Finding high-order Hadamard matrices by using quantum computers

Andriyan Bayu Suksmono; Yuichiro Minato

Home/Archive/arXiv

arXiv · 2009.10919

Finding high-order Hadamard matrices by using quantum computers

Andriyan Bayu Suksmono·Yuichiro Minato

View original source ↗Read source document ↗Export metadata ↓

Abstract

Solving hard problems is one of the most important issues in computing to be addressed by a quantum computer. Previously, we have shown that the H-SEARCH; which is the problem of finding a Hadamard matrix (H-matrix) among all possible binary matrices of corresponding order, is a hard problem that can be solved by a quantum computer. However, due to the limitation on the number of qubits and connections in present day quantum processors, only low orders H-SEARCH are implementable. In this paper, we show that by adopting classical construction/search techniques of the H-matrix, we can develop new quantum computing methods to find higher order H-matrices. Especially, the Turyn-based quantum computing method can be further developed to find an arbitrarily high order H-matrix by balancing the classical and quantum resources. This method is potentially capable to find some unknown H-matrices of practical and scientific interests, where a classical computer alone cannot do because of the exponential grow of the complexity. We present some results of finding H-matrix of order more than one hundred and a prototypical experiment to find even higher order matrix by using the classical-quantum resource balancing method. Although heuristic optimizations generally only achieve approximate solutions, whereas the exact one should be determined by exhaustive listing; which is difficult to perform, in the H-SEARCH we can assure such exactness in polynomial time by checking the orthogonality of the solution. Since quantum advantage over the classical computing should have been measured by comparing the performance in solving a problem up to a definitive solution, the proposed method may lead to an alternate route for demonstrating practical quantum supremacy in the near future.

Explore related subjects

quant-ph

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Andriyan Bayu Suksmono, Yuichiro Minato. 2020-10-21. Finding high-order Hadamard matrices by using quantum computers. https://arxiv.org/abs/2009.10919

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Quantum Authenticated Key Expansion with Key Recycling

Data privacy and authentication are two main security requirements for remote access and cloud services. While QKD has been explored to address data privacy concerns, oftentimes its use is separate from the client authentication protocol despite implicitly providing authentication. Here, we present a quantum authentication key expansion (QAKE) protocol that (1) integrates both authentication and key expansion within a single protocol, and (2) provides key recycling property - allowing all authentication keys to be reused. We analyse the security of the protocol in a QAKE framework adapted from a classical authentication key exchange (AKE) framework, providing separate security conditions for authentication and data privacy. We experimentally implemented the protocol with appropriate post-selection. Additional results on the security of pseudorandom basis generation in QAKE and decoy state BB84 are provided.

quant-ph↗

arXiv2026

Entanglement as Difference: Reduction-induced Minimal Partial Entropy Difference

Bipartite mixed-state quantum entanglement (QE) and its measures play a crucial role in both theoretical research and practical quantum applications. Its internal structure is far more complex and less well understood compared with bipartite pure-state QE. Some existing measures involve inherently intractable global optimizations, while others are only applicable to highly limited-dimensional quantum systems. Here based on the inherent feature that bipartite QE systems nonseparable necessarily implies that local reduced density matrix differs from its \textquotedblleft native\textquotedblright density matrix, we propose a more physical and intuitive measure termed Reduction-induced Minimal Partial Entropy Difference to quantify arbitrary bipartite mixed-state QE. Partial Von Neumann Entropy is only a pure-state special case of this method. This measure offers intrinsic structural %perspective insights into bipartite QE characterization, thereby establishing itself as a valuable complementary measure. Its intuitive and clear physical picture, combined with relatively low computational complexity and wide applicability, facilitates exploring its potential quantum information applications, hence its conceptual framework and line of thought deserve to be further developed to describe and quantify multipartite QE in the future.

quant-ph↗

arXiv2026

Non-local mass superpositions and optical clock interferometry in atomic ensemble quantum networks

Quantum networks are emerging as powerful platforms for sensing, communication, and fundamental tests of physics. We propose a programmable quantum sensing network based on entangled atomic ensembles, where optical clock qubits realize mass superpositions arising via mass-energy equivalence, as in atom and atom-clock interferometry. Our approach uniquely combines scalability to large atom numbers with minimal control requirements, relying only on collective addressing of internal atomic states. This enables the creation of both non-local and local superpositions with spatial separations beyond those achievable in conventional matter-wave interferometry with single atoms. Starting from Bell-type seed states distributed via photonic channels, collective operations within atomic ensembles coherently build many-body mass superpositions sensitive to gravitational redshift. The resulting architecture implements a non-local Ramsey interferometer, where gravitationally induced phase shifts are imprinted on non-local entangled states and are read out through local measurements at the network nodes. Beyond extending the spatial reach of mass superpositions, our scheme establishes a scalable, programmable platform to probe the interface of quantum mechanics and gravity, and offers a new experimental pathway to test atom and atom-clock interferometer proposals, e.g. for probing gravitational dephasing, in a network-based quantum laboratory.

quant-ph↗