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Ising machines have recently been attracting attention due to their apparent ability to solve5 difficult combinatorial problems using analog operational principles. Oscillator Ising Machines6 (OIM) are especially attractive because they can be implemented easily as integrated circuits (ICs)7 in standard CMOS electronics. We explore the performance of OIM for decoding noisy Multi-User8 MIMO signals, a problem of considerable interest in modern telecommunications. Our results9 indicate that OIM-based decoding achieves error rates almost as good as the optimal Maximum10 Likelihood method, over a wide range of practical signal-to-noise (SNR) values. At high SNR11 values, OIM achieves ~20x fewer errors than LMMSE, a decoding method used widely in industry12 today. We also investigate the influence of parameter precision on decoding performance, finding13 that using 6 or more bits of precision largely retains OIM’s advantages across all SNR values. We14 estimate that straightforward CMOS OIM implementations can easily solve MU-MIMO decoding15 problems in under 10ns, more than 100x faster than current industrial requirements. We conclude16 that oscillator Ising machines can be effective for real-world applications, possibly serving as an17 important enabler for future telecommunication standards. Our results and data provide guidance18 for designing hardware OIM prototypes specialized for MU-MIMO decoding. 

Almost all practical systems rely heavily on physical parameters. As a result, parameter sensitivity, or the extent to which perturbations in parameter values affect the state of a system, is intrinsically connected to system design and optimization. We present TADsens, a method for computing the parameter sensitivities of an output of a differential algebraic equation (DAE) system. Specifically, we provide rigorous, insightful theory for adjoint sensitivity computation of DAEs, along with an efficient and numerically well-posed algorithm implemented in Berkeley MAPP. Our theory and implementation advances resolve longstanding issues that have impeded adoption of adjoint transient sensitivities in circuit simulators for over 5 decades. We present results and comparisons on two nonlinear analog circuits. TADsens is numerically well posed and accurate, and faster by a factor of 300 over direct sensitivity computation on a circuit with over 150 unknowns and 600 parameters. 

Ising machines have been attracting attention due to their ability to use mixed discrete/continuous mechanisms to solve difficult combinatorial optimization problems. We present BLIM, a novel Ising machine scheme that uses latches (bistable elements) with controllable gains as Ising spins. We show that networks of coupled latches have a Lyapunov or “energy” function that matches the Ising Hamiltonian in discrete operation, enabling them to function as Ising machines. This result is established in a general coupled-element Ising machine framework that is not limited to BLIM. Operating the latches periodically in analog/continuous mode, during which bistability is removed, helps the system traverse to better minima. CMOS realizations of BLIM have desirable practical features; implementation in other physical domains is an intriguing possibility.