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.
values
state
orstate_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.).
metadata
elapsed_time
: Time to evaluate the physical quantity
The output of band_structure has the following structure.
values
kpt
: Coordinate of the k-pointband
: Energy band (“conduction band” or “valence band”)value
: Energy
metadata
elapsed_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
}
},
...
},
}