Dynamic Range Reduction via Branch-and-Bound

TL;DR

This paper presents a principled Branch-and-Bound algorithm that reduces the precision requirements in QUBO problems by leveraging dynamic range, validated through experiments on a quantum annealer.

Contribution

The paper introduces a novel Branch-and-Bound method that adaptively reduces precision in QUBO problems based on dynamic range, improving efficiency for quantum annealing.

Findings

Effective precision reduction demonstrated on quantum annealer

Dynamic range-based approach improves problem complexity management

Algorithm outperforms baseline methods in experiments

Abstract

The demand for high-performance computing in machine learning and artificial intelligence has led to the development of specialized hardware accelerators like Tensor Processing Units (TPUs), Graphics Processing Units (GPUs), and Field-Programmable Gate Arrays (FPGAs). A key strategy to enhance these accelerators is the reduction of precision in arithmetic operations, which increases processing speed and lowers latency - crucial for real-time AI applications. Precision reduction minimizes memory bandwidth requirements and energy consumption, essential for large-scale and mobile deployments, and increases throughput by enabling more parallel operations per cycle, maximizing hardware resource utilization. This strategy is equally vital for solving NP-hard quadratic unconstrained binary optimization (QUBO) problems common in machine learning, which often require high precision for accurate representation. Special hardware solvers, such as quantum annealers, benefit significantly from precision reduction. This paper introduces a fully principled Branch-and-Bound algorithm for reducing precision needs in QUBO problems by utilizing dynamic range as a measure of complexity. Experiments validate our algorithm's effectiveness on an actual quantum annealer.