qutrit-entropy-estimation

name	qutrit-entropy-estimation
description	Von Neumann entropy estimation in multi-qutrit quantum systems via variational quantum algorithms and classical neural networks. Use when estimating quantum entropy for d-level systems (qudits), selecting VQA ansatze for entropy estimation, or benchmarking quantum vs classical approaches for quantum information metrics. Covers SU(3)-inspired hardware-efficient ansatze, parameter sweep methodology, and CNN-based density matrix entropy estimation.
metadata	{"arxiv_id":"2606.20504","published":"2026-06-18","authors":"Sai Sakunthala Guddanti, Anil Prabhakar, Ria Rushin Joseph"}

Qutrit Entropy Estimation

Core Concept

Von Neumann entropy estimation for multi-qutrit systems using two complementary approaches: variational quantum algorithms (VQAs) with hardware-efficient SU(3)-inspired ansatze and classical CNNs trained on density matrix representations. Key finding: estimation accuracy is primarily determined by the number of trainable parameters, not ansatz architecture type — providing a practical guideline for ansatz selection.

Mathematical Framework

For a d-dimensional quantum system with density matrix rho:

S(rho) = -Tr(rho * log2(rho)) = -sum_i lambda_i * log2(lambda_i)

where lambda_i are eigenvalues of rho. For multi-qutrit systems (d = 3^n), direct eigendecomposition is exponentially costly.

VQA Approach

Ansatz Construction

1. SU(3) decomposition: Decompose SU(3) into elementary gates using generalized Gell-Mann matrices
2. Hardware-efficient layers: Alternate parametrized single-qutrit rotations with entangling gates
3. Cost function: Minimize difference between predicted and measured expectation values
4. Parameter counting: Accuracy scales with trainable parameter count, not architecture complexity

11 Ansatz Families Evaluated

• Sequential vs parallel rotation layers
• Different entangling gate topologies (ring, star, all-to-all)
• Varying numbers of variational layers
• Different SU(3) parameterizations (Euler angle vs exponential map)

CNN Approach

1. Input: Real and imaginary parts of density matrix (flattened)
2. Architecture: Convolutional layers capturing local correlations
3. Output: Scalar entropy estimate
4. Training: Supervised on exact entropy values from eigendecomposition

Key Findings

• Parameter count is the dominant factor: Two ansatze with similar parameter counts achieve similar accuracy regardless of architecture
• Classical CNNs match VQAs: For systems up to 3 qutrits, CNNs achieve comparable accuracy to VQAs in noise-free simulation
• Noise sensitivity: VQA accuracy degrades with hardware noise; CNNs are noise-free but require training data

Usage Patterns

Pattern 1: Ansatz Selection by Parameter Budget

Given a maximum circuit depth/parameter budget:

1. Count trainable parameters for candidate ansatze
2. Select ansatz maximizing parameters within budget
3. Architecture choice within same parameter class has secondary effect

Pattern 2: VQA vs Classical Trade-off

• Use VQAs when: running on quantum hardware, need real-time estimation
• Use CNNs when: noise-free simulation available, can afford training phase

Pattern 3: Scalability Analysis

• Parameter count ~ O(d^2) per layer for d-dimensional systems
• For n qutrits: d = 3^n, so parameters scale as O(9^n)
• Classical CNN parameters scale polynomially in d

Pitfalls

• Noise assumption: Results are for noise-free simulators — hardware noise changes the VQA vs CNN trade-off
• System size: Limited to 3 qutrits in evaluation — scaling beyond this is untested
• SU(3) gate compilation: SU(3) gates may require decomposition into native hardware gates, increasing effective circuit depth

Activation: qutrit entropy, von Neumann entropy estimation, SU(3) ansatz, quantum entropy VQA, qudit entropy, density matrix CNN, quantum information entropy, variational entropy estimation, multi-qutrit systems