Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2505.07312 · npj Quantum Information

Beyond boson sampling: higher spin sampling as a practical path to quantum supremacy

Chon‐Fai Kam, En-Jui Kuo

Published Apr 17, 2026• 0 citations
arXivHTMLPDF

Abstract

Abstract Since the dawn of quantum computation science, a range of quantum algorithms have been proposed, yet few have experimentally demonstrated a definitive quantum advantage. Shor’s algorithm, while renowned, has not been realized at a scale to outperform classical methods. In contrast, Fock-state boson sampling has been theoretically established, under standard complexity-theoretic assumptions, as a promising route toward quantum computational advantage. However, most existing experimental realizations of boson sampling to date have been based on Gaussian boson sampling, in which the input states consist of squeezed states of light. In this work, we introduce a higher-spin ( S ) sampling framework and show that it provides a practical path toward quantum computational advantage. We derive a quasi-linear scaling relation between the number of sites m and the number of spins n , namely m ~ n 1+ ϵ , where ϵ = 3/(2 S ) decreases with increasing spin quantum number. This suggests that, within a spin system, Fock-state boson sampling can be implemented in a quasi-linear mode regime ( m = Ω ( n 1+ ϵ )), significantly reducing experimental resource requirements.

DOI
10.1038/s41534-026-01246-7

Related papers

Non-linear Boson Sampling

Nicolò Spagnolo, Daniel J. Brod, Ernesto F. Galvão +1 more

Abstract Boson Sampling is a task that is conjectured to be computationally hard for a classical computer, but which can be efficiently solved by linear-optical interferometers with Fock state inputs. Significant advances have been reported in the last few years, with demonstrations of small- and medium-scale devices, as well as implementations of variants such as Gaussian Boson Sampling. Besides the relevance of this class of computational models in the quest for unambiguous experimental demonstrations of quantum advantage, recent results have also proposed the first applications for hybrid quantum computing. Here, we introduce the adoption of non-linear photon–photon interactions in the Boson Sampling framework, and analyze the enhancement in complexity via an explicit linear-optical simulation scheme. By extending the computational expressivity of Boson Sampling, the introduction of non-linearities promises to disclose novel functionalities for this class of quantum devices. Hence, our results are expected to lead to new applications of near-term, restricted photonic quantum computers.

arXiv:2110.13788•npj Quantum Information•Jan 9, 2023•24 citations

Faster classical boson sampling

Peter Clifford, Raphaël Clifford A

Abstract Since its introduction boson sampling has been the subject of intense study in the world of quantum computing. In the context of Fock-state boson sampling, the task is to sample independently from the set of all n × n submatrices built from possibly repeated rows of a larger m × n complex matrix according to a probability distribution related to the permanents of the submatrices. Experimental systems exploiting quantum photonic effects can in principle perform the task at great speed. For classical computing, Aaronson and Arkhipov (2011) showed that exact boson sampling problem cannot be solved in polynomial time unless the polynomial hierarchy collapses to the third level. Indeed for a number of years the fastest known exact classical algorithm ran in O ( m + n − 1 n n 2 n ) time per sample, emphasising the potential speed advantage of quantum computation. The advantage was reduced by Clifford and Clifford (2018), who gave a significantly faster classical solution taking O ( n 2 n + poly ( m , n ) ) time and linear space, matching the complexity of computing the permanent of a single matrix when m is polynomial in n. We continue by presenting an algorithm for Fock boson sampling whose average-case time complexity is much faster when m is proportional to n. In particular, when m = n our algorithm runs in approximately O(n · 1.69 n ) time on average. This result further increases the problem size needed to establish quantum computational advantage via the Fock scheme of boson sampling.

arXiv:2005.04214•Physica Scripta•May 2, 2024•21 citations

Gaussian Boson Sampling

Craig S. Hamilton, Regina Kruse, Linda Sansoni +3 more

Boson sampling has emerged as a tool to explore the advantages of quantum over classical computers as it does not require universal control over the quantum system, which favors current photonic experimental platforms. Here, we introduce Gaussian Boson sampling, a classically hard-to-solve problem that uses squeezed states as a nonclassical resource. We relate the probability to measure specific photon patterns from a general Gaussian state in the Fock basis to a matrix function called the Hafnian, which answers the last remaining question of sampling from Gaussian states. Based on this result, we design Gaussian Boson sampling, a #P hard problem, using squeezed states. This demonstrates that Boson sampling from Gaussian states is possible, with significant advantages in the photon generation probability, compared to existing protocols.

arXiv:1612.01199•Physical Review Letters•Oct 23, 2017•503 citations

Gaussian boson sampling: Benchmarking quantum advantage

Ned Goodman, Alexander S. Dellios, Margaret D. Reid +1 more

Quantum computers solve intractable problems which classically require an exponentially long time to compute. With the development of large-scale experiments that claim quantum advantage, a vital issue has now emerged. What are the errors, and how do they affect the complexity of the problem solved? Large-scale Gaussian boson sampling (GBS) experiments give an example in which random numbers are generated. Despite classical hardness, these have computable benchmarks for checking data validity. While there are other quantum computing architectures, Gaussian boson sampling is uniquely testable at all scales. Several large, pioneering quantum computing (QC) experiments have been carried out to investigate quantum advantage. Here, we introduce a highly scalable but classical algorithm that can solve GBS approximately. Our numerical simulation of the output count data is closer to the exact solution than current experiments up to 1152 modes. This algorithm outperforms all previous classical, approximate algorithms and scales efficiently to larger experiments. Our results show that effects beyond losses can cause the errors that allow classical simulability. This work will lead to more precise algorithms and is a step towards understanding how QC quantum advantage is affected by the underlying physics.

quant-pharXiv:2604.12330•Apr 15, 2026•0 citations

Quantum Computational Supremacy via High-Dimensional Gaussian Boson Sampling

Abhinav Deshpande, Arthur Mehta, Trevor J. Vincent +10 more

Photonics is a promising platform for demonstrating quantum computational supremacy (QCS) by convincingly outperforming the most powerful classical supercomputers on a well-defined computational task. Despite this promise, existing photonics proposals and demonstrations face significant hurdles. Experimentally, current implementations of Gaussian boson sampling lack programmability or have prohibitive loss rates. Theoretically, there is a comparative lack of rigorous evidence for the classical hardness of GBS. In this work, we make significant progress in improving both the theoretical evidence and experimental prospects. On the theory side, we provide strong evidence for the hardness of Gaussian boson sampling, placing it on par with the strongest theoretical proposals for QCS. On the experimental side, we propose a new QCS architecture, high-dimensional Gaussian boson sampling, which is programmable and can be implemented with low loss rates using few optical components. We show that particular classical algorithms for simulating GBS are vastly outperformed by high-dimensional Gaussian boson sampling experiments at modest system sizes. This work thus opens the path to demonstrating QCS with programmable photonic processors.

•Feb 24, 2021•6 citations

Quantum computational advantage via high-dimensional Gaussian boson sampling

Abhinav Deshpande, Arthur Mehta, Trevor J. Vincent +10 more

Photonics is a promising platform for demonstrating a quantum computational advantage (QCA) by outperforming the most powerful classical supercomputers on a well-defined computational task. Despite this promise, existing proposals and demonstrations face challenges. Experimentally, current implementations of Gaussian boson sampling (GBS) lack programmability or have prohibitive loss rates. Theoretically, there is a comparative lack of rigorous evidence for the classical hardness of GBS. In this work, we make progress in improving both the theoretical evidence and experimental prospects. We provide evidence for the hardness of GBS, comparable to the strongest theoretical proposals for QCA. We also propose a QCA architecture we call high-dimensional GBS, which is programmable and can be implemented with low loss using few optical components. We show that particular algorithms for simulating GBS are outperformed by high-dimensional GBS experiments at modest system sizes. This work thus opens the path to demonstrating QCA with programmable photonic processors.

arXiv:2102.12474•Science Advances•Jan 5, 2022•106 citations
Abstract Since the dawn of quantum computation science, a range of quantum algorithms have been proposed, yet few have experimentally demonstrated a definitive quantum advantage. Shor’s algorithm, while renowned, has not been realized at a scale to outperform classical methods. In contrast, Fock-state boson sampling has been theoretically established, under standard complexity-theoretic assumptions, as a promising route toward quantum computational advantage. However, most existing experimental realizations of boson sampling to date have been based on Gaussian boson sampling, in which the input states consist of squeezed states of light. In this work, we introduce a higher-spin ( S ) sampling framework and show that it provides a practical path toward quantum computational advantage. We derive a quasi-linear scaling relation between the number of sites m and the number of spins n , namely m ~ n 1+ ϵ , where ϵ = 3/(2 S ) decreases with increasing spin quantum number. This suggests that, within a spin system, Fock-state boson sampling can be implemented in a quasi-linear mode regime ( m = Ω ( n 1+ ϵ )), significantly reducing experimental resource requirements.
Abstract Boson Sampling is a task that is conjectured to be computationally hard for a classical computer, but which can be efficiently solved by linear-optical interferometers with Fock state inputs. Significant advances have been reported in the last few years, with demonstrations of small- and medium-scale devices, as well as implementations of variants such as Gaussian Boson Sampling. Besides the relevance of this class of computational models in the quest for unambiguous experimental demonstrations of quantum advantage, recent results have also proposed the first applications for hybrid quantum computing. Here, we introduce the adoption of non-linear photon–photon interactions in the Boson Sampling framework, and analyze the enhancement in complexity via an explicit linear-optical simulation scheme. By extending the computational expressivity of Boson Sampling, the introduction of non-linearities promises to disclose novel functionalities for this class of quantum devices. Hence, our results are expected to lead to new applications of near-term, restricted photonic quantum computers.
Abstract Since its introduction boson sampling has been the subject of intense study in the world of quantum computing. In the context of Fock-state boson sampling, the task is to sample independently from the set of all n × n submatrices built from possibly repeated rows of a larger m × n complex matrix according to a probability distribution related to the permanents of the submatrices. Experimental systems exploiting quantum photonic effects can in principle perform the task at great speed. For classical computing, Aaronson and Arkhipov (2011) showed that exact boson sampling problem cannot be solved in polynomial time unless the polynomial hierarchy collapses to the third level. Indeed for a number of years the fastest known exact classical algorithm ran in O ( m + n − 1 n n 2 n ) time per sample, emphasising the potential speed advantage of quantum computation. The advantage was reduced by Clifford and Clifford (2018), who gave a significantly faster classical solution taking O ( n 2 n + poly ( m , n ) ) time and linear space, matching the complexity of computing the permanent of a single matrix when m is polynomial in n. We continue by presenting an algorithm for Fock boson sampling whose average-case time complexity is much faster when m is proportional to n. In particular, when m = n our algorithm runs in approximately O(n · 1.69 n ) time on average. This result further increases the problem size needed to establish quantum computational advantage via the Fock scheme of boson sampling.
Boson sampling has emerged as a tool to explore the advantages of quantum over classical computers as it does not require universal control over the quantum system, which favors current photonic experimental platforms. Here, we introduce Gaussian Boson sampling, a classically hard-to-solve problem that uses squeezed states as a nonclassical resource. We relate the probability to measure specific photon patterns from a general Gaussian state in the Fock basis to a matrix function called the Hafnian, which answers the last remaining question of sampling from Gaussian states. Based on this result, we design Gaussian Boson sampling, a #P hard problem, using squeezed states. This demonstrates that Boson sampling from Gaussian states is possible, with significant advantages in the photon generation probability, compared to existing protocols.
Quantum computers solve intractable problems which classically require an exponentially long time to compute. With the development of large-scale experiments that claim quantum advantage, a vital issue has now emerged. What are the errors, and how do they affect the complexity of the problem solved? Large-scale Gaussian boson sampling (GBS) experiments give an example in which random numbers are generated. Despite classical hardness, these have computable benchmarks for checking data validity. While there are other quantum computing architectures, Gaussian boson sampling is uniquely testable at all scales. Several large, pioneering quantum computing (QC) experiments have been carried out to investigate quantum advantage. Here, we introduce a highly scalable but classical algorithm that can solve GBS approximately. Our numerical simulation of the output count data is closer to the exact solution than current experiments up to 1152 modes. This algorithm outperforms all previous classical, approximate algorithms and scales efficiently to larger experiments. Our results show that effects beyond losses can cause the errors that allow classical simulability. This work will lead to more precise algorithms and is a step towards understanding how QC quantum advantage is affected by the underlying physics.
Photonics is a promising platform for demonstrating quantum computational supremacy (QCS) by convincingly outperforming the most powerful classical supercomputers on a well-defined computational task. Despite this promise, existing photonics proposals and demonstrations face significant hurdles. Experimentally, current implementations of Gaussian boson sampling lack programmability or have prohibitive loss rates. Theoretically, there is a comparative lack of rigorous evidence for the classical hardness of GBS. In this work, we make significant progress in improving both the theoretical evidence and experimental prospects. On the theory side, we provide strong evidence for the hardness of Gaussian boson sampling, placing it on par with the strongest theoretical proposals for QCS. On the experimental side, we propose a new QCS architecture, high-dimensional Gaussian boson sampling, which is programmable and can be implemented with low loss rates using few optical components. We show that particular classical algorithms for simulating GBS are vastly outperformed by high-dimensional Gaussian boson sampling experiments at modest system sizes. This work thus opens the path to demonstrating QCS with programmable photonic processors.
Photonics is a promising platform for demonstrating a quantum computational advantage (QCA) by outperforming the most powerful classical supercomputers on a well-defined computational task. Despite this promise, existing proposals and demonstrations face challenges. Experimentally, current implementations of Gaussian boson sampling (GBS) lack programmability or have prohibitive loss rates. Theoretically, there is a comparative lack of rigorous evidence for the classical hardness of GBS. In this work, we make progress in improving both the theoretical evidence and experimental prospects. We provide evidence for the hardness of GBS, comparable to the strongest theoretical proposals for QCA. We also propose a QCA architecture we call high-dimensional GBS, which is programmable and can be implemented with low loss using few optical components. We show that particular algorithms for simulating GBS are outperformed by high-dimensional GBS experiments at modest system sizes. This work thus opens the path to demonstrating QCA with programmable photonic processors.