Researcher-in-the-Loop Evolutionary Discovery of Entanglement-Assisted Quantum Code Families

Authors: Jae-Hyun Baek, Byung-Sun Won, Jon-Lark Kim

Submitted to arXiv on 30 Oct. 2026

Abstract

LLM-guided program evolution can produce mathematical constructions, but validity, generality, and reproducibility require distinct evidence. We develop a researcher-in-the-loop discovery pipeline that combines program evolution, exact evaluation, mathematical generalization, certified nonexistence checks, and formal proof checking. We apply it to entanglement-assisted quantum error-correcting codes (EAQECCs). Starting from tasks that did not specify a family formula, evolved programs produced finite qubit constructions whose structure researchers generalized to the family $[[n,1,n-1;n-q-1]]_q$ for prime powers $q\ge3$ at $n\ge2q+1$ and for $q=2$ at odd $n\ge5$. Lean checks the algebraic certificate underlying this family. Together with entanglement lifting, the family closes 54 gaps in archived EAQECC tables. The released evidence includes 115 verified code records, ten nonexistence results with checked DRAT proofs, family implementations, and preserved search programs for exact checks and seeded replay. In a controlled cohort of eight paired generation blocks, validation-selected iterative programs achieve success in 46.1% and 31.6% of held-out executions at unseen lengths $n=13,15$, compared with 19.5% and 3.1% for independently generated programs. In this setting, program evolution and researcher analysis turn finite computational discoveries into a proved family with independently checkable evidence.

The papers around it, by date and closeness

Higher is closer to this paper; left is older. Lines join papers close to each other: groups of lines are sub-topics. Select a point to see why it is there. Back to the summary of this paper

Closest papers Prior work it builds on Papers that cite it

Papers around this one

Ranked by how close their title and abstract are to this paper’s. Select some to read them together.

Closest papers

Close Another approach to the problem
Quantum Error Correction via Noise Guessing Decoding
Diogo Cruz, Francisco A. Monteiro, Bruno C. Coutinho · 2022 · Quantum Physics · cited 23 times · AI summary available

Noise Guessing Decoding constructs and decodes quantum error-correction codes across chosen block lengths, while this paper discovers and proves a family of entanglement-assisted codes.

Abstract
Quantum error correction codes (QECCs) play a central role both in quantum communications and in quantum computation, given how error-prone quantum technologies are. Practical quantum error correction codes, such as stabilizer codes, are generally structured to suit a specific use, and present rigid code lengths and code rates, limiting their adaptability to changing requirements. This paper shows that it is possible to both construct and decode QECCs that can attain the maximum performance of the finite blocklength regime, for any chosen code length and when the code rate is sufficiently high. A recently proposed strategy for decoding classical codes called GRAND (guessing random additive n…
Close Broader context
Implementation of quantum imaginary-time evolution method on NISQ devices: Nonlocal approximation
Hirofumi Nishi, Taichi Kosugi, Yu-ichiro Matsushita · 2020 · npj Quantum Inf 7, 85 (2021) · cited 103 times · AI summary available

Nonlocal approximation reduces circuit depth for quantum imaginary-time evolution on NISQ devices, rather than constructing entanglement-assisted error-correcting codes.

Abstract
The imaginary-time evolution method is widely known to be efficient for obtaining the ground state in quantum many-body problems on a classical computer. A recently proposed quantum imaginary-time evolution method (QITE) faces problems of deep circuit depth and difficulty in the implementation on noisy intermediate-scale quantum (NISQ) devices. In this study, a nonlocal approximation is developed to tackle this difficulty. We found that by removing the locality condition or local approximation (LA), which was imposed when the imaginary-time evolution operator is converted to a unitary operator, the quantum circuit depth is significantly reduced. We propose two-step approximation methods base…
Close Broader context
Logical Error Rates for a [[4,2,2]]-Encoded Variational Quantum Eigensolver Ansatz
Meenambika Gowrishankar, Daniel Claudino, Jerimiah Wright et al. · 2024 · Quantum Physics · cited 9 times · Not summarized yet

This paper measures how a [[4,2,2]] code affects logical error rates in a VQE application, whereas the main paper constructs a family of entanglement-assisted codes.

Abstract
Application benchmarks that run on noisy, intermediate-scale quantum (NISQ) computing devices require techniques for mitigating errors to improve accuracy and precision. Quantum error detection codes offer a framework by which to encode quantum computations and identify when errors occur. However, the subsequent logical error rate depends on the encoded application circuit as well as the underlying noise. Here, we quantify how the [[4,2,2]] quantum error detection code improves the logical error rate, accuracy, and precision of an encoded variational quantum eigensolver (VQE) application. We benchmark the performance of the encoded VQE for estimating the energy of the hydrogen molecule with …
Close Same method, another problem
Code Evolution Graphs: Understanding Large Language Model Driven Design of Algorithms
Niki van Stein, Anna V. Kononova, Lars Kotthoff et al. · 2025 · Neural and Evolutionary Computing · cited 21 times · AI summary available

Code Evolution Graphs analyzes how LLM-generated algorithms change during evolutionary prompting, a process also used in the main paper to discover code constructions.

Abstract
Large Language Models (LLMs) have demonstrated great promise in generating code, especially when used inside an evolutionary computation framework to iteratively optimize the generated algorithms. However, in some cases they fail to generate competitive algorithms or the code optimization stalls, and we are left with no recourse because of a lack of understanding of the generation process and generated codes. We present a novel approach to mitigate this problem by enabling users to analyze the generated codes inside the evolutionary process and how they evolve over repeated prompting of the LLM. We show results for three benchmark problem classes and demonstrate novel insights. In particular…
Close Broader context
Bridging Entanglement and Magic Resources through Operator Space
Neil Dowling, Kavan Modi, Gregory A. L. White · 2025 · Quantum Physics · cited 35 times · AI summary available

This paper relates operator entanglement to magic resources in quantum circuits, not to entanglement-assisted error-correcting code construction.

Abstract
Local operator entanglement (LOE) dictates the complexity of simulating Heisenberg evolution using tensor network methods, and serves as strong dynamical signature of quantum chaos. We show that LOE is also sensitive to how non-Clifford a unitary is: its magic resources. In particular, we prove that LOE is always upper-bound by three distinct magic monotones: $T$-count, unitary nullity, and operator stabilizer Rényi entropy. Moreover, in the average case for large, random circuits, LOE and magic monotones approximately coincide. Our results imply that an operator evolution that is expensive to simulate using tensor network methods must also be inefficient using both stabilizer and Pauli trun…
Close Broader context
Determining eigenstates and thermal states on a quantum computer using quantum imaginary time evolution
Mario Motta, Chong Sun, Adrian Teck Keng Tan et al. · 2019 · Nature Physics 16, 205-210 (2020) · cited 866 times · AI summary available

This paper develops quantum imaginary-time evolution for finding eigenstates and thermal states, rather than evolving programs to discover quantum codes.

Abstract
The accurate computation of Hamiltonian ground, excited, and thermal states on quantum computers stands to impact many problems in the physical and computer sciences, from quantum simulation to machine learning. Given the challenges posed in constructing large-scale quantum computers, these tasks should be carried out in a resource-efficient way. In this regard, existing techniques based on phase estimation or variational algorithms display potential disadvantages; phase estimation requires deep circuits with ancillae, that are hard to execute reliably without error correction, while variational algorithms, while flexible with respect to circuit depth, entail additional high-dimensional clas…
Close Broader context
Quantum eigenvalue processing
Guang Hao Low, Yuan Su · 2024 · Quantum Physics · cited 60 times · AI summary available

Quantum eigenvalue processing transforms eigenvalues of block-encoded operators, a separate quantum algorithmic problem from code-family discovery.

Abstract
Many problems in linear algebra -- such as those arising from non-Hermitian physics and differential equations -- can be solved on a quantum computer by processing eigenvalues of the non-normal input matrices. However, the existing Quantum Singular Value Transformation (QSVT) framework is ill-suited to this task, as eigenvalues and singular values are different in general. We present a Quantum EigenValue Transformation (QEVT) framework for applying arbitrary polynomial transformations on eigenvalues of block-encoded non-normal operators, and a related Quantum EigenValue Estimation (QEVE) algorithm for operators with real spectra. QEVT has query complexity to the block encoding nearly recover…
Close Broader context
Benchmarking highly entangled states on a 60-atom analog quantum simulator
Adam L. Shaw, Zhuo Chen, Joonhee Choi et al. · 2023 · Quantum Physics · cited 107 times · AI summary available

This paper benchmarks entanglement in a 60-atom simulator, whereas the main paper studies algebraic constructions of entanglement-assisted quantum error-correcting codes.

Abstract
Quantum systems have entered a competitive regime where classical computers must make approximations to represent highly entangled quantum states. However, in this beyond-classically-exact regime, fidelity comparisons between quantum and classical systems have so far been limited to digital quantum devices, and it remains unsolved how to estimate the actual entanglement content of experiments. Here we perform fidelity benchmarking and mixed-state entanglement estimation with a 60-atom analog Rydberg quantum simulator, reaching a high entanglement entropy regime where exact classical simulation becomes impractical. Our benchmarking protocol involves extrapolation from comparisons against many…

Go further

A literature review from its research question Premium+
An email the day a new paper comes this close Premium
The people and institutions who publish on its topic Premium

How are these papers found?

We compare the title and abstract of this paper with those of every paper summarized on this site, and with the papers Semantic Scholar recommends, those it cites and those citing it (for a much-cited paper, its most recent citations and, from OpenAlex, the most cited ones). Among the prior work and the follow-ups, the papers that use each other in depth, a method it uses and the much-cited follow-ups come a little higher. The levels (very close, close, related) come from the similarity of the texts, not from a judgment of quality; * marks a paper without an abstract, compared by its title. The sentence under a paper is written by an AI from the two abstracts: check it in the papers. A paper marked not relevant by three readers leaves the list.

Updated on 2 November 2026.