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

IEEE/LEOS Summer Topical Meetings

Solving the two-way Number-Partitioning Problem using a Spatial-Photonic Ising Machine

Vikram Ramesh, Vighnesh Natarajan, Anil Prabhakar

Published Jul 1, 2021• 0 citations
Publisher

Abstract

We demonstrate an adiabatic evolution scheme to evolve from the ground state of a known Hamiltonian to a Mattis-spin glass Hamiltonian, which corresponds to solving a two-way Number-Partitioning Problem (NPP), using a Spatial-Photonic Ising Machine (SPIM) with a magnified readout plane.
DOI
10.1109/sum48717.2021.9505909

Related papers

A spatial-photonic Ising machine to solve the two-way\n number-partitioning problem

Vikram Ramesh, Vighnesh Natarajan, Anil Prabhakar

We evaluate the performance of different algorithms in minimizing the Hamiltonian of a spatial-photonic Ising machine (SPIM). We then encode the number-partitioning problem on the SPIM and adiabatically arrive at good solutions for the problem for over 16000 spins, with a time complexity that only scales linearly with problem size. Finally, we benchmark our machine performance against the classical solver, Gurobi, and also a D-Wave 5000+ quantum annealer. With just one spatial light modulator, and and adiabatic evolution scheme for the phase, our results surpass current state-of-the-art SPIMs. We reduce hardware costs, and can solve larger problems more efficiently.

arXiv:2110.01616•Oct 3, 2021•2 citations

Fully Programmable Spatial Photonic Ising Machine by Focal Plane Division

Daniele Veraldi, Davide Pierangeli, Silvia Gentilini +10 more

Ising machines are an emerging class of hardware that promises ultrafast and energy-efficient solutions to NP-hard combinatorial optimization problems. Spatial photonic Ising machines (SPIMs) exploit optical computing in free space to accelerate the computation, showcasing parallelism, scalability, and low power consumption. However, current SPIMs can implement only a restricted class of problems. This partial programmability is a critical limitation that hampers their benchmark. Achieving full programmability of the device while preserving its scalability is an open challenge. Here, we report a fully programmable SPIM achieved through a novel operation method based on the division of the focal plane. In our scheme, a general Ising problem is decomposed into a set of Mattis Hamiltonians, whose energies are simultaneously computed optically by measuring the intensity on different regions of the camera sensor. Exploiting this concept, we experimentally demonstrate the computation with high success probability of ground-state solutions of up to 32-spin Ising models on unweighted maximum cut graphs with and without ferromagnetic bias. Simulations of the hardware prove a favorable scaling of the accuracy with the number of spin. Our fully programmable SPIM enables the implementation of many quadratic unconstrained binary optimization problems, further establishing SPIMs as a leading paradigm in non-von Neumann hardware.

arXiv:2410.10689•Physical Review Letters•Feb 14, 2025•24 citations

Enhanced, fully connected 360 000-spin spatial photonic Ising machine

Junze Yao, Rongwei Zhu, Junjie Yu

The spatial photonic Ising machine (SPIM) is a promising architecture that leverages the scalability and parallelism of photons to solve Ising problems in combinatorial optimization. SPIMs have been held back fundamentally by limited computational accuracy. This study overcomes that limitation through a hybrid approach, integrating aberration correction with a dynamic algorithm to update simultaneously a number of flipped spins, rather than just one. The method demonstrably improves computational accuracy and presents a way for SPIMs to scale to significantly larger systems (order 10${}^{5}$ spins), a milestone on the path to practical application.

Physical Review Applied•Sep 25, 2025•5 citations

Optimization with photonic wave-based annealers

Anil Prabhakar, Parth S Shah, Gautham Umasankar +4 more

Many NP-hard combinatorial optimization (CO) problems can be cast as a quadratic unconstrained binary optimization model, which maps naturally to an Ising model. The final spin configuration in the Ising model can adiabatically arrive at a solution to a Hamiltonian, given a known set of interactions between spins. We enhance two photonic Ising machines (PIMs) and compare their performance against classical (Gurobi) and quantum (D-Wave) solvers. The temporal multiplexed coherent Ising machine (TMCIM) uses the bistable response of an electro-optic modulator to mimic the spin up and down states. We compare TMCIM performance on Max-cut problems. A spatial photonic Ising machine (SPIM) convolves the wavefront of a coherent laser beam with the pixel distribution of a spatial light modulator to adiabatically achieve a minimum energy configuration, and solve a number partitioning problem (NPP). Our computational results on Max-cut indicate that classical solvers are still a better choice, while our NPP results show that SPIM is better as the problem size increases. In both cases, connectivity in Ising hardware is crucial for performance. Our results also highlight the importance of better understanding which CO problems are most likely to benefit from which type of PIM. This article is part of the theme issue 'Quantum annealing and computation: challenges and perspectives'.

Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences•Dec 4, 2022•14 citations

Encoding Arbitrary Ising Hamiltonians on Spatial Photonic Ising Machines

Jason Sakellariou, Alexis Askitopoulos, Georgios Pastras +1 more

Photonic Ising machines constitute an emergent new paradigm of computation geared toward tackling combinatorial optimization problems that can be reduced to the problem of finding the ground state of an Ising model. Spatial photonic Ising machines (SPIMs) have proven advantageous for simulating fully connected large-scale spin systems. Fine control of a general interaction matrix J has been accomplished so far only through matrix decomposition methods. We introduce and experimentally validate a SPIM instance that enables direct control over the full interaction matrix, allowing the encoding of Ising Hamiltonians with arbitrary couplings and connectivity. We demonstrate the conformity of the experimentally measured Ising energy with the theoretically expected value and then proceed to solve both the unweighted and weighted graph partitioning problems, showcasing a systematic convergence to an optimal solution via simulated annealing. Our approach significantly expands the applicability of SPIMs for real-world applications, as it is more efficient than matrix decomposition methods in the case of sparse problems. It paves the way to encoding the full range of NP problems that are known to be equivalent to Ising models on SPIM devices.

Physical Review Letters•May 20, 2025•12 citations

Encoding arbitrary Ising Hamiltonians on Spatial Photonic Ising Machines

Jason Sakellariou, Alexis Askitopoulos, Georgios Pastras +1 more

Photonic Ising Machines constitute an emergent new paradigm of computation, geared towards tackling combinatorial optimization problems that can be reduced to the problem of finding the ground state of an Ising model. Spatial Photonic Ising Machines have proven to be advantageous for simulating fully connected large-scale spin systems. However, fine control of a general interaction matrix $J$ has so far only been accomplished through eigenvalue decomposition methods that either limit the scalability or increase the execution time of the optimization process. We introduce and experimentally validate a SPIM instance that enables direct control over the full interaction matrix, enabling the encoding of Ising Hamiltonians with arbitrary couplings and connectivity. We demonstrate the conformity of the experimentally measured Ising energy with the theoretically expected values and then proceed to solve both the unweighted and weighted graph partitioning problems, showcasing a systematic convergence to an optimal solution via simulated annealing. Our approach greatly expands the applicability of SPIMs for real-world applications without sacrificing any of the inherent advantages of the system, and paves the way to encoding the full range of NP problems that are known to be equivalent to Ising models, on SPIM devices.

arXiv:2407.09161•Jul 12, 2024•1 citation
We evaluate the performance of different algorithms in minimizing the Hamiltonian of a spatial-photonic Ising machine (SPIM). We then encode the number-partitioning problem on the SPIM and adiabatically arrive at good solutions for the problem for over 16000 spins, with a time complexity that only scales linearly with problem size. Finally, we benchmark our machine performance against the classical solver, Gurobi, and also a D-Wave 5000+ quantum annealer. With just one spatial light modulator, and and adiabatic evolution scheme for the phase, our results surpass current state-of-the-art SPIMs. We reduce hardware costs, and can solve larger problems more efficiently.
Ising machines are an emerging class of hardware that promises ultrafast and energy-efficient solutions to NP-hard combinatorial optimization problems. Spatial photonic Ising machines (SPIMs) exploit optical computing in free space to accelerate the computation, showcasing parallelism, scalability, and low power consumption. However, current SPIMs can implement only a restricted class of problems. This partial programmability is a critical limitation that hampers their benchmark. Achieving full programmability of the device while preserving its scalability is an open challenge. Here, we report a fully programmable SPIM achieved through a novel operation method based on the division of the focal plane. In our scheme, a general Ising problem is decomposed into a set of Mattis Hamiltonians, whose energies are simultaneously computed optically by measuring the intensity on different regions of the camera sensor. Exploiting this concept, we experimentally demonstrate the computation with high success probability of ground-state solutions of up to 32-spin Ising models on unweighted maximum cut graphs with and without ferromagnetic bias. Simulations of the hardware prove a favorable scaling of the accuracy with the number of spin. Our fully programmable SPIM enables the implementation of many quadratic unconstrained binary optimization problems, further establishing SPIMs as a leading paradigm in non-von Neumann hardware.
The spatial photonic Ising machine (SPIM) is a promising architecture that leverages the scalability and parallelism of photons to solve Ising problems in combinatorial optimization. SPIMs have been held back fundamentally by limited computational accuracy. This study overcomes that limitation through a hybrid approach, integrating aberration correction with a dynamic algorithm to update simultaneously a number of flipped spins, rather than just one. The method demonstrably improves computational accuracy and presents a way for SPIMs to scale to significantly larger systems (order 105{}^{5}5 spins), a milestone on the path to practical application.
Many NP-hard combinatorial optimization (CO) problems can be cast as a quadratic unconstrained binary optimization model, which maps naturally to an Ising model. The final spin configuration in the Ising model can adiabatically arrive at a solution to a Hamiltonian, given a known set of interactions between spins. We enhance two photonic Ising machines (PIMs) and compare their performance against classical (Gurobi) and quantum (D-Wave) solvers. The temporal multiplexed coherent Ising machine (TMCIM) uses the bistable response of an electro-optic modulator to mimic the spin up and down states. We compare TMCIM performance on Max-cut problems. A spatial photonic Ising machine (SPIM) convolves the wavefront of a coherent laser beam with the pixel distribution of a spatial light modulator to adiabatically achieve a minimum energy configuration, and solve a number partitioning problem (NPP). Our computational results on Max-cut indicate that classical solvers are still a better choice, while our NPP results show that SPIM is better as the problem size increases. In both cases, connectivity in Ising hardware is crucial for performance. Our results also highlight the importance of better understanding which CO problems are most likely to benefit from which type of PIM. This article is part of the theme issue 'Quantum annealing and computation: challenges and perspectives'.
Photonic Ising machines constitute an emergent new paradigm of computation geared toward tackling combinatorial optimization problems that can be reduced to the problem of finding the ground state of an Ising model. Spatial photonic Ising machines (SPIMs) have proven advantageous for simulating fully connected large-scale spin systems. Fine control of a general interaction matrix J has been accomplished so far only through matrix decomposition methods. We introduce and experimentally validate a SPIM instance that enables direct control over the full interaction matrix, allowing the encoding of Ising Hamiltonians with arbitrary couplings and connectivity. We demonstrate the conformity of the experimentally measured Ising energy with the theoretically expected value and then proceed to solve both the unweighted and weighted graph partitioning problems, showcasing a systematic convergence to an optimal solution via simulated annealing. Our approach significantly expands the applicability of SPIMs for real-world applications, as it is more efficient than matrix decomposition methods in the case of sparse problems. It paves the way to encoding the full range of NP problems that are known to be equivalent to Ising models on SPIM devices.
Photonic Ising Machines constitute an emergent new paradigm of computation, geared towards tackling combinatorial optimization problems that can be reduced to the problem of finding the ground state of an Ising model. Spatial Photonic Ising Machines have proven to be advantageous for simulating fully connected large-scale spin systems. However, fine control of a general interaction matrix JJJ has so far only been accomplished through eigenvalue decomposition methods that either limit the scalability or increase the execution time of the optimization process. We introduce and experimentally validate a SPIM instance that enables direct control over the full interaction matrix, enabling the encoding of Ising Hamiltonians with arbitrary couplings and connectivity. We demonstrate the conformity of the experimentally measured Ising energy with the theoretically expected values and then proceed to solve both the unweighted and weighted graph partitioning problems, showcasing a systematic convergence to an optimal solution via simulated annealing. Our approach greatly expands the applicability of SPIMs for real-world applications without sacrificing any of the inherent advantages of the system, and paves the way to encoding the full range of NP problems that are known to be equivalent to Ising models, on SPIM devices.