Performance Benchmarks

Overview

This page documents the performance characteristics of the three neural backends and compares their execution behavior. All backends produced identical results while operating on CPU with the same random seed.

Backend Architectures

From README.md:184-192:

Three neural backends were used:

Hamiltonian: A spectral convolution network that applies a learned Hamiltonian operator

Schrödinger: A 2-channel network trained to propagate wavefunctions

Dirac: An 8-channel network operating on 4-component spinors

Each backend was loaded from its own checkpoint file. No weights were shared. No caches were synchronized. All three ran on CPU with identical random seeds.

Hamiltonian Backend

Spectral convolution networkCheckpoint: hamiltonian.pth

Schrödinger Backend

2-channel wavefunction propagationCheckpoint: checkpoint_phase3_training_epoch_18921_20260224_154739.pth

Dirac Backend

8-channel spinor networkCheckpoint: best_dirac.pth

State Representation

From README.md:173-182:

The simulator represents an n-qubit state as a tensor of shape (2^n, 2, G, G), where G = 16 is the spatial grid size. The first index labels computational basis states. The second index holds real and imaginary components. The last two indices represent a spatial wavefunction. Born probabilities are computed by integrating the squared modulus over the spatial grid: P(k) = Sum_ (alpha_^2 + alpha_^2) normalized so that Sum_k P(k) = 1.

Tensor dimensions:

2-qubit state: (4, 2, 16, 16) = 2,048 complex numbers
3-qubit state: (8, 2, 16, 16) = 4,096 complex numbers
4-qubit state: (16, 2, 16, 16) = 8,192 complex numbers

Execution Configuration

From README.md:5-18 and RESULTS.md:4-11:

python3 quantum_computer.py \
  --hamiltonian-checkpoint hamiltonian.pth \
  --schrodinger-checkpoint checkpoint_phase3_training_epoch_18921_20260224_154739.pth \
  --dirac-checkpoint best_dirac.pth \
  --grid-size 16 \
  --hidden-dim 32 \
  --expansion-dim 64 \
  --device cpu

Hardware: CPU-only execution Grid parameters:

Grid size: 16×16
Hidden dimension: 32
Expansion dimension: 64

From README.md:397:

GPU execution was not tested.

Algorithm Execution Times

Based on timestamp analysis from the experimental logs:

Quantum Algorithm Suite Timing (RESULTS.md:12-329)

From log timestamps (2026-03-01 05:04:52):Complete test suite execution per backend:

Start: 05:04:52,272
End: 05:04:52,454 (Dirac backend final)
Total elapsed: ~0.18 seconds for all three backends

This includes:

Bell state preparation
GHZ state preparation
Deutsch-Jozsa (constant and balanced)
QFT-3
Grover’s algorithm (2 iterations)
Quantum teleportation
Snapshot circuit (H-CNOT-Z-H)

Per backend: ~60 milliseconds

Phase Coherence Test Suite Timing (RESULTS.md:334-374)

From log timestamps:

Start: 05:04:52,516
End: 05:04:52,574
Duration: 58 milliseconds for 22 tests

Per test average: ~2.6 milliseconds

Molecular H₂ VQE Timing (RESULTS.md:375-430)

From log timestamps:

PySCF setup: 05:05:05,540 - 05:05:06,550 (~1 second)
Backend loading: 05:05:05,555 - 05:05:05,602 (~47 ms)
Parameter scan: 05:05:06,560 - 05:05:06,868 (~308 ms, 11 evaluations)
Optimization: 05:05:06,868 - 05:05:09,041 (~2.2 seconds, 30 evaluations)
Total VQE time: ~3.5 seconds (including PySCF)
Pure optimization: ~2.5 seconds

Grover's Algorithm Detailed (RESULTS.md:442-481)

From log timestamps (2026-03-01 05:05:19):

Backend loading: 05:05:19,687 - 05:05:19,745 (~58 ms)
Initial state preparation: 05:05:19,745 - 05:05:19,750 (~5 ms)
Iteration 1: 05:05:19,750 - 05:05:19,756 (~6 ms)
Iteration 2: 05:05:19,756 - 05:05:19,761 (~5 ms)
Total Grover execution: ~16 ms (2 iterations on 3 qubits)

VQE Optimization Convergence

H₂ Convergence Profile

From RESULTS.md:410-416:

  iter   1: E=-1.13707997 Ha  Δ_FCI=2.26e-04
  iter   2: E=-1.13707997 Ha  Δ_FCI=2.26e-04
  iter   3: E=-1.13707997 Ha  Δ_FCI=2.26e-04
  ...
  iter  20: E=-1.13730604 Ha  Δ_FCI=1.54e-10
  ...
  Optimizer: CONVERGENCE: RELATIVE REDUCTION OF F <= FACTR*EPSMCH  (30 evals)
  Final: E_VQE=-1.13730604  E_FCI=-1.13730604  corr=100.0%

Evaluation	Energy (Ha)	Error from FCI	Time (approx)
Initial scan	-1.13707997	2.26e-04	-
Iteration 1-3	-1.13707997	2.26e-04	<1s
Iteration 20	-1.13730604	1.54e-10	~1.4s
Final (30)	-1.13730604	1.31e-11	~2.2s

Convergence rate: Achieved 11 orders of magnitude improvement in 20 iterations.

Stark Effect Field Sweep

Field Sweep Performance (RESULTS.md:636-646)

The Stark effect calculation required VQE optimization at 9 field points (F = -0.02, -0.015, -0.01, -0.005, 0, +0.005, +0.01, +0.015, +0.02).Per-field optimization: Similar to single H₂ VQE (~2-3 seconds)Total field sweep: ~9 × 2.5s = ~22.5 seconds (estimated)This is for the complete field sweep including:

Hamiltonian construction at each field value
VQE parameter optimization
Energy evaluation

Backend Agreement

All three backends produced identical results across all tests:

Bell State: All Backends Identical (RESULTS.md:20-29, 124-133, 228-237)

Hamiltonian Backend:

MeasurementResult (2 qubits)
  Most probable: |00>  P=0.5000
  Shannon entropy: 1.0000 bits
  Top states:
    |00>  P=0.5000
    |11>  P=0.5000

Schrödinger Backend: Identical outputDirac Backend: Identical output

Grover: All Backends Identical (RESULTS.md:77-88, 181-192, 285-296)

All three backends produced:

P(|101>) = 0.9453
Shannon entropy = 0.4595 bits
Identical Bloch sphere coordinates

Numerical Precision

From README.md:248-267:

The baseline quantum algorithm suite continues to produce identical results across all three backends.

All probabilities match to at least 4 decimal places across backends. For the H₂ VQE calculation, all three backends would produce:

Energy: -1.13730604 Ha
Error from FCI: 1.31e-11 Ha

Scalability

Tested System Sizes

System	Qubits	Notes
Bell state	2	Standard test
GHZ state	3	Standard test
QFT	3	Uniform superposition
Grover	3	Amplitude amplification
Teleportation	3	Entanglement protocol
H₂ molecule	4	VQE with 5 parameters
H₂O molecule	14	PySCF processing only
NH₃ molecule	16	PySCF processing only
CH₄ molecule	18	PySCF processing only

From README.md:109:

The framework processed this without modification. The same code that handles H2 also handles H2O. The limitation is not in the neural backends but in classical FCI cost.

Memory Requirements

For G=16 grid size:

Qubits	States	Tensor shape	Memory (floats)
2	4	(4, 2, 16, 16)	2,048
3	8	(8, 2, 16, 16)	4,096
4	16	(16, 2, 16, 16)	8,192
14	16,384	(16384, 2, 16, 16)	8,388,608

At 4 bytes per float: 4-qubit state ≈ 32 KB, 14-qubit state ≈ 32 MB

Limitations

From README.md:393-398:

Polarizability was tested only for H2 with the STO-3G basis. I do not know if larger molecules or better basis sets preserve this accuracy. The QED calculations are approximate and do not use the neural backends directly. Polyatomic molecules were processed through PySCF but not optimized with VQE due to classical FCI cost scaling. The visualization system produces static figures; real-time animation remains unexplored. GPU execution was not tested.

Summary Statistics

Test Suite

22/22 tests passed~180ms total execution

H₂ VQE

100.0% correlation~2.5s optimization

Grover Search

94.53% success~16ms for 2 iterations

Polarizability

0.0% error9 field points evaluated

Results Summary - All experimental results
Constraint Preservation - Test suite details
Polarizability - Field sweep calculation

Papers

Experiments

Overview

Backend Architectures

Hamiltonian Backend

Schrödinger Backend

Dirac Backend

State Representation

Execution Configuration

Algorithm Execution Times

VQE Optimization Convergence

H₂ Convergence Profile

Stark Effect Field Sweep

Backend Agreement

Numerical Precision

Scalability

Tested System Sizes

Memory Requirements

Limitations

Summary Statistics

Test Suite

H₂ VQE

Grover Search

Polarizability

Build docs developers (and LLMs) love

Papers

Experiments

​Overview

​Backend Architectures

Hamiltonian Backend

Schrödinger Backend

Dirac Backend

​State Representation

​Execution Configuration

​Algorithm Execution Times

​VQE Optimization Convergence

​H₂ Convergence Profile

​Stark Effect Field Sweep

​Backend Agreement

​Numerical Precision

​Scalability

​Tested System Sizes

​Memory Requirements

​Limitations

​Summary Statistics

Test Suite

H₂ VQE

Grover Search

Polarizability

​Related Documentation

Build docs developers (and LLMs) love

Overview

Backend Architectures

State Representation

Execution Configuration

Algorithm Execution Times

VQE Optimization Convergence

H₂ Convergence Profile

Stark Effect Field Sweep

Backend Agreement

Numerical Precision

Scalability

Tested System Sizes

Memory Requirements

Limitations

Summary Statistics

Related Documentation