Scalable Emulation of Sign-Problem−-Free Hamiltonians with Room Temperature p-bits

The growing field of quantum computing is based on the concept of a q-bit which is a delicate superposition of 0 and 1, requiring cryogenic temperatures for its physical realization along with challenging coherent coupling techniques for entangling them. By contrast, a probabilistic bit or a p-bit is a robust classical entity that fluctuates between 0 and 1, and can be implemented at room temperature using present-day technology. Here, we show that a probabilistic coprocessor built out of room temperature p-bits can be used to accelerate simulations of a special class of quantum many-body systems that are sign-problem$-$free or stoquastic, leveraging the well-known Suzuki-Trotter decomposition that maps a $d$-dimensional quantum many body Hamiltonian to a $d$+1-dimensional classical Hamiltonian. This mapping allows an efficient emulation of a quantum system by classical computers and is commonly used in software to perform Quantum Monte Carlo (QMC) algorithms. By contrast, we show that a compact, embedded MTJ-based coprocessor can serve as a highly efficient hardware-accelerator for such QMC algorithms providing several orders of magnitude improvement in speed compared to optimized CPU implementations. Using realistic device-level SPICE simulations we demonstrate that the correct quantum correlations can be obtained using a classical p-circuit built with existing technology and operating at room temperature. The proposed coprocessor can serve as a tool to study stoquastic quantum many-body systems, overcoming challenges associated with physical quantum annealers.Comment: Fixed minor typos and expanded Appendi

Autonomous Probabilistic Coprocessing with Petaflips per Second

In this paper we present a concrete design for a probabilistic (p-) computer based on a network of p-bits, robust classical entities fluctuating between -1 and +1, with probabilities that are controlled through an input constructed from the outputs of other p-bits. The architecture of this probabilistic computer is similar to a stochastic neural network with the p-bit playing the role of a binary stochastic neuron, but with one key difference: there is no sequencer used to enforce an ordering of p-bit updates, as is typically required. Instead, we explore \textit{sequencerless} designs where all p-bits are allowed to flip autonomously and demonstrate that such designs can allow ultrafast operation unconstrained by available clock speeds without compromising the solution's fidelity. Based on experimental results from a hardware benchmark of the autonomous design and benchmarked device models, we project that a nanomagnetic implementation can scale to achieve petaflips per second with millions of neurons. A key contribution of this paper is the focus on a hardware metric $-$ flips per second $-$ as a problem and substrate-independent figure-of-merit for an emerging class of hardware annealers known as Ising Machines. Much like the shrinking feature sizes of transistors that have continually driven Moore's Law, we believe that flips per second can be continually improved in later technology generations of a wide class of probabilistic, domain specific hardware.Comment: 13 pages, 8 figures, 1 tabl

Heterogeneous Reconfigurable Fabrics for In-circuit Training and Evaluation of Neuromorphic Architectures

A heterogeneous device technology reconfigurable logic fabric is proposed which leverages the cooperating advantages of distinct magnetic random access memory (MRAM)-based look-up tables (LUTs) to realize sequential logic circuits, along with conventional SRAM-based LUTs to realize combinational logic paths. The resulting Hybrid Spin/Charge FPGA (HSC-FPGA) using magnetic tunnel junction (MTJ) devices within this topology demonstrates commensurate reductions in area and power consumption over fabrics having LUTs constructed with either individual technology alone. Herein, a hierarchical top-down design approach is used to develop the HSCFPGA starting from the configurable logic block (CLB) and slice structures down to LUT circuits and the corresponding device fabrication paradigms. This facilitates a novel architectural approach to reduce leakage energy, minimize communication occurrence and energy cost by eliminating unnecessary data transfer, and support auto-tuning for resilience. Furthermore, HSC-FPGA enables new advantages of technology co-design which trades off alternative mappings between emerging devices and transistors at runtime by allowing dynamic remapping to adaptively leverage the intrinsic computing features of each device technology. HSC-FPGA offers a platform for fine-grained Logic-In-Memory architectures and runtime adaptive hardware. An orthogonal dimension of fabric heterogeneity is also non-determinism enabled by either low-voltage CMOS or probabilistic emerging devices. It can be realized using probabilistic devices within a reconfigurable network to blend deterministic and probabilistic computational models. Herein, consider the probabilistic spin logic p-bit device as a fabric element comprising a crossbar-structured weighted array. The Programmability of the resistive network interconnecting p-bit devices can be achieved by modifying the resistive states of the array\u27s weighted connections. Thus, the programmable weighted array forms a CLB-scale macro co-processing element with bitstream programmability. This allows field programmability for a wide range of classification problems and recognition tasks to allow fluid mappings of probabilistic and deterministic computing approaches. In particular, a Deep Belief Network (DBN) is implemented in the field using recurrent layers of co-processing elements to form an n x m1 x m2 x ::: x mi weighted array as a configurable hardware circuit with an n-input layer followed by i ≥ 1 hidden layers. As neuromorphic architectures using post-CMOS devices increase in capability and network size, the utility and benefits of reconfigurable fabrics of neuromorphic modules can be anticipated to continue to accelerate