arXiv subjects

John P. Hayes

Publications and source records attributed to John P. Hayes.

9 recordsLinked to original sources

arXiv2021

CeMux: Maximizing the Accuracy of Stochastic Mux Adders and an Application to Filter Design

Stochastic computing (SC) is a low-cost computational paradigm that has promising applications in digital filter design, image processing and neural networks. Fundamental to these applications is the weighted addition operation which is most often implemented by a multiplexer (mux) tree. Mux-based adders have very low area but typically require long bit-streams to reach practical accuracy thresholds when the number of summands is large. In this work, we first identify the main contributors to mux adder error. We then demonstrate with analysis and experiment that two new techniques, precise sampling and full correlation, can target and mitigate these error sources. Implementing these techniques in hardware leads to the design of CeMux (Correlation-enhanced Multiplexer), a stochastic mux adder that is significantly more accurate and uses much less area than traditional weighted adders. We compare CeMux to other SC and hybrid designs for an electrocardiogram filtering case study that employs a large digital filter. One major result is that CeMux is shown to be accurate even for large input sizes. CeMux's higher accuracy leads to a latency reduction of 4x to 16x over other designs. Further, CeMux uses about 35% less area than existing designs, and we demonstrate that a small amount of accuracy can be traded for a further 50% reduction in area. Finally, we compare CeMux to a conventional binary design and we show that CeMux can achieve a 50 to 73% area reduction for similar power and latency as the conventional design, but at a slightly higher level of error.

cs.ET↗

arXiv2017

Energy-Efficient Hybrid Stochastic-Binary Neural Networks for Near-Sensor Computing

Recent advances in neural networks (NNs) exhibit unprecedented success at transforming large, unstructured data streams into compact higher-level semantic information for tasks such as handwriting recognition, image classification, and speech recognition. Ideally, systems would employ near-sensor computation to execute these tasks at sensor endpoints to maximize data reduction and minimize data movement. However, near- sensor computing presents its own set of challenges such as operating power constraints, energy budgets, and communication bandwidth capacities. In this paper, we propose a stochastic- binary hybrid design which splits the computation between the stochastic and binary domains for near-sensor NN applications. In addition, our design uses a new stochastic adder and multiplier that are significantly more accurate than existing adders and multipliers. We also show that retraining the binary portion of the NN computation can compensate for precision losses introduced by shorter stochastic bit-streams, allowing faster run times at minimal accuracy losses. Our evaluation shows that our hybrid stochastic-binary design can achieve 9.8x energy efficiency savings, and application-level accuracies within 0.05% compared to conventional all-binary designs.

cs.AR↗

arXiv2007

Checking Equivalence of Quantum Circuits and States

Quantum computing promises exponential speed-ups for important simulation and optimization problems. It also poses new CAD problems that are similar to, but more challenging, than the related problems in classical (non-quantum) CAD, such as determining if two states or circuits are functionally equivalent. While differences in classical states are easy to detect, quantum states, which are represented by complex-valued vectors, exhibit subtle differences leading to several notions of equivalence. This provides flexibility in optimizing quantum circuits, but leads to difficult new equivalence-checking issues for simulation and synthesis. We identify several different equivalence-checking problems and present algorithms for practical benchmarks, including quantum communication and search circuits, which are shown to be very fast and robust for hundreds of qubits.

quant-ph↗

arXiv2004

Is Quantum Search Practical?

Quantum algorithms and circuits can, in principle, outperform the best non-quantum (classical) techniques for some hard computational problems. However, this does not necessarily lead to useful applications. To gauge the practical significance of a quantum algorithm, one must weigh it against the best conventional techniques applied to useful instances of the same problem. Grover's quantum search algorithm is one of the most widely studied. We identify requirements for Grover's algorithm to be useful in practice: (1) a search application S where classical methods do not provide sufficient scalability; (2) an instantiation of Grover's algorithm Q(S) for S that has a smaller asymptotic worst-case runtime than any classical algorithm C(S) for S; (3) Q(S) with smaller actual runtime for practical instances of S than that of any C(S). We show that several commonly-suggested applications fail to satisfy these requirements, and outline directions for future work on quantum search.

quant-ph↗

arXiv2004

Fault Testing for Reversible Circuits

Applications of reversible circuits can be found in the fields of low-power computation, cryptography, communications, digital signal processing, and the emerging field of quantum computation. Furthermore, prototype circuits for low-power applications are already being fabricated in CMOS. Regardless of the eventual technology adopted, testing is sure to be an important component in any robust implementation. We consider the test set generation problem. Reversibility affects the testing problem in fundamental ways, making it significantly simpler than for the irreversible case. For example, we show that any test set that detects all single stuck-at faults in a reversible circuit also detects all multiple stuck-at faults. We present efficient test set constructions for the standard stuck-at fault model as well as the usually intractable cell-fault model. We also give a practical test set generation algorithm, based on an integer linear programming formulation, that yields test sets approximately half the size of those produced by conventional ATPG.

quant-ph↗

arXiv2004

Graph-based simulation of quantum computation in the density matrix representation

Quantum-mechanical phenomena are playing an increasing role in information processing, as transistor sizes approach the nanometer level, and quantum circuits and data encoding methods appear in the securest forms of communication. Simulating such phenomena efficiently is exceedingly difficult because of the vast size of the quantum state space involved. A major complication is caused by errors (noise) due to unwanted interactions between the quantum states and the environment. Consequently, simulating quantum circuits and their associated errors using the density matrix representation is potentially significant in many applications, but is well beyond the computational abilities of most classical simulation techniques in both time and memory resources. The size of a density matrix grows exponentially with the number of qubits simulated, rendering array-based simulation techniques that explicitly store the density matrix intractable. In this work, we propose a new technique aimed at efficiently simulating quantum circuits that are subject to errors. In particular, we describe new graph-based algorithms implemented in the simulator QuIDDPro/D. While previously reported graph-based simulators operate in terms of the state-vector representation, these new algorithms use the density matrix representation. To gauge the improvements offered by QuIDDPro/D, we compare its simulation performance with an optimized array-based simulator called QCSim. Empirical results, generated by both simulators on a set of quantum circuit benchmarks involving error correction, reversible logic, communication, and quantum search, show that the graph-based approach far outperforms the array-based approach.

quant-ph↗

arXiv2003

Improving Gate-Level Simulation of Quantum Circuits

Simulating quantum computation on a classical computer is a difficult problem. The matrices representing quantum gates, and the vectors modeling qubit states grow exponentially with an increase in the number of qubits. However, by using a novel data structure called the Quantum Information Decision Diagram (QuIDD) that exploits the structure of quantum operators, a useful subset of operator matrices and state vectors can be represented in a form that grows polynomially with the number of qubits. This subset contains, but is not limited to, any equal superposition of n qubits, any computational basis state, n-qubit Pauli matrices, and n-qubit Hadamard matrices. It does not, however, contain the discrete Fourier transform (employed in Shor's algorithm) and some oracles used in Grover's algorithm. We first introduce and motivate decision diagrams and QuIDDs. We then analyze the runtime and memory complexity of QuIDD operations. Finally, we empirically validate QuIDD-based simulation by means of a general-purpose quantum computing simulator QuIDDPro implemented in C++. We simulate various instances of Grover's algorithm with QuIDDPro, and the results demonstrate that QuIDDs asymptotically outperform all other known simulation techniques. Our simulations also show that well-known worst-case instances of classical searching can be circumvented in many specific cases by data compression techniques.

quant-ph↗

arXiv2003

Reversible Logic Circuit Synthesis

Reversible or information-lossless circuits have applications in digital signal processing, communication, computer graphics and cryptography. They are also a fundamental requirement in the emerging field of quantum computation. We investigate the synthesis of reversible circuits that employ a minimum number of gates and contain no redundant input-output line-pairs (temporary storage channels). We prove constructively that every even permutation can be implemented without temporary storage using NOT, CNOT and TOFFOLI gates. We describe an algorithm for the synthesis of optimal circuits and study the reversible functions on three wires, reporting distributions of circuit sizes. We study circuit decompositions of reversible circuits where gates of the same type are next to each other. Finally, in an application important to quantum computing, we synthesize oracle circuits for Grover's search algorithm, and show a significant improvement over a previously proposed synthesis algorithm.

quant-ph↗

arXiv2002

Gate-Level Simulation of Quantum Circuits

While thousands of experimental physicists and chemists are currently trying to build scalable quantum computers, it appears that simulation of quantum computation will be at least as critical as circuit simulation in classical VLSI design. However, since the work of Richard Feynman in the early 1980s little progress was made in practical quantum simulation. Most researchers focused on polynomial-time simulation of restricted types of quantum circuits that fall short of the full power of quantum computation. Simulating quantum computing devices and useful quantum algorithms on classical hardware now requires excessive computational resources, making many important simulation tasks infeasible. In this work we propose a new technique for gate-level simulation of quantum circuits which greatly reduces the difficulty and cost of such simulations. The proposed technique is implemented in a simulation tool called the Quantum Information Decision Diagram (QuIDD) and evaluated by simulating Grover's quantum search algorithm. The back-end of our package, QuIDD Pro, is based on Binary Decision Diagrams, well-known for their ability to efficiently represent many seemingly intractable combinatorial structures. This reliance on a well-established area of research allows us to take advantage of existing software for BDD manipulation and achieve unparalleled empirical results for quantum simulation.

quant-ph↗