The Physics of Computation: Fundamental Limits and the Honest Boundaries of Post-Classical Computing

In the paper's words

Phase III of the Qubit Delusion series. Examines fundamental physical limits on computation: Landauer bound, Margolus-Levitin theorem, Bremermann limit, Bekenstein bound. Shows that quantum error-correction overhead (1e2-1e3 physical operations per logical operation) multiplies thermodynamic cost beyond what any polynomial algorithmic speedup can overcome.

The abstract, verbatim, and its opening sentence is the claim. Every line below is quoted from the text.

Numbers it reports

1. For a qubit with an energy splitting of 5 GHz --- typical for superconducting qubits --- the Margolus-Levitin bound gives a minimum gate time of approximately 0.05 nanoseconds.

   from 3.1 The Bound

2. Current superconducting gates operate at ~10-100 ns, which is within a factor of 200-2000 of the fundamental limit.

   from 3.1 The Bound

3. The per-measurement time is ~1.6 ns --- already within a factor of 30 of the Margolus-Levitin bound at 5 GHz.

   from 3.2 The Clock Speed Implication

4. The Bekenstein bound limits the amount of information that can be stored in a region of space of radius R containing energy E: $I \leq 2\pi RE$ / (ħ c ln 2) For a 1 kg, 10 cm radius system, the Bekenstein bound is approximately 2.6 × 10^41 bits --- an unimaginably large number.

   from 4.2 The Bekenstein Bound: Information Density

5. The wall-plug energy per physical quantum operation is approximately (10^4 W) / (10^3 qubits × 10^7 operations/second) ≈ 10^-6 joules per physical operation --- a factor of 10^9 above the Landauer bound and a factor of 10^9 worse than a classical gate.

   from 4.3 The Real Constraint: Energy Efficiency, Not Information Density

6. We assess the leading platforms against this criterion: Superconducting (IBM, Google): With wall-plug energy ~10^-3 joules per logical operation and ~O(exp(n)) classical factoring cost vs. ~O(poly(n)) quantum, Shor's algorithm would achieve joules-per- solution advantage for sufficiently large n.

   from 6.2 Can Any Proposed Architecture Meet This Criterion?

How it is done

1. It is a question about fundamental limits: the thermodynamic cost of information processing (Landauer 1961), the maximum rate at which a quantum system can evolve between distinguishable states (Margolus-Levitin 1998), and the ultimate bound on computational throughput imposed by the finite energy and information density of any physical system (Bremermann 1962, Bekenstein 1981).

   from 1. Introduction: The Question Physics Must Answer

2. Does the Landauer bound apply differently to quantum information?

   from 2.2 The Quantum Generalization

3. The Landauer bound gives the fundamental thermodynamic minimum.

   from 2.4 The Cryogenic Overhead

4. For a qubit with an energy splitting of 5 GHz --- typical for superconducting qubits --- the Margolus-Levitin bound gives a minimum gate time of approximately 0.05 nanoseconds.

   from 3.1 The Bound

What would falsify it

1. The paper concludes with a falsifiable criterion for "physical computational advantage" and an assessment of whether any existing or proposed quantum architecture satisfies it.

   from 1. Introduction: The Question Physics Must Answer

2. We propose a single, falsifiable criterion for evaluating any computational paradigm --- classical, quantum, or otherwise: A device exhibits "physical computational advantage" if it solves a commercially relevant problem at lower total energy cost (joules per solution) than any classical alternative.

   from 6.1 Joules Per Solution

3. What should be funded: Research programs that directly target the joules-per-solution criterion, with falsifiable milestones and independent verification.

   from 7. Conclusion: The Honest Boundaries

Where the claim stops

1. The Landauer bound does not privilege quantum over classical; the advantage, if it exists, is algorithmic, not thermodynamic.

   from 7. Conclusion: The Honest Boundaries

2. What physics does NOT permit: Physics does not permit violating the energy-efficiency trade-off.

   from 7. Conclusion: The Honest Boundaries

3. The thermodynamic arithmetic does not work.

   from 7. Conclusion: The Honest Boundaries

Where to read

1. 1. Introduction: The Question Physics Must Answer458 words · 2 min
2. 2. The Landauer Principle: What Erasing Information Costs807 words · 4 min
3. 3. The Margolus-Levitin Theorem: Quantum Speed Limits498 words · 2 min
4. 4. The Bremermann Limit and Bekenstein Bound409 words · 2 min
5. 5. Reversible Computing: The Forgotten Path493 words · 2 min
6. 6. The Falsifiable Criterion586 words · 3 min
7. 7. Conclusion: The Honest Boundaries654 words · 3 min