Quantum Computing and Noise-based Logic Achieve Exponential Parallelism, with INBL Limited to Boolean Operations and Lacking Superposition for 0.5 Operations

Exponential parallelism represents a fundamental advance in computational systems, promising significant benefits across diverse scientific and industrial fields, and Laszlo B. Kish from Texas A and M University, along with colleagues, comprehensively examines two distinct approaches to achieving this: quantum computing and Instantaneous Noise-based Logic. This feature paper presents a comparative analysis of their practical capabilities, limitations, and potential applications, moving beyond purely theoretical considerations. While quantum computers harness the power of superposition within expansive Hilbert spaces to achieve universality for all computational tasks, Instantaneous Noise-based Logic leverages the product space of classical noise processes, currently limited to Boolean logic but offering compelling advantages for specific problems. Notably, the research demonstrates that for search tasks, such as looking up a phone number, Instantaneous Noise-based Logic surpasses even the quadratic speedup offered by Grover’s algorithm, achieving an exponential speedup with logarithmic time complexity, and importantly, this can be realised with considerably simpler hardware potentially integrated into existing computer architectures.

Quantum computers utilize superposition to represent all 2 n possible binary strings simultaneously, forming the basis for entanglement and interference crucial to quantum computation. This enables quantum algorithms, such as Deutsch-Jozsa, Grover’s search, and Shor’s factoring, to achieve computational advantages over classical methods by processing many input values in parallel and amplifying correct outputs. Researchers also explored INBL, a classical approach that exploits the statistical properties of noise signals to achieve high-dimensional computation.

The study engineered a system where information is encoded using random telegraph waves, creating product spaces that scale exponentially with the number of noise bits, mirroring the complexity of quantum systems. Each noise-bit possesses two values, represented by periodically clocked random telegraph waves generated by a true random number generator. Strings and binary numbers are represented as products of these independent waves, effectively encoding them as random telegraph waves themselves. The team proved that INBL is universally capable of Boolean logic, enabling the instantaneous implementation of core gates and deterministic computation of any Boolean function.

Notably, while INBL can achieve equivalent computational complexity to quantum computers for algorithms like Deutsch-Jozsa, it currently lacks the gate functionalities necessary to implement Shor’s algorithm. However, for search tasks, such as phonebook lookup, INBL demonstrates an exponential speedup, requiring only logarithmic time compared to Grover’s algorithm. This work establishes that INBL can emulate certain exponential advantages of quantum computation while remaining firmly rooted in classical determinism and hardware simplicity. Experiments revealed that for search tasks, such as a phonebook lookup, INBL delivers an exponential speedup, requiring only logarithmic time, in contrast to classical algorithms. The team successfully executed parallel operations across a full noise hyperspace to solve exponential configuration search challenges, instantaneously operating on all 2 n possible binary numbers, analogous to a superposed quantum state.

Measurements confirm that INBL can process exponentially large amplitudes, equivalent to 2 n random two-state words, which would overwhelm a conventional analog computer, but are feasible with digital computers due to a logarithmic transformation. This is achieved through two key compressions: a compression of the universe represented by the noise-based system, and a bandwidth compression that maintains computational efficiency. Researchers highlight a deep structural analogy between quantum and INBL universes, both built upon tensor product spaces, demonstrating that INBL can reproduce exponential features of quantum computing deterministically. While quantum computers rely on delicate quantum states and complex error correction, INBL operates with inherent stability, immune to decoherence, and is implementable with modest modifications to conventional computer architectures equipped with a true random number generator. Both approaches harness exponentially large computational spaces, achieved through superposition in computing and the product space of classical noise processes in INBL. While computing offers universality for all computational operations, current INBL frameworks are limited to Boolean logic. Despite this limitation, the study demonstrates that INBL and computing can achieve equivalent performance for specific problem classes, such as the Deutsch-Jozsa algorithm.

Notably, INBL exhibits a significant advantage in search tasks, like phonebook lookup, achieving an exponential speedup with logarithmic time complexity, compared to the quadratic speedup offered by Grover’s algorithm in computing. The researchers highlight that INBL’s potential stems from its simpler hardware requirements, potentially integrating with conventional computer architectures using existing random number generators, and its inherent avoidance of the decoherence issues that plague computing systems. The authors acknowledge that INBL currently lacks the full universality of computing, with ongoing work focused on expanding its gate set. Future research will likely explore the practical realization of INBL hardware and its application to specific computational problems where its speed and simplicity offer advantages.