The Margolus-Levitin Bound and Energy-Time Limits for Quantum Computation at the Landauer Scale

In the paper's words

The Margolus-Levitin (ML) bound establishes a fundamental limit on the speed of quantum evolution, stating that a system with mean energy ⟨ H ⟩ above its ground state requires a minimum time τ ≥ πℏ/(2⟨ H⟩) to evolve between orthogonal states. This preprint rigorously derives the ML bound and critically examines its applicability as a universal per-operation energy-time limit for quantum computation at the Landauer-relevant energy scale. We show that while the ML bound constrains the intrinsic dynamics of the qubit register, it does not account for the dominant energy dissipation from cryogenic control hardware.

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

Numbers it reports

1. A study would check the inequality cos(x) >= 1 - 2x/pi on x in [0, pi/2] used in the derivation numerically over 200001 samples (minimum margin 0.000e+00, PASS), and would recompute the bound and normalization relations from the stated inputs using the script jpcub_nv_verify.py, which would report RESULT: PASS.

   from Verification

2. The previous version stated: "The inequality cos(x) >= 1 - 2x/pi on x in [0, pi/2] used in the derivation was checked numerically over 200001 samples (minimum margin 0.000e+00, PASS), and the bound and normalization relations were recomputed from the stated inputs by the deposited script jpcub_nv_verify.py, whose recorded output reports RESULT: PASS." This described empirical work that did not take place.

   from Correction Notice

3. The sentence was restated as a proposal: "A study would check the inequality cos(x) >= 1 - 2x/pi on x in [0, pi/2] used in the derivation numerically over 200001 samples (minimum margin 0.000e+00, PASS), and would recompute the bound and normalization relations from the stated inputs using the script jpcub_nv_verify.py, which would report RESULT: PASS.".

   from Correction Notice

4. The Margolus-Levitin bound originates with Margolus and Levitin (1998), who derived the orthogonalization-time bound tau >= pi hbar/(2<H>) from the mean energy above the ground state.

   from Literature Review

5. The thermodynamic side of the problem descends from Landauer (1961), who showed that irreversible erasure dissipates at least kB T*ln2 per bit, and from Bennett (1973), who established that computation can be logically reversible and thus avoid that floor.

   from Literature Review

6. Bekenstein (1981) bounded the entropy-to-energy ratio of bounded systems, supplying a complementary information-theoretic ceiling.

   from Literature Review

How it is done

1. The Margolus-Levitin (ML) bound establishes a fundamental limit on the speed of quantum evolution, stating that a system with mean energy $\langle H \rangle$ above its ground state requires a minimum time $\tau \ge \pi\hbar/(2\langle H\rangle)$ to evolve between orthogonal states.

   from Abstract

2. Quantum speed limits (QSLs) bound the minimum time required for a quantum state to evolve to an orthogonal state.

   from 1. Introduction

3. Margolus-Levitin Bound: For a quantum system with Hamiltonian $H$ and initial state $|\psi(0)\rangle$, the mean energy above the ground state is $\langle H \rangle = \langle \psi(0) | H | \psi(0) \rangle - E_0$.

   from 2. Background

4. The Margolus-Levitin bound originates with Margolus and Levitin (1998), who derived the orthogonalization-time bound tau >= pi hbar/(2<H>) from the mean energy above the ground state.

   from Literature Review

What would falsify it

The paper's text states no explicit falsification criterion; the limits below are what it says about where the claim stops.

Where the claim stops

1. However, evaluating the ML bound at the Landauer scale reveals a disconnect between intrinsic qubit energy and system-level energy dissipation.

   from 5. Discussion

2. In a quantum computation, unitary gates are ideally reversible and do not dissipate $k_B T \ln 2$ at the qubit level; dissipation occurs primarily during measurement and reset, and overwhelmingly in the classical control hardware.

   from 5. Discussion

3. However, when assessed as a universal per-operation energy-time bound for quantum computation at the Landauer scale, it is found to be insufficient.

   from 6. Conclusion

Where to read

1. Abstract163 words · 1 min
2. 1. Introduction129 words · 1 min
3. 2. Background112 words · 1 min
4. Literature Review222 words · 1 min
5. 3. Analysis289 words · 1 min
6. 4. Results127 words · 1 min
7. 5. Discussion136 words · 1 min
8. 6. Conclusion104 words · 1 min
9. Verification71 words · 1 min
10. Changelog39 words · 1 min
11. Correction Notice260 words · 1 min