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Probabilistic computing with pbits is emerging as a computational paradigm for machine learning and for facing combinatorial optimization problems (COPs) with the so-called probabilistic Ising machines (PIMs). From a hardware point of view,…
A new technique is demonstrated for carrying out exact positive-P phase-space simulations of the coherent Ising machine quantum computer. By suitable design of the coupling matrix, general hard optimization problems can be solved. Here,…
An introduction to the application of combinatorial optimization methods to ground state calculations of frustrated, disordered systems is given. We discuss the interface problem in the random bond Ising ferromagnet, the random field Ising…
Computation with the Ising model is central to future computing technologies like quantum annealing, adiabatic quantum computing, and thermodynamic classical computing. Traditionally, computed values have been equated with ground states.…
We study a family of models for an $N_1 \times N_2$ matrix worth of Ising spins $S_{aB}$. In the large $N_i$ limit we show that the spins soften, so that the partition function is described by a bosonic matrix integral with a single…
Coupled electronic oscillators have recently been explored as a compact, integrated circuit- and room temperature operation- compatible hardware platform to design Ising machines. However, such implementations presently require the…
We explore the potential of spatial-photonic Ising machines (SPIMs) to address computationally intensive Ising problems that employ low-rank and circulant coupling matrices. Our results indicate that the performance of SPIMs is critically…
Degenerate optomechanical parametric oscillators are optical resonators in which a mechanical degree of freedom is coupled to a cavity mode that is nonlinearly amplified via parametric down-conversion of an external pumping laser. Below a…
Analog computing using bosonic computational states is a leading approach to surpassing the computational speed and energy limitations of von Neumann architectures. But the challenges of manufacturing large-scale photonic integrated…
A new family of free fermionic quantum spin chains with multispin interactions was recently introduced. Here we show that it is possible to build standard quantum Ising chains -- but with inhomogeneous couplings -- which have the same…
We present a new family of zero-field Ising models over N binary variables/spins obtained by consecutive "gluing" of planar and $O(1)$-sized components along with subsets of at most three vertices into a tree. The polynomial time algorithm…
A quantum simulator is a well controlled quantum system that can simulate the behavior of another quantum system which may require exponentially large classical computing resources to understand otherwise. In the 1980s, Feynman proposed the…
Ising machines are specialized computers for finding the lowest energy states of Ising spin models, onto which many practical combinatorial optimization problems can be mapped. Simulated bifurcation (SB) is a quantum-inspired parallelizable…
We explore the coherent dynamics in a small network of three coupled parametric oscillators and demonstrate the effect of frustration on the persistent beating between them. Since a single-mode parametric oscillator represents an analog of…
It is challenging to scale Ising machines for industrial-level problems due to algorithm or hardware limitations. Although higher-order Ising models provide a more compact encoding, they are, however, hard to physically implement. This work…
Non-orthogonal multiple access (NOMA) technique is important for achieving a high data rate in next-generation wireless communications. A key challenge to fully utilizing the effectiveness of the NOMA technique is the optimization of the…
In recent years, hardware implementations of Ising machines have emerged as a viable alternative to quantum computing for solving hard optimization problems among other applications. Unlike quantum hardware, dense connectivity can be…
We present a protocol to store a polynomial number of arbitrary bit strings, encoded as spin configurations, in the approximately degenerate low-energy manifold of an all-to-all connected Ising spin glass. The iterative protocol is inspired…
The "folding algorithm"\cite{fold1} is a matrix product state algorithm for simulating quantum systems that involves a spatial evolution of a matrix product state. Hence, the computational effort of this algorithm is controlled by the…
Since the invention of the solid-state transistor, the overwhelming majority of computers followed the von Neumann architecture that strictly separates logic operations and memory. Today, there is a revived interest in alternative…