Incorporating rank-free coupling and external field via an amplitude-only modulated spatial photonic Ising machine

Ising machines have emerged as effective solvers for combinatorial optimization problems, such as NP-hard problems, machine learning, and financial modeling. Recent spatial photonic Ising machines (SPIMs) excel in multi-node optimization and spin glass simulations, leveraging their large-scale and fully connected characteristics. However, existing laser diffraction-based SPIMs usually sacrifice time efficiency or spin count to encode high-rank spin-spin coupling and external fields, limiting their scalability for real-world applications. Here, we demonstrate an amplitude-only modulated rank-free spatial photonic Ising machine (AR-SPIM) with 200 iterations per second. By re-formulating an arbitrary Ising Hamiltonian as the sum of Hadamard products, followed by loading the corresponding matrices/vectors onto an aligned amplitude spatial light modulator and digital micro-mirrors device, we directly map a 797-spin Ising model with external fields (nearly 9-bit precision, -255 to 255) into an incoherent light field, eliminating the need for repeated and auxiliary operations. Serving as encoding accuracy metrics, the linear coefficient of determination and Pearson correlation coefficient between measured light intensities and Ising Hamiltonians exceed 0.9800, with values exceed 0.9997 globally. The AR-SPIM achieves less than 0.3% error rate for ground-state search of biased Max-cut problems with arbitrary ranks and weights, enables complex phase transition observations, and facilitates scalable spin counts for sparse Ising problems via removing zero-valued Hadamard product terms. This reconfigurable AR-SPIM can be further developed to support large-scale machine-learning training and deployed for practical applications in discrete optimization and quantum many-body simulations.

Discovering autonomous quantum error correction via deep reinforcement learning

Quantum error correction is essential for fault-tolerant quantum computing. However, standard methods relying on active measurements may introduce additional errors. Autonomous quantum error correction (AQEC) circumvents this by utilizing engineered dissipation and drives in bosonic systems, but identifying practical encoding remains challenging due to stringent Knill-Laflamme conditions. In this work, we utilize curriculum learning enabled deep reinforcement learning to discover Bosonic codes under approximate AQEC framework to resist both single-photon and double-photon losses. We present an analytical solution of solving the master equation under approximation conditions, which can significantly accelerate the training process of reinforcement learning. The agent first identifies an encoded subspace surpassing the breakeven point through rapid exploration within a constrained evolutionary time-frame, then strategically fine-tunes its policy to sustain this performance advantage over extended temporal horizons. We find that the two-phase trained agent can discover the optimal set of codewords, i.e., the Fock states $\ket{4}$ and $\ket{7}$ considering the effect of both single-photon and double-photon loss. We identify that the discovered code surpasses the breakeven threshold over a longer evolution time and achieve the state-of-art performance. We also analyze the robustness of the code against the phase damping and amplitude damping noise. Our work highlights the potential of curriculum learning enabled deep reinforcement learning in discovering the optimal quantum error correct code especially in early fault-tolerant quantum systems.

Arbitrarily-high-dimensional reconciliation via cross-rotation for continuous-variable quantum key distribution

Multidimensional rotation serves as a powerful tool for enhancing information reconciliation and extending the transmission distance in continuous-variable quantum key distribution (CV-QKD). However, the lack of closed-form orthogonal transformations for high-dimensional rotations has limited the maximum reconciliation efficiency to channels with 8 dimensions over the past decade. This paper presents a cross-rotation scheme to overcome this limitation and enable reconciliation in arbitrarily high dimensions, constrained to even multiples of 8. The key treatment involves reshaping the string vector into matrix form and applying orthogonal transformations to its columns and rows in a cross manner, thereby increasing the reconciliation dimension by one order per cross-rotation while significantly reducing the communication overhead over the classical channel. A rigorous performance analysis is also presented from the perspective of achievable sum-rate. Simulation results demonstrate that 64-dimensional cross-rotation nearly approaches the upper bound, making it a recommended choice for practical implementations.

Joint parameter estimation and multidimensional reconciliation for CV-QKD

Accurate quantum channel parameter estimation is essential for effective information reconciliation in continuous-variable quantum key distribution (CV-QKD). However, conventional maximum likelihood (ML) estimators rely on a large amount of discarded data (or pilot symbols), leading to a significant loss in symbol efficiency. Moreover, the separation between the estimation and reconciliation phases can introduce error propagation. In this paper, we propose a novel joint message-passing scheme that unifies channel parameter estimation and information reconciliation within a Bayesian framework. By leveraging the expectation-maximization (EM) algorithm, the proposed method simultaneously estimates unknown parameters during decoding, eliminating the need for separate ML estimation. Furthermore, we introduce a hybrid multidimensional rotation scheme that removes the requirement for norm feedback, significantly reducing classical channel overhead. To the best of our knowledge, this is the first work to unify multidimensional reconciliation and channel parameter estimation in CV-QKD, providing a practical solution for high-efficiency reconciliation with minimal pilots.

Towards Heisenberg limit without critical slowing down via quantum reinforcement learning

Critical ground states of quantum many-body systems have emerged as vital resources for quantum-enhanced sensing. Traditional methods to prepare these states often rely on adiabatic evolution, which may diminish the quantum sensing advantage. In this work, we propose a quantum reinforcement learning (QRL)-enhanced critical sensing protocol for quantum many-body systems with exotic phase diagrams. Starting from product states and utilizing QRL-discovered gate sequences, we explore sensing accuracy in the presence of unknown external magnetic fields, covering both local and global regimes. Our results demonstrate that QRL-learned sequences reach the finite quantum speed limit and generalize effectively across systems of arbitrary size, ensuring accuracy regardless of preparation time. This method can robustly achieve Heisenberg and super-Heisenberg limits, even in noisy environments with practical Pauli measurements. Our study highlights the efficacy of QRL in enabling precise quantum state preparation, thereby advancing scalable, high-accuracy quantum critical sensing.