Quantum device result¶
In this section, we will output the results of the quantum computer (simulator) calculations.
Quantum Device
VQE Log
Evaluated Properties
We will explain these items in sections below.
Quantum device¶
Output information of QuantumDevice specified in the input.
Output example¶
"quantum_device": {
"type": "SAMPLING_SIMULATOR"
}
VQE log¶
The log of VQE is output as follows
opt_params: parameters of optimized VQE (Note 3)cost_hist: History of the cost function for each statehistory: History of the cost function in each cycle of VQE.state: Electronic state (output only for VQD)
nfev: The number of times the cost function is evaluatednit: the number of cycles of VQEelapsed_time: calculation time of VQE in seconds.energy_hist: (Note 1, 4)history: The energy history of a VQE for each cycle (a.u.)state: the electronic state of the VQE
success: convergence information of the optimizationmessage: Message returned by the optimization routine. The contents vary depending on the optimization method.optimized_orbital: Optimized molecular orbital in OOVQE.quantum_resources: Information about computational resources for quantum computation.circuit: Information on quantum circuits (Ansatz part)num_qubit: Number of Qubitnum_parameter: number of parameters.num_gate: total number of gates.num_1qubit_gate: number of 1qubit gates.num_2qubit_gate: number of 2qubit gates.
sampling: Information about sampling (note 2)num_observable_groups: number of concurrent groups in the cost function (see Observable grouping for concurrent groups).total_shots: the total number of shots
estimated_execution_time: estimated execution time (note 2)superconductor: Estimated execution time in seconds for a superconducting quantum computer.trapped_ion: Estimated execution time (in seconds) using an ion trap-type quantum computer.
(Note 1) If the type of ansatz is FERMIONIC_ADAPTIVE, no output is
given.
(Note 2) Only output if the type of quantum_device is
SAMPLING_SIMULATOR.
(Note 3) The optimized parameters and the cost/energy histories are not
outputted when a value other than NONE is selected for type of
orbital_optimization.
(Note 4) The optimized parameters and the cost/energy histories are not
outputted when a value is selected MCVQE for type of solver,
and other than NONE is selected for type of
orbital_optimization.
Output example¶
"vqe_log": {
"opt_params": [
-0.9416036864094274,
1.5079628003756818,
...
],
"cost_hist": [
{
"history": [
-2.288522129847763,
-2.5728929940924505,
...
]
}
],
"nfev": 280,
"nit": 15,
"elapsed_time": 0.2707430289999999,
"energy_hist": [
{
"history": [
-0.9417947301166705,
-1.0902403282499935,
...
],
"state": 0
},
{
"state": 1,
"history": [
-0.4049326696144223,
-0.3924123375924636,
...
]
}
],
"success": true,
"message": "",
"quantum_resources": {
"circuit": {
"num_qubit": 4,
"num_parameter": 1,
"num_gate": 112,
"num_1qubit_gate": 16,
"num_2qubit_gate": 96
},
"sampling": {
"num_observable_groups": 5,
"total_shots": 220000
},
"estimated_execution_time": {
"superconductor": 121.31250955205853,
"trapped_ion": 104866.66666666666
}
},
"optimized_orbital": [
{
"mo_energy": [
-0.5954972513211284,
0.7144441932583552
],
"mo_coeff": [
[
0.5445586947820809,
1.2620659398031695
],
[
0.5445586947820809,
-1.2620659398031695
]
],
"molecular_orbital_data":{
"data": "[Molden Format]..."
"format": "MOLDEN",
}
state: 0
},
...
]
}
Evaluated properties¶
Output the following physical quantities as a list.
energy: energy of the electronic state (a.u.)
num_electrons: total number of electrons
multiplicity: spin multiplicity
sz_number: z-axis component of total spin
dipole_moment: the permanent dipole moment (a.u.)
oscillator_strength: the oscillator strength (a.u.)
transition_dipole_moment: transition dipole moments (a.u.)
gradient: first derivative of the nuclear coordinates (a.u.)
hessian: second derivative in nuclear coordinates (a.u.)
vibrational analysis: eigenfrequencies (1/cm) and vibration modes of the analysis
The output of each quantity has the following structure.
valuesstateorstate_pair: the output electronic state or its pairvalue: Calculated value of the physical quantity.sample_std: Calculated sample standard deviation (energy, dipole_moment only. Unavaliable when MCVQE solver is used.).
metadataelapsed_time: Time to evaluate the physical quantity
The output of band_structure has the following structure.
valueskpt: Coordinate of the k-pointband: Energy band (“conduction band” or “valence band”)value: Energy
metadataelapsed_time: Time to evaluate the physical quantity
algorithm: Algorithm used to find quasi-particle band energies (QSE or QEOM)
Given an observable represented as a sum of Pauli operators \(P_i\) with coefficients \(c_i\)
the sample standard deviation \(\sigma\) is calculated as follows: when the sample variance of the Pauli operator is \(Var(P_i)\) and the number of shots is \(n\),
However, this is valid only when no grouping of the Pauli operators is performed (NO_GROUPING is selected). When grouping is applied, covariance of the expectation values of the Pauli operators within the same groups is also incorporated.
Dipole moment¶
The value of dipole_moment outputs the values of the permanent
dipole moments in \(x, y, z\) direction as a list.
Transition dipole moment¶
The value of transition_dipole_moment outputs a list of the
values of the \(x, y, z\) direction of the transition dipole moments
as a real part and an imaginary part. Quantum computing may result in
the imaginary part of the transition dipole moments.
VQD calculates the absolute values only.
Oscillator Strength¶
The value of oscillator_strength outputs the value of the
oscillator strength.
Gradient¶
The value of gradient outputs first-order derivative of the
energy \(E\) with respect to the input nuclear coordinates
as the following list:
Hessian.¶
The value of heissian outputs second-order derivative of the
energy \(E\) with respect to the input nuclear coordinates
as a double list corresponding to the following matrix
Vibrational Analysis¶
In the value of the vibrational_analysis, each natural frequency
(1/cm) of the vibration mode and the corresponding vibration mode
normal_mode are calculated. The vector components of the vibration
mode correspond to
Output Example.¶
"evaluated_properties": [
{
"energy": {
"values": [
{"state": 0, "value": -1.1362360604901143},
{"state": 1, "value": -0.47828919430555683}
],
"metadata": {
"elapsed_time": 0.000997585000000134
}
},
},
{
"num_electrons": {
"values": [
{"state": 0, "value": 2.0},
{"state": 1, "value": 2.0},
],
"metadata": {
"elapsed_time": 0.000009585000000134
}
},
},
{
"multiplicity": {
"values": [
{"state": 0, "value": 1.0},
{"state": 1, "value": 3.0},
],
"metadata": {
"elapsed_time": 0.000007585000000134
}
},
},
{
"sz_number": {"values": [
{"state": 0, "value": 0.0},
{"state": 1, "value": 0.0},
],
"metadata": {
"elapsed_time": 0.000005578000000134
}
},
},
{
"dipole_moment": {
"values": [{"state": 0, "value": [0.0, 0.0, -1.1143463019003264e-07]}],
"metadata": {
"elapsed_time": 0.0004000680000000312
}
}
},
{
"transition_dipole_moment": {
"values": [
{
"state_pair": [0, 1],
"value": [
{"real": 0.0, "imag": 0.0},
{"real": 0.0, "imag": 0.0},
{"real": 1.683007710279183e-07, "imag": 0.0}
]
}
],
"metadata": {
"elapsed_time": 0.0022338280000000488
}
}
},
{
"gradient": {
"values": [
{
"state": 0,
"value": [0.0, 0.0, 0.03522682150310957, 0.0, 0.0, -0.035226821562505006],
"type": "HAMILTONIAN_NUMERICAL"
}
],
"metadata": {
"elapsed_time": 0.673054386
}
}
},
{
"hessian": {
"values": [
{
"value": [
[-0.02609510201324114, 0.0, 0.0, 0.02671120741221516, 0.0, 0.0],
[0.0, -0.02609510201324114, 0.0, 0.0, 0.026711207412215148, 0.0],
[0.0, 0.0, 0.5951536730703917, 0.0, 0.0, -0.5952415631144654],
[0.02671120741221516, 0.0, 0.0, -0.02609510201324114, 0.0, 0.0],
[0.0, 0.026711207412215148, 0.0, 0.0, -0.02609510201324114,0.0],
[0.0, 0.0, -0.5952415631470315, 0.0, 0.0, 0.5950908117050806]
],
"state": 0
}
],
"metadata": {
"elapsed_time": 5.235920265000001
}
}
},
{
"vibrational_analysis": {
"values": {
"state": 0,
"value": [
{
"frequency": {
"imag": 8.323188334444037,
"real": 0.0
},
"normal_mode": [
0.37024605639968616,
-0.5991240303578433,
0.0,
0.37024605639968616,
-0.5991240303578433,
0.0,
]
},{
...
},
],
"metadata": {
"elapsed_time": 4.942824509999998
}
},
...
},
}