Semidefinite Programming for Optimal Quantum Cloning: A Computational Framework

• URL: http://arxiv.org/abs/2605.21274v1
• Date: Wed, 20 May 2026 15:05:38 GMT
• Title: Semidefinite Programming for Optimal Quantum Cloning: A Computational Framework
• Abstract summary: We reformulate cloning optimization as a search over completely positive trace-preserving maps using the Choi-Jamiolkowski isomorphism and Semidefinite Programming.<n>We treat universal, phase-covariant, asymmetric, and entanglement cloning scenarios, providing a unified computational catalogue of explicit, implementable Kraus representations across all major cloning families.<n>As an application, we analyse optimal cloning attacks on BB84 under depolarizing noise, demonstrating how the extracted operators enable quantitative security analysis in realistic noisy quantum channels.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: While algebraic derivations establish theoretical limits for quantum cloning, practical implementations require explicit operator representations that are often unavailable analytically. We present a computational framework that reformulates cloning optimization as a search over completely positive trace-preserving maps using the Choi-Jamiolkowski isomorphism and Semidefinite Programming. The framework (i) numerically certifies global optimality through primal-dual strong duality and (ii) automatically extracts operational Kraus operators from the optimal Choi matrix via spectral decomposition. We systematically treat universal, phase-covariant, asymmetric, and entanglement cloning scenarios, providing -for the first time - a unified computational catalogue of explicit, implementable Kraus representations across all major cloning families, including higher-order processes and arbitrary input state distributions. As an application, we analyse optimal cloning attacks on BB84 under depolarizing noise, demonstrating how the extracted operators enable quantitative security analysis in realistic noisy quantum channels. An open-source implementation enables community validation and extension.

Related papers

• A variational quantum eigensolver-based cutting plane framework for semidefinite programming problems [0.0]
  We present the first end-to-end implementation of a variational quantum eigensolver within a cutting-plane framework.<n>We show that the variational oracle closes 32 to 82% of the initial optimality gap against a near-constant 75 to 82% for the exact oracle.<n>We report these findings and discuss their implications for near-term hybrid quantum-classical approaches.
  arXiv  Detail & Related papers  (2026-09-02T05:49:11Z)
• Pure and mixed Dicke state ansatz for equality and inequality constraints in variational quantum eigensolver [0.0]
  Combinatorial optimization can be addressed with quantum computing through variational quantum algorithms.<n>A central challenge is to design an ansatz expressive enough to explore the feasible subspace of the Hilbert space where the optimal solution lies.<n>We propose the first feasibility-preserving mixed Dicke state ansatz for Hamming weight constrained optimization.
  arXiv  Detail & Related papers  (2026-06-07T08:10:09Z)
• Optimal pure state cloning and transposition are complementary channels [0.4666493857924358]
  State cloning and state transposition are fundamental transformations which, despite being desirable, cannot be perfectly realised.<n>We show that the best physically allowed realisation of both transformations arises from a single physical process described by an isometry.
  arXiv  Detail & Related papers  (2026-03-24T18:11:29Z)
• Certified bounds on optimization problems in quantum theory [2.8417851789786686]
  We introduce a rigorous framework for extracting exact rational optimization on non-commutative problems from numerical data.<n>An extension to sparsity and symmetry-adapted semidefinite relaxations is also provided compared to the general scheme.
  arXiv  Detail & Related papers  (2025-12-19T15:44:15Z)
• Are Randomized Quantum Linear Systems Solvers Practical? [0.0]
  randomized quantum algorithms have been proposed in the context of quantum simulation and quantum linear algebra.<n>We provide explicit bounds on all relevant parameters that control the total error for a randomized quantum linear systems solver.<n>Our work serves as a bridge between theoretical algorithmic proposals and efficient hardware implementations.
  arXiv  Detail & Related papers  (2025-10-15T17:12:55Z)
• Mechanisms for Quantum Advantage in Global Optimization of Nonconvex Functions [6.135587835061064]
  We show new theoretical mechanisms for quantum speedup in the global optimization of non-asymotic functions.<n>We formalize these ideas by proving that a real-space quantum algorithm (RsAA) achieves provably on-time runtimes.
  arXiv  Detail & Related papers  (2025-10-03T17:40:31Z)
• Graph-based Clustering Revisited: A Relaxation of Kernel $k$-Means Perspective [73.18641268511318]
  We propose a graph-based clustering algorithm that only relaxes the orthonormal constraint to derive clustering results.<n>To ensure a doubly constraint into a gradient, we transform the non-negative constraint into a class probability parameter.
  arXiv  Detail & Related papers  (2025-09-23T09:14:39Z)
• Cloning Games, Black Holes and Cryptography [50.022147589030304]
  We introduce a new toolkit for analyzing cloning games.<n>This framework allows us to analyze a new cloning game based on binary phase states.<n>We show that the binary phase variantally optimal bound offers quantitative insights into information scrambling in idealized models of black holes.
  arXiv  Detail & Related papers  (2024-11-07T14:09:32Z)
• Quantum Goemans-Williamson Algorithm with the Hadamard Test and Approximate Amplitude Constraints [62.72309460291971]
  We introduce a variational quantum algorithm for Goemans-Williamson algorithm that uses only $n+1$ qubits. Efficient optimization is achieved by encoding the objective matrix as a properly parameterized unitary conditioned on an auxilary qubit. We demonstrate the effectiveness of our protocol by devising an efficient quantum implementation of the Goemans-Williamson algorithm for various NP-hard problems.
  arXiv  Detail & Related papers  (2022-06-30T03:15:23Z)
• The vacuum provides quantum advantage to otherwise simulatable architectures [49.1574468325115]
  We consider a computational model composed of ideal Gottesman-Kitaev-Preskill stabilizer states. We provide an algorithm to calculate the probability density function of the measurement outcomes.
  arXiv  Detail & Related papers  (2022-05-19T18:03:17Z)
• Reinforcement Learning from Partial Observation: Linear Function Approximation with Provable Sample Efficiency [111.83670279016599]
  We study reinforcement learning for partially observed decision processes (POMDPs) with infinite observation and state spaces. We make the first attempt at partial observability and function approximation for a class of POMDPs with a linear structure.
  arXiv  Detail & Related papers  (2022-04-20T21:15:38Z)
• Efficient Neural Network Analysis with Sum-of-Infeasibilities [64.31536828511021]
  Inspired by sum-of-infeasibilities methods in convex optimization, we propose a novel procedure for analyzing verification queries on networks with extensive branching functions. An extension to a canonical case-analysis-based complete search procedure can be achieved by replacing the convex procedure executed at each search state with DeepSoI.
  arXiv  Detail & Related papers  (2022-03-19T15:05:09Z)
• Faster Algorithm and Sharper Analysis for Constrained Markov Decision Process [56.55075925645864]
  The problem of constrained decision process (CMDP) is investigated, where an agent aims to maximize the expected accumulated discounted reward subject to multiple constraints. A new utilities-dual convex approach is proposed with novel integration of three ingredients: regularized policy, dual regularizer, and Nesterov's gradient descent dual. This is the first demonstration that nonconcave CMDP problems can attain the lower bound of $mathcal O (1/epsilon)$ for all complexity optimization subject to convex constraints.
  arXiv  Detail & Related papers  (2021-10-20T02:57:21Z)
• Process-optimized phase covariant quantum cloning [4.974890682815778]
  We compute the optimal global fidelity for phase-covariant cloning machines via semi-definite programming optimization. We also consider optimal simulations of the cloning and transpose cloning map, both by a direct optimization and by a composition of component-wise QCMs.
  arXiv  Detail & Related papers  (2021-07-07T07:00:40Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.