[Paper Review] Speedup in quantum computation is associated with attenuation of processing probability

Karl Svozil|ArXiv.org|Dec 6, 1994

Quantum Computing Algorithms and Architecture3 references3 citations

TL;DR

This paper demonstrates that quantum speedup, while theoretically possible via superposition, is counterbalanced by a corresponding reduction in the probability of detecting the correct computational outcome. The key result is that the average detection rate across all paths scales inversely with the number of parallel paths, implying no net speedup over classical nondeterministic computation.

ABSTRACT

Quantum coherence allows the computation of an arbitrary number of distinct computational paths in parallel. Based on quantum parallelism it has been conjectured that exponential or even larger speedups of computations are possible. Here it is shown that, although in principle correct, any speedup is accompanied by an associated attenuation of detection rates. Thus, on the average, no effective speedup is obtained relative to classical (nondeterministic) devices.

Motivation & Objective

• To investigate whether quantum parallelism leads to effective computational speedup in practice.
• To analyze the trade-off between the number of computational paths explored in superposition and the probability of detecting the correct result.
• To determine whether exponential quantum speedup is achievable when accounting for measurement probabilities.
• To challenge the assumption that quantum parallelism inherently enables faster computation by introducing a physical constraint on detection rates.

Proposed method

• Analyzes quantum computation as a process where multiple paths are explored simultaneously via superposition.
• Models the detection probability of the correct computational outcome as inversely proportional to the number of parallel paths.
• Applies principles of quantum amplitude interference to show that increasing path count reduces detection likelihood.
• Uses a theoretical framework based on quantum state evolution and measurement to quantify the trade-off between path diversity and detection efficiency.
• Compares quantum computation to classical nondeterministic computation under the same detection constraints.
• Derives that the expected detection rate scales as 1/N for N parallel paths, negating any average speedup.

Experimental results

Research questions

• RQ1 Can quantum parallelism lead to a net speedup when detection probabilities are considered?
• RQ2 What is the relationship between the number of computational paths and the probability of detecting the correct result?
• RQ3 Is exponential quantum speedup feasible if detection rates decrease proportionally with path count?
• RQ4 How does the average detection rate in quantum computation compare to classical nondeterministic computation?
• RQ5 Does the principle of quantum superposition lead to a practical advantage when measurement outcomes are probabilistic?

Key findings

• Any quantum speedup based on parallel path exploration is counterbalanced by a proportional decrease in detection probability.
• The detection rate for the correct result scales as 1/N, where N is the number of parallel computational paths.
• On average, quantum computation does not outperform classical nondeterministic devices due to this inverse scaling.
• The paper concludes that no effective speedup is achieved relative to classical methods when detection rates are accounted for.
• The theoretical possibility of exponential speedup is invalidated by the physical constraint of diminishing detection probabilities.
• The trade-off between path diversity and detection efficiency imposes a fundamental limit on practical quantum advantage.