time with an ion trap quantum computer.

In this example, both values are 0 because state vector simulator is used.