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Optimal Quantum Circuit Design via Unitary Neural Networks

M. Zomorodi, H. Amini, M. Abbaszadeh, J. Sohrabi, V. Salari, P. Plawiak

TL;DR

The paper tackles the challenge of translating quantum algorithms into hardware-ready circuits by training a neural network with unitary weights to learn the input–output mapping of a quantum computation, effectively constructing a unitary $U$ with $UU^\dagger = I$ that can be transpiled into a gate-level circuit. The authors explore representations of quantum circuits via gate sequences and unitary matrices, and implement a training regime that enforces unitarity, using Gram-Schmidt to project updates back into the unitary group $U(n)$. They demonstrate near-perfect generalization to unseen inputs across multiple circuit configurations (random, entanglement, and full-adders) and discuss data availability and scalability to multi-layer designs. This data-driven approach offers a practical pathway for quantum logic synthesis by learning circuit functionality directly from input-output mappings and then leveraging transpilation for hardware compatibility.

Abstract

The process of translating a quantum algorithm into a form suitable for implementation on a quantum computing platform is crucial but yet challenging. This entails specifying quantum operations with precision, a typically intricate task. In this paper, we present an alternative approach: an automated method for synthesizing the functionality of a quantum algorithm into a quantum circuit model representation. Our methodology involves training a neural network model using diverse input-output mappings of the quantum algorithm. We demonstrate that this trained model can effectively generate a quantum circuit model equivalent to the original algorithm. Remarkably, our observations indicate that the trained model achieves near-perfect mapping of unseen inputs to their respective outputs.

Optimal Quantum Circuit Design via Unitary Neural Networks

TL;DR

The paper tackles the challenge of translating quantum algorithms into hardware-ready circuits by training a neural network with unitary weights to learn the input–output mapping of a quantum computation, effectively constructing a unitary with that can be transpiled into a gate-level circuit. The authors explore representations of quantum circuits via gate sequences and unitary matrices, and implement a training regime that enforces unitarity, using Gram-Schmidt to project updates back into the unitary group . They demonstrate near-perfect generalization to unseen inputs across multiple circuit configurations (random, entanglement, and full-adders) and discuss data availability and scalability to multi-layer designs. This data-driven approach offers a practical pathway for quantum logic synthesis by learning circuit functionality directly from input-output mappings and then leveraging transpilation for hardware compatibility.

Abstract

The process of translating a quantum algorithm into a form suitable for implementation on a quantum computing platform is crucial but yet challenging. This entails specifying quantum operations with precision, a typically intricate task. In this paper, we present an alternative approach: an automated method for synthesizing the functionality of a quantum algorithm into a quantum circuit model representation. Our methodology involves training a neural network model using diverse input-output mappings of the quantum algorithm. We demonstrate that this trained model can effectively generate a quantum circuit model equivalent to the original algorithm. Remarkably, our observations indicate that the trained model achieves near-perfect mapping of unseen inputs to their respective outputs.
Paper Structure (13 sections, 2 theorems, 21 equations, 5 figures, 1 table, 3 algorithms)

This paper contains 13 sections, 2 theorems, 21 equations, 5 figures, 1 table, 3 algorithms.

Table of Contents

  1. Introduction
  2. Quantum circuit synthesis with neural networks
  3. Neural networks for building quantum circuits
  4. Training Process
  5. Results and discussion
  6. Data Availability
  7. Appendix
  8. Unitary weight matrix
  9. Training neural network for quantum circuit design
  10. Gram-schmidt process for unitary Weight matrix
  11. Training Process
  12. Algorithms
  13. References

Key Result

Theorem 3.1

For any matrix $M \in \mathbb{C}^{n\times{n}}$, there is a small value $\delta > 0$ such that $M + \epsilon I$ is nonsingular for $\epsilon \in \mathbb{C}$ and $0 < |\epsilon| < \delta$.

Figures (5)

  • Figure 1: General protocol for quantum circuit synthesis including neural network training and the resulting quantum circuit after the transpilation in Qiskit.
  • Figure 2: The flowchart summary of the entire process of designing quantum circuits by using neural networks.
  • Figure 3: A) Random circuit with 4-qubits and circuit level 17. B) Implementation of entanglement state with 2-qubits and circuit level two. C) A quantum full adder with 4 qubits and circuit level five. D) A quantum full adder with 5 qubits and 6 circuit level.
  • Figure 4: The results of model training (Accuracy/R2)
  • Figure 5: The results of model training (Loss/MSE)

Theorems & Definitions (2)

  • Theorem 3.1: Horn
  • Proposition 1