Real Example Notebook Results¶

Executed outputs from the domain-oriented notebooks in notebooks/real_examples/. These examples use small reproducible physics, mathematics, or dynamical-system tasks.

Environment¶

Generated: stable
Git commit: stable
Python: 3.12.1
Package version: 0.2.14
Matplotlib backend: Agg

Summary¶

Notebook	Text result blocks	Plots
notebooks/real_examples/01-rabi-oscillation-parameter-inference.ipynb	3	2
notebooks/real_examples/02-ising-correlation-temperature-classifier.ipynb	3	2
notebooks/real_examples/03-lorenz-regime-classifier.ipynb	3	2
notebooks/real_examples/04-condensed-matter-tfim-phase-classifier.ipynb	3	2
notebooks/real_examples/05-pendulum-trajectory-surrogate.ipynb	3	2
notebooks/real_examples/06-damped-oscillator-parameter-inference.ipynb	3	2
notebooks/real_examples/07-tfim-hamiltonian-parameter-inference.ipynb	3	2
notebooks/real_examples/08-quantum-kernel-phase-discovery.ipynb	3	2
notebooks/real_examples/09-potential-energy-curve-interpolation.ipynb	3	2
notebooks/real_examples/10-lorenz-quantum-reservoir-regime-classifier.ipynb	3	2
notebooks/real_examples/11-noisy-oscillator-quantum-reservoir-inference.ipynb	3	2
notebooks/real_examples/12-heat-equation-diffusivity-inference.ipynb	3	2
notebooks/real_examples/13-kepler-orbit-regime-classifier.ipynb	3	2
notebooks/real_examples/14-vibrating-membrane-eigenfrequency-surrogate.ipynb	3	2
notebooks/real_examples/15-arrhenius-reaction-activation-energy-inference.ipynb	3	2
notebooks/real_examples/16-wave-equation-boundary-condition-classifier.ipynb	3	2
notebooks/real_examples/17-optical-diffraction-anomaly-detection.ipynb	3	2

Quantum Dynamics: Rabi Oscillation Parameter Inference¶

Notebook: notebooks/real_examples/01-rabi-oscillation-parameter-inference.ipynb

Result block 1:

Dataset
+-------------------+---------------------+
| Metric            | Value               |
+-------------------+---------------------+
| Samples           | 58                  |
| feature_shape     | [58, 3]             |
| Measurement times | [0.45, 0.95, 1.55]  |
| Omega range       | [0.721799, 2.38716] |
+-------------------+---------------------+

Result block 2:

Results
+-------------------+------------+
| Metric            | Value      |
+-------------------+------------+
| Quantum omega MAE | 0.0393237  |
| Quantum omega MSE | 0.00319466 |
| Ridge omega MAE   | 0.0273694  |
| Initial loss      | 0.580552   |
| Final loss        | 0.00697781 |
| Loss steps        | 72         |
+-------------------+------------+

Result block 3:

Validation
Dataset
+---------------+-----------------------------------------+
| Metric        | Value                                   |
+---------------+-----------------------------------------+
| Problem       | rabi_frequency_inference                |
| Features      | [P_e(t=0.45), P_e(t=0.95), P_e(t=1.55)] |
| Target        | rabi_frequency_omega                    |
| Train samples | 40                                      |
| Test samples  | 18                                      |
+---------------+-----------------------------------------+

Results
+-------------------+------------+
| Metric            | Value      |
+-------------------+------------+
| Quantum omega MAE | 0.0393237  |
| Quantum omega MSE | 0.00319466 |
| Ridge omega MAE   | 0.0273694  |
| Initial loss      | 0.580552   |
| Final loss        | 0.00697781 |
| Loss steps        | 72         |
+-------------------+------------+

Sample recoveries
1. Actual Omega: 1.999511, Quantum Omega: 2.027799, Ridge Omega: 1.981000
2. Actual Omega: 2.296350, Quantum Omega: 2.222178, Ridge Omega: 2.256309
3. Actual Omega: 1.474035, Quantum Omega: 1.486740, Ridge Omega: 1.458339
4. Actual Omega: 1.918194, Quantum Omega: 1.940107, Ridge Omega: 1.933709
5. Actual Omega: 1.762004, Quantum Omega: 1.732852, Ridge Omega: 1.756742
6. Actual Omega: 1.762079, Quantum Omega: 1.713610, Ridge Omega: 1.772137

Interpretation
The quantum inverse model trained successfully and recovers Rabi frequency within the validation tolerance.
The baseline is included as a sanity check; this validates package usage rather than quantum advantage.

Passed: True

Statistical Physics: Ising Temperature Classification¶

Notebook: notebooks/real_examples/02-ising-correlation-temperature-classifier.ipynb

Result block 1:

Dataset
+-------------------+--------------+
| Metric            | Value        |
+-------------------+--------------+
| Samples           | 48           |
| feature_shape     | [48, 3]      |
| Labels            | [24, 24]     |
| Temperature range | [1.35, 3.45] |
+-------------------+--------------+

Result block 2:

Results
+-------------------------+------------------+
| Metric                  | Value            |
+-------------------------+------------------+
| Quantum kernel accuracy | 0.933333         |
| Logistic accuracy       | 0.933333         |
| Confusion matrix        | [[8, 0], [1, 6]] |
| Kernel train shape      | [33, 33]         |
| Kernel diagonal minimum | 1                |
| Kernel symmetry error   | 6.66134e-16      |
+-------------------------+------------------+

Result block 3:

Validation
Dataset
+-------------------+--------------------------------------------------------------------------------------------------------+
| Metric            | Value                                                                                                  |
+-------------------+--------------------------------------------------------------------------------------------------------+
| Problem           | ising_temperature_regime_classification                                                                |
| Lattice size      | 8                                                                                                      |
| Samples           | 48                                                                                                     |
| Feature names     | [absolute_magnetization, nearest_neighbor_correlation, energy_density]                                 |
| Test temperatures | [1.959, 1.685, 3.137, 2.05, 2.589, 3.333, 1.654, 3.254, 3.215, 1.533, 2.98, 1.837, 1.411, 3.45, 1.776] |
| Test labels       | [0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0]                                                          |
| Test predictions  | [0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0]                                                          |
+-------------------+--------------------------------------------------------------------------------------------------------+

Results
+-------------------------+------------------+
| Metric                  | Value            |
+-------------------------+------------------+
| Quantum kernel accuracy | 0.933333         |
| Logistic accuracy       | 0.933333         |
| Confusion matrix        | [[8, 0], [1, 6]] |
| Kernel train shape      | [33, 33]         |
| Kernel diagonal minimum | 1                |
| Kernel symmetry error   | 6.66134e-16      |
+-------------------------+------------------+

Interpretation
The Ising features separate low- and high-temperature regimes for this small Monte Carlo dataset.
The quantum kernel and logistic baseline are sanity-checked side by side; this validates workflow correctness, not quantum advantage.

Passed: True

Nonlinear Dynamics: Lorenz Regime Classification¶

Notebook: notebooks/real_examples/03-lorenz-regime-classifier.ipynb

Result block 1:

Dataset
+---------------+----------+
| Metric        | Value    |
+---------------+----------+
| Samples       | 44       |
| feature_shape | [44, 3]  |
| Labels        | [22, 22] |
| Rho range     | [16, 38] |
+---------------+----------+

Result block 2:

Results
+-------------------------+------------------+
| Metric                  | Value            |
+-------------------------+------------------+
| Quantum kernel accuracy | 1                |
| Logistic accuracy       | 1                |
| Confusion matrix        | [[7, 0], [0, 7]] |
| Kernel train shape      | [30, 30]         |
| Kernel diagonal minimum | 1                |
| Kernel symmetry error   | 6.66134e-16      |
+-------------------------+------------------+

Result block 3:

Validation
Dataset
+------------------+---------------------------------------------------------------------------------------------------------+
| Metric           | Value                                                                                                   |
+------------------+---------------------------------------------------------------------------------------------------------+
| Problem          | lorenz_parameter_regime_classification                                                                  |
| Samples          | 44                                                                                                      |
| Feature names    | [mean_tail_z, std_tail_x, mean_abs_dx_tail]                                                             |
| Test rho values  | [16.571, 16, 19.429, 35.619, 38, 36.095, 16.286, 21.714, 37.048, 33.238, 28.952, 34.19, 16.857, 20.571] |
| Test labels      | [0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0]                                                              |
| Test predictions | [0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0]                                                              |
+------------------+---------------------------------------------------------------------------------------------------------+

Results
+-------------------------+------------------+
| Metric                  | Value            |
+-------------------------+------------------+
| Quantum kernel accuracy | 1                |
| Logistic accuracy       | 1                |
| Confusion matrix        | [[7, 0], [0, 7]] |
| Kernel train shape      | [30, 30]         |
| Kernel diagonal minimum | 1                |
| Kernel symmetry error   | 6.66134e-16      |
+-------------------------+------------------+

Interpretation
The Lorenz summary features distinguish the two chosen parameter regimes for this reproducible simulator.
The quantum kernel and logistic baseline are both sanity checks; this validates package usage rather than quantum advantage.

Passed: True

Condensed Matter: TFIM Phase Classification¶

Notebook: notebooks/real_examples/04-condensed-matter-tfim-phase-classifier.ipynb

Result block 1:

Dataset
+---------------+----------+
| Metric        | Value    |
+---------------+----------+
| Samples       | 48       |
| feature_shape | [48, 2]  |
| Labels        | [24, 24] |
+---------------+----------+

Result block 2:

Results
+-------------------------+-------------+
| Metric                  | Value       |
+-------------------------+-------------+
| Quantum kernel accuracy | 1           |
| Logistic accuracy       | 1           |
| Kernel train shape      | [33, 33]    |
| Kernel diagonal minimum | 1           |
| Kernel symmetry error   | 4.44089e-16 |
+-------------------------+-------------+

Result block 3:

Validation
Dataset
+------------------+----------------------------------------------------------------------------------------------------------+
| Metric           | Value                                                                                                    |
+------------------+----------------------------------------------------------------------------------------------------------+
| Problem          | finite_size_tfim_phase_classification                                                                    |
| N spins          | 4                                                                                                        |
| Samples          | 48                                                                                                       |
| Feature names    | [nearest_neighbor_zz_correlation, transverse_x_magnetization]                                            |
| Test fields      | [0.473, 1.463, 1.686, 0.697, 0.952, 0.346, 1.207, 0.378, 1.176, 1.527, 1.303, 0.505, 1.08, 1.016, 0.856] |
| Test labels      | [0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0]                                                            |
| Test predictions | [0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0]                                                            |
+------------------+----------------------------------------------------------------------------------------------------------+

Results
+-------------------------+-------------+
| Metric                  | Value       |
+-------------------------+-------------+
| Quantum kernel accuracy | 1           |
| Logistic accuracy       | 1           |
| Kernel train shape      | [33, 33]    |
| Kernel diagonal minimum | 1           |
| Kernel symmetry error   | 4.44089e-16 |
+-------------------------+-------------+

Interpretation
The TFIM feature set is cleanly separable in this finite-size example.
Both the quantum kernel model and the logistic baseline solve the held-out split perfectly, so this validates the workflow rather than demonstrating quantum advantage.

Passed: True

Dynamical Systems: Pendulum Trajectory Surrogate¶

Notebook: notebooks/real_examples/05-pendulum-trajectory-surrogate.ipynb

Result block 1:

Dataset
+---------------+----------------------+
| Metric        | Value                |
+---------------+----------------------+
| Samples       | 54                   |
| feature_shape | [54, 3]              |
| Target range  | [-0.57019, 0.562638] |
+---------------+----------------------+

Result block 2:

Results
+------------------+-----------+
| Metric           | Value     |
+------------------+-----------+
| Quantum test MAE | 0.241666  |
| Quantum test MSE | 0.0977921 |
| Ridge test MAE   | 0.261172  |
| Initial loss     | 0.557283  |
| Final loss       | 0.0745353 |
| Loss steps       | 75        |
+------------------+-----------+

Result block 3:

Validation
Dataset
+---------------+-------------------------------------------+
| Metric        | Value                                     |
+---------------+-------------------------------------------+
| Problem       | small_angle_pendulum_trajectory_surrogate |
| Features      | [theta0, omega0, time]                    |
| Target        | theta_at_time                             |
| Train samples | 37                                        |
| Test samples  | 17                                        |
+---------------+-------------------------------------------+

Results
+------------------+-----------+
| Metric           | Value     |
+------------------+-----------+
| Quantum test MAE | 0.241666  |
| Quantum test MSE | 0.0977921 |
| Ridge test MAE   | 0.261172  |
| Initial loss     | 0.557283  |
| Final loss       | 0.0745353 |
| Loss steps       | 75        |
+------------------+-----------+

Sample predictions
1. Actual: -0.340563, Quantum: -0.148739, Ridge: -0.148951
2. Actual: 0.295556, Quantum: 0.136990, Ridge: -0.018507
3. Actual: -0.075147, Quantum: -0.212564, Ridge: -0.145427
4. Actual: -0.244626, Quantum: 0.147142, Ridge: 0.100026
5. Actual: 0.392050, Quantum: 0.164307, Ridge: 0.110848
6. Actual: 0.036099, Quantum: 0.153176, Ridge: 0.111547

Interpretation
The quantum regressor trained successfully and reduced the optimization loss.
The held-out error is reasonable for a compact illustrative surrogate, but individual predictions can still be visibly imperfect.
The ridge baseline is included as a sanity benchmark; no quantum advantage is claimed.

Passed: True

Inverse Problems: Damped Oscillator Parameter Inference¶

Notebook: notebooks/real_examples/06-damped-oscillator-parameter-inference.ipynb

Result block 1:

Dataset
+---------------+-----------------------+
| Metric        | Value                 |
+---------------+-----------------------+
| Samples       | 60                    |
| feature_shape | [60, 2]               |
| Gamma range   | [0.0702778, 0.574796] |
+---------------+-----------------------+

Result block 2:

Results
+-------------------+-----------+
| Metric            | Value     |
+-------------------+-----------+
| Quantum gamma MAE | 0.0562714 |
| Ridge gamma MAE   | 0.0177185 |
| Initial loss      | 0.829008  |
| Final loss        | 0.0328188 |
| Loss steps        | 85        |
+-------------------+-----------+

Result block 3:

Validation
Dataset
+---------------+-------------------------------------+
| Metric        | Value                               |
+---------------+-------------------------------------+
| Problem       | damped_oscillator_damping_inference |
| Features      | [x(t=0.7), x(t=1.4)]                |
| Target        | damping_gamma                       |
| Train samples | 42                                  |
| Test samples  | 18                                  |
+---------------+-------------------------------------+

Results
+-------------------+-----------+
| Metric            | Value     |
+-------------------+-----------+
| Quantum gamma MAE | 0.0562714 |
| Ridge gamma MAE   | 0.0177185 |
| Initial loss      | 0.829008  |
| Final loss        | 0.0328188 |
| Loss steps        | 85        |
+-------------------+-----------+

Sample recoveries
1. Actual gamma: 0.405297, Quantum gamma: 0.502452, Ridge gamma: 0.415919
2. Actual gamma: 0.299665, Quantum gamma: 0.396080, Ridge gamma: 0.318860
3. Actual gamma: 0.085770, Quantum gamma: 0.130895, Ridge gamma: 0.094191
4. Actual gamma: 0.442487, Quantum gamma: 0.448133, Ridge gamma: 0.447158
5. Actual gamma: 0.142181, Quantum gamma: 0.133497, Ridge gamma: 0.155010
6. Actual gamma: 0.477434, Quantum gamma: 0.514308, Ridge gamma: 0.466378

Interpretation
The quantum inverse model trained successfully and recovers damping coefficients within the validation tolerance.
The ridge baseline is stronger on this simple inverse problem, so this validates package usage rather than quantum advantage.

Passed: True

Condensed Matter: TFIM Hamiltonian Parameter Inference¶

Notebook: notebooks/real_examples/07-tfim-hamiltonian-parameter-inference.ipynb

Result block 1:

Dataset
+----------+---------------------------------+
| Metric   | Value                           |
+----------+---------------------------------+
| Problem  | TFIM transverse-field inference |
| Samples  | 24                              |
| Features | [<Z>, <X>, <ZZ>, E0/N]          |
| Target   | transverse field h              |
+----------+---------------------------------+

Result block 2:

Results
+-------------------------+-----------+
| Metric                  | Value     |
+-------------------------+-----------+
| Trainable kernel h MAE  | 0.0483953 |
| Quantum GPR h MAE       | 0.147426  |
| Ridge h MAE             | 0.0103647 |
| Kernel-target alignment | 0.466965  |
+-------------------------+-----------+

Result block 3:

Validation
Dataset
+---------------+---------------------------------+
| Metric        | Value                           |
+---------------+---------------------------------+
| problem       | tfim_transverse_field_inference |
| n_train       | 16                              |
| n_test        | 8                               |
| feature_count | 4                               |
+---------------+---------------------------------+

Results
+-----------------------------+-----------+
| Metric                      | Value     |
+-----------------------------+-----------+
| trainable_kernel_h_mae      | 0.0483953 |
| quantum_gpr_h_mae           | 0.147426  |
| ridge_h_mae                 | 0.0103647 |
| trainable_kernel_alignment  | 0.466965  |
| trainable_kernel_loss_final | -0.466965 |
+-----------------------------+-----------+

Sample predictions
+----------+--------------------+---------------+
| actual_h | trainable_kernel_h | quantum_gpr_h |
+----------+--------------------+---------------+
| 1.19783  | 1.17612            | 1.14429       |
| 0.480435 | 0.488462           | 0.481546      |
| 1.4587   | 1.45176            | 1.44352       |
| 1.85     | 1.80081            | 1.61504       |
+----------+--------------------+---------------+

Passed
+--------+-------+
| Metric | Value |
+--------+-------+
| passed | True  |
+--------+-------+

Condensed Matter: Quantum Kernel Phase Discovery¶

Notebook: notebooks/real_examples/08-quantum-kernel-phase-discovery.ipynb

Result block 1:

Dataset
+----------+-----------------------------------------+
| Metric   | Value                                   |
+----------+-----------------------------------------+
| Problem  | TFIM phase discovery/classification     |
| Samples  | 36                                      |
| Classes  | {0: 'ferromagnetic', 1: 'paramagnetic'} |
| Features | [<Z>, <X>, <ZZ>, E0/N]                  |
+----------+-----------------------------------------+

Result block 2:

Results
+--------------------------+--------------------+
| Metric                   | Value              |
+--------------------------+--------------------+
| Quantum kernel accuracy  | 1                  |
| One-class phase accuracy | 0.727273           |
| Logistic accuracy        | 1                  |
| Kernel PCA eigenvalues   | [4.69121, 3.03512] |
+--------------------------+--------------------+

Result block 3:

Validation
Dataset
+---------------+----------------------+
| Metric        | Value                |
+---------------+----------------------+
| problem       | tfim_phase_discovery |
| n_train       | 25                   |
| n_test        | 11                   |
| feature_count | 4                    |
+---------------+----------------------+

Results
+--------------------------+--------------------+
| Metric                   | Value              |
+--------------------------+--------------------+
| quantum_kernel_accuracy  | 1                  |
| one_class_phase_accuracy | 0.727273           |
| logistic_accuracy        | 1                  |
| kpca_eigenvalues         | [4.69121, 3.03512] |
+--------------------------+--------------------+

Sample predictions
+----------+--------+--------+-----------+
| h        | actual | kernel | one_class |
+----------+--------+--------+-----------+
| 0.709562 | 0      | 0      | 0         |
| 0.525813 | 0      | 0      | 0         |
| 0.387803 | 0      | 0      | 1         |
| 0.707049 | 0      | 0      | 0         |
| 1.64825  | 1      | 1      | 1         |
+----------+--------+--------+-----------+

Passed
+--------+-------+
| Metric | Value |
+--------+-------+
| passed | True  |
+--------+-------+

Molecular Physics: Potential Energy Curve Interpolation¶

Notebook: notebooks/real_examples/09-potential-energy-curve-interpolation.ipynb

Result block 1:

Dataset
+-----------------+-------------------------------+
| Metric          | Value                         |
+-----------------+-------------------------------+
| Problem         | Morse potential interpolation |
| Training points | 18                            |
| Held-out points | 24                            |
| Features        | [bond length r, r^2]          |
| Target          | potential energy              |
+-----------------+-------------------------------+

Result block 2:

Results
+---------------------------------+-----------+
| Metric                          | Value     |
+---------------------------------+-----------+
| Quantum GPR energy MAE          | 0.0221625 |
| Quantum kernel ridge energy MAE | 0.073289  |
| Ridge energy MAE                | 0.572759  |
+---------------------------------+-----------+

Result block 3:

Validation
Dataset
+---------+-------------------------------+
| Metric  | Value                         |
+---------+-------------------------------+
| problem | morse_potential_interpolation |
| n_train | 18                            |
| n_test  | 24                            |
+---------+-------------------------------+

Results
+---------------------------------+-------------+
| Metric                          | Value       |
+---------------------------------+-------------+
| quantum_gpr_energy_mae          | 0.0221625   |
| quantum_kernel_ridge_energy_mae | 0.073289    |
| ridge_energy_mae                | 0.572759    |
| quantum_gpr_energy_mse          | 0.000778001 |
+---------------------------------+-------------+

Sample predictions
+----------+---------------+--------------------+
| r        | actual_energy | quantum_gpr_energy |
+----------+---------------+--------------------+
| 0.79878  | -0.0330634    | 0.0471411          |
| 0.896341 | -1.82574      | -1.78565           |
| 0.945122 | -2.50641      | -2.50454           |
| 0.993902 | -3.06713      | -3.0818            |
| 1.09146  | -3.88831      | -3.88523           |
+----------+---------------+--------------------+

Passed
+--------+-------+
| Metric | Value |
+--------+-------+
| passed | True  |
+--------+-------+

Dynamical Systems: Lorenz Quantum Reservoir Regime Classification¶

Notebook: notebooks/real_examples/10-lorenz-quantum-reservoir-regime-classifier.ipynb

Result block 1:

Dataset
+----------+----------------------------------------+
| Metric   | Value                                  |
+----------+----------------------------------------+
| Problem  | Lorenz regime classification           |
| Samples  | 40                                     |
| Classes  | {0: 'settled/periodic', 1: 'chaotic'}  |
| Features | [std_x, std_y, std_z, mean_step_speed] |
+----------+----------------------------------------+

Result block 2:

Results
+----------------------------+----------+
| Metric                     | Value    |
+----------------------------+----------+
| Quantum reservoir accuracy | 0.916667 |
| Quantum kernel accuracy    | 1        |
| Logistic accuracy          | 1        |
+----------------------------+----------+

Result block 3:

Validation
Dataset
+---------------+---------------------------------------------+
| Metric        | Value                                       |
+---------------+---------------------------------------------+
| problem       | lorenz_regime_classification_with_reservoir |
| n_train       | 28                                          |
| n_test        | 12                                          |
| feature_count | 4                                           |
+---------------+---------------------------------------------+

Results
+----------------------------+----------+
| Metric                     | Value    |
+----------------------------+----------+
| quantum_reservoir_accuracy | 0.916667 |
| quantum_kernel_accuracy    | 1        |
| logistic_accuracy          | 1        |
+----------------------------+----------+

Sample predictions
+---------+--------+-----------+--------+
| rho     | actual | reservoir | kernel |
+---------+--------+-----------+--------+
| 31.3047 | 1      | 1         | 1      |
| 26.8206 | 1      | 1         | 1      |
| 16.8081 | 0      | 0         | 0      |
| 30.7191 | 1      | 0         | 1      |
| 19.0278 | 0      | 0         | 0      |
+---------+--------+-----------+--------+

Passed
+--------+-------+
| Metric | Value |
+--------+-------+
| passed | True  |
+--------+-------+

Dynamical Systems: Noisy Oscillator Quantum Reservoir Inference¶

Notebook: notebooks/real_examples/11-noisy-oscillator-quantum-reservoir-inference.ipynb

Result block 1:

Dataset
+----------+------------------------------------------+
| Metric   | Value                                    |
+----------+------------------------------------------+
| Problem  | damped oscillator damping inference      |
| Samples  | 40                                       |
| Features | [x(t=0.2), x(t=0.7), x(t=1.2), x(t=1.7)] |
| Target   | damping coefficient gamma                |
+----------+------------------------------------------+

Result block 2:

Results
+-----------------------------+-----------+
| Metric                      | Value     |
+-----------------------------+-----------+
| Quantum reservoir gamma MAE | 0.112894  |
| Quantum GPR gamma MAE       | 0.114993  |
| Ridge gamma MAE             | 0.0389513 |
+-----------------------------+-----------+

Result block 3:

Validation
Dataset
+---------------+---------------------------------------+
| Metric        | Value                                 |
+---------------+---------------------------------------+
| problem       | damped_oscillator_reservoir_inference |
| n_train       | 28                                    |
| n_test        | 12                                    |
| feature_count | 4                                     |
+---------------+---------------------------------------+

Results
+-----------------------------+-----------+
| Metric                      | Value     |
+-----------------------------+-----------+
| quantum_reservoir_gamma_mae | 0.112894  |
| quantum_gpr_gamma_mae       | 0.114993  |
| ridge_gamma_mae             | 0.0389513 |
+-----------------------------+-----------+

Sample predictions
+--------------+-----------------+-----------+
| actual_gamma | reservoir_gamma | gpr_gamma |
+--------------+-----------------+-----------+
| 0.087205     | 0.224281        | 0.207131  |
| 0.312743     | 0.397964        | 0.493448  |
| 0.289192     | 0.236855        | 0.338626  |
| 0.102039     | 0.269038        | 0.186091  |
| 0.266321     | 0.282579        | 0.560718  |
+--------------+-----------------+-----------+

Passed
+--------+-------+
| Metric | Value |
+--------+-------+
| passed | True  |
+--------+-------+

Mathematical Physics: Heat Equation Diffusivity Inference¶

Notebook: notebooks/real_examples/12-heat-equation-diffusivity-inference.ipynb

Result block 1:

Dataset
+----------+---------------------------------------------------------+
| Metric   | Value                                                   |
+----------+---------------------------------------------------------+
| Problem  | heat equation diffusivity inference                     |
| Samples  | 42                                                      |
| Features | [T(x=0.15), T(x=0.32), T(x=0.50), T(x=0.68), T(x=0.85)] |
| Target   | thermal diffusivity alpha                               |
+----------+---------------------------------------------------------+

Result block 2:

Results
+--------------------------+------------+
| Metric                   | Value      |
+--------------------------+------------+
| Quantum GPR alpha MAE    | 0.00397051 |
| Quantum kernel alpha MAE | 0.0035871  |
| Ridge alpha MAE          | 0.00231943 |
+--------------------------+------------+

Result block 3:

Validation
Dataset
+---------------+-------------------------------------+
| Metric        | Value                               |
+---------------+-------------------------------------+
| problem       | heat_equation_diffusivity_inference |
| n_train       | 29                                  |
| n_test        | 13                                  |
| feature_count | 5                                   |
+---------------+-------------------------------------+

Results
+--------------------------+-------------+
| Metric                   | Value       |
+--------------------------+-------------+
| quantum_gpr_alpha_mae    | 0.00397051  |
| quantum_kernel_alpha_mae | 0.0035871   |
| ridge_alpha_mae          | 0.00231943  |
| quantum_gpr_alpha_mse    | 3.74068e-05 |
+--------------------------+-------------+

Sample predictions
+--------------+-------------------+----------------------+
| actual_alpha | quantum_gpr_alpha | quantum_kernel_alpha |
+--------------+-------------------+----------------------+
| 0.140964     | 0.143786          | 0.141828             |
| 0.0818125    | 0.0805856         | 0.081059             |
| 0.0623477    | 0.0652269         | 0.0651202            |
| 0.0632763    | 0.0645743         | 0.0634716            |
| 0.0408202    | 0.0472838         | 0.0445351            |
+--------------+-------------------+----------------------+

Passed
+--------+-------+
| Metric | Value |
+--------+-------+
| passed | True  |
+--------+-------+

Celestial Mechanics: Kepler Orbit Regime Classification¶

Notebook: notebooks/real_examples/13-kepler-orbit-regime-classifier.ipynb

Result block 1:

Dataset
+----------+--------------------------------------------------------------------------------------------+
| Metric   | Value                                                                                      |
+----------+--------------------------------------------------------------------------------------------+
| Problem  | Kepler orbit eccentricity regime classification                                            |
| Samples  | 44                                                                                         |
| Features | [r(theta=0.00), r(theta=1.05), r(theta=2.09), r(theta=3.14), r(theta=4.19), r(theta=5.24)] |
| Classes  | {0: 'low eccentricity', 1: 'high eccentricity'}                                            |
+----------+--------------------------------------------------------------------------------------------+

Result block 2:

Results
+----------------------------+----------+
| Metric                     | Value    |
+----------------------------+----------+
| Quantum kernel accuracy    | 1        |
| Quantum reservoir accuracy | 0.857143 |
| Logistic accuracy          | 1        |
+----------------------------+----------+

Result block 3:

Validation
Dataset
+---------------+------------------------------------+
| Metric        | Value                              |
+---------------+------------------------------------+
| problem       | kepler_orbit_regime_classification |
| n_train       | 30                                 |
| n_test        | 14                                 |
| feature_count | 6                                  |
+---------------+------------------------------------+

Results
+----------------------------+----------+
| Metric                     | Value    |
+----------------------------+----------+
| quantum_kernel_accuracy    | 1        |
| quantum_reservoir_accuracy | 0.857143 |
| logistic_accuracy          | 1        |
+----------------------------+----------+

Sample predictions
+--------------+---------------+-----------------------+
| eccentricity | actual_regime | quantum_kernel_regime |
+--------------+---------------+-----------------------+
| 0.672496     | 1             | 1                     |
| 0.209142     | 0             | 0                     |
| 0.806813     | 1             | 1                     |
| 0.624022     | 1             | 1                     |
| 0.0893147    | 0             | 0                     |
+--------------+---------------+-----------------------+

Passed
+--------+-------+
| Metric | Value |
+--------+-------+
| passed | True  |
+--------+-------+

Mathematical Physics: Vibrating Membrane Eigenfrequency Surrogate¶

Notebook: notebooks/real_examples/14-vibrating-membrane-eigenfrequency-surrogate.ipynb

Result block 1:

Dataset
+----------+------------------------------------------------+
| Metric   | Value                                          |
+----------+------------------------------------------------+
| Problem  | rectangular membrane eigenfrequency surrogate  |
| Samples  | 24                                             |
| Features | [length_x, length_y, wave_speed, aspect_ratio] |
| Target   | fundamental frequency                          |
+----------+------------------------------------------------+

Result block 2:

Results
+----------------------------------------+-----------+
| Metric                                 | Value     |
+----------------------------------------+-----------+
| Quantum kernel frequency MAE           | 0.0662286 |
| Trainable quantum kernel frequency MAE | 0.0524166 |
| Ridge frequency MAE                    | 0.033425  |
+----------------------------------------+-----------+

Result block 3:

Validation
Dataset
+---------------+---------------------------------------------+
| Metric        | Value                                       |
+---------------+---------------------------------------------+
| problem       | vibrating_membrane_eigenfrequency_surrogate |
| n_train       | 16                                          |
| n_test        | 8                                           |
| feature_count | 4                                           |
+---------------+---------------------------------------------+

Results
+----------------------------------------+------------+
| Metric                                 | Value      |
+----------------------------------------+------------+
| quantum_kernel_frequency_mae           | 0.0662286  |
| trainable_quantum_kernel_frequency_mae | 0.0524166  |
| ridge_frequency_mae                    | 0.033425   |
| quantum_kernel_frequency_mse           | 0.00699331 |
+----------------------------------------+------------+

Sample predictions
+------------------+--------------------------+---------------------+
| actual_frequency | quantum_kernel_frequency | trainable_frequency |
+------------------+--------------------------+---------------------+
| 0.390723         | 0.430414                 | 0.31475             |
| 0.627319         | 0.633867                 | 0.647667            |
| 0.458232         | 0.525136                 | 0.418127            |
| 0.641746         | 0.584093                 | 0.630248            |
| 0.402231         | 0.494952                 | 0.342284            |
+------------------+--------------------------+---------------------+

Passed
+--------+-------+
| Metric | Value |
+--------+-------+
| passed | True  |
+--------+-------+

Chemical Physics: Arrhenius Activation Energy Inference¶

Notebook: notebooks/real_examples/15-arrhenius-reaction-activation-energy-inference.ipynb

Result block 1:

Dataset
+----------+--------------------------------------------------------------+
| Metric   | Value                                                        |
+----------+--------------------------------------------------------------+
| Problem  | Arrhenius activation energy inference                        |
| Samples  | 38                                                           |
| Features | [C(T=295 K), C(T=315 K), C(T=335 K), C(T=355 K), C(T=375 K)] |
| Target   | activation energy Ea                                         |
+----------+--------------------------------------------------------------+

Result block 2:

Results
+-----------------------+----------+
| Metric                | Value    |
+-----------------------+----------+
| Quantum GPR Ea MAE    | 0.416631 |
| Quantum kernel Ea MAE | 0.424169 |
| Ridge Ea MAE          | 0.793175 |
+-----------------------+----------+

Result block 3:

Validation
Dataset
+---------------+---------------------------------------+
| Metric        | Value                                 |
+---------------+---------------------------------------+
| problem       | arrhenius_activation_energy_inference |
| n_train       | 26                                    |
| n_test        | 12                                    |
| feature_count | 5                                     |
+---------------+---------------------------------------+

Results
+--------------------------------------+----------+
| Metric                               | Value    |
+--------------------------------------+----------+
| quantum_gpr_activation_energy_mae    | 0.416631 |
| quantum_kernel_activation_energy_mae | 0.424169 |
| ridge_activation_energy_mae          | 0.793175 |
| quantum_gpr_activation_energy_mse    | 0.637986 |
+--------------------------------------+----------+

Sample predictions
+--------------------------+--------------------+-----------------------+
| actual_activation_energy | quantum_gpr_energy | quantum_kernel_energy |
+--------------------------+--------------------+-----------------------+
| 17.2036                  | 17.3653            | 17.3632               |
| 10.1722                  | 10.0827            | 10.0883               |
| 11.5282                  | 11.494             | 11.4831               |
| 16.5089                  | 16.7723            | 16.7452               |
| 7.94759                  | 10.5749            | 10.7777               |
+--------------------------+--------------------+-----------------------+

Passed
+--------+-------+
| Metric | Value |
+--------+-------+
| passed | True  |
+--------+-------+

Mathematical Physics: Wave Equation Boundary Condition Classification¶

Notebook: notebooks/real_examples/16-wave-equation-boundary-condition-classifier.ipynb

Result block 1:

Dataset
+----------+--------------------------------------------------+
| Metric   | Value                                            |
+----------+--------------------------------------------------+
| Problem  | wave equation boundary condition classification  |
| Samples  | 42                                               |
| Features | [f1/f1, f2/f1, f3/f1, f4/f1, scaled fundamental] |
| Classes  | {0: 'fixed-fixed', 1: 'fixed-free'}              |
+----------+--------------------------------------------------+

Result block 2:

Results
+----------------------------+----------+
| Metric                     | Value    |
+----------------------------+----------+
| Quantum kernel accuracy    | 1        |
| Quantum reservoir accuracy | 0.846154 |
| Logistic accuracy          | 1        |
+----------------------------+----------+

Result block 3:

Validation
Dataset
+---------------+-------------------------------------------------+
| Metric        | Value                                           |
+---------------+-------------------------------------------------+
| problem       | wave_equation_boundary_condition_classification |
| n_train       | 29                                              |
| n_test        | 13                                              |
| feature_count | 5                                               |
+---------------+-------------------------------------------------+

Results
+----------------------------+----------+
| Metric                     | Value    |
+----------------------------+----------+
| quantum_kernel_accuracy    | 1        |
| quantum_reservoir_accuracy | 0.846154 |
| logistic_accuracy          | 1        |
+----------------------------+----------+

Sample predictions
+-----------------+-------------------------+--------------------+
| actual_boundary | quantum_kernel_boundary | reservoir_boundary |
+-----------------+-------------------------+--------------------+
| 0               | 0                       | 0                  |
| 0               | 0                       | 0                  |
| 0               | 0                       | 0                  |
| 0               | 0                       | 0                  |
| 0               | 0                       | 0                  |
+-----------------+-------------------------+--------------------+

Passed
+--------+-------+
| Metric | Value |
+--------+-------+
| passed | True  |
+--------+-------+

Optics: Diffraction Pattern Anomaly Classification¶

Notebook: notebooks/real_examples/17-optical-diffraction-anomaly-detection.ipynb

Result block 1:

Dataset
+--------------------+-------------------------------------------------------------------------------------------------------+
| Metric             | Value                                                                                                 |
+--------------------+-------------------------------------------------------------------------------------------------------+
| Problem            | optical diffraction anomaly classification                                                            |
| Nominal profiles   | 24                                                                                                    |
| Anomalous profiles | 24                                                                                                    |
| Features           | [I(theta=-3.0), I(theta=-2.0), I(theta=-1.0), I(theta=0.0), I(theta=1.0), I(theta=2.0), I(theta=3.0)] |
| Classes            | {0: 'nominal', 1: 'anomalous'}                                                                        |
+--------------------+-------------------------------------------------------------------------------------------------------+

Result block 2:

Results
+----------------------------+----------+
| Metric                     | Value    |
+----------------------------+----------+
| Quantum kernel accuracy    | 1        |
| Quantum reservoir accuracy | 0.466667 |
| Logistic accuracy          | 1        |
| Quantum anomaly recall     | 1        |
+----------------------------+----------+

Result block 3:

Validation
Dataset
+---------------+--------------------------------------------+
| Metric        | Value                                      |
+---------------+--------------------------------------------+
| problem       | optical_diffraction_anomaly_classification |
| n_train       | 33                                         |
| n_test        | 15                                         |
| feature_count | 7                                          |
+---------------+--------------------------------------------+

Results
+----------------------------+----------+
| Metric                     | Value    |
+----------------------------+----------+
| quantum_kernel_accuracy    | 1        |
| quantum_reservoir_accuracy | 0.466667 |
| logistic_accuracy          | 1        |
| quantum_anomaly_recall     | 1        |
+----------------------------+----------+

Sample predictions
+--------------+---------------------------+----------------------+
| actual_label | quantum_kernel_prediction | reservoir_prediction |
+--------------+---------------------------+----------------------+
| 0            | 0                         | 1                    |
| 1            | 1                         | 1                    |
| 0            | 0                         | 1                    |
| 1            | 1                         | 1                    |
| 0            | 0                         | 1                    |
+--------------+---------------------------+----------------------+

Passed
+--------+-------+
| Metric | Value |
+--------+-------+
| passed | True  |
+--------+-------+

Reproduce¶

Regenerate notebook result pages from committed notebook outputs:

python docs/pages/generate_results.py --skip-api-results