Simulating lattice quantum electrodynamics on a quantum computer
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Bibliographic record
Abstract
Abstract U(1) lattice gauge theories (LGTs) offer a way to simulate quantum electrodynamics, one of the three forces unified by the Standard Model of particles physics. Here we provide complete, quantum-gate-by-quantum-gate algorithms to simulate U(1) LGTs on a fault-tolerant quantum computer. We further perform rigorous error analysis in order to derive concrete estimates of the quantum computational resources required for an accurate simulation of U(1) LGTs using a second-order product formula. We show that U(1) LGTs in any spatial dimension can be simulated using <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mover> <mml:mi>O</mml:mi> <mml:mo stretchy="false">˜</mml:mo> </mml:mover> <mml:mo stretchy="false">(</mml:mo> <mml:msup> <mml:mi>T</mml:mi> <mml:mrow> <mml:mfrac> <mml:mn>3</mml:mn> <mml:mn>2</mml:mn> </mml:mfrac> </mml:mrow> </mml:msup> <mml:msup> <mml:mi>N</mml:mi> <mml:mrow> <mml:mfrac> <mml:mn>3</mml:mn> <mml:mn>2</mml:mn> </mml:mfrac> </mml:mrow> </mml:msup> <mml:mi mathvariant="normal">Λ</mml:mi> <mml:msup> <mml:mi>ϵ</mml:mi> <mml:mrow> <mml:mo>−</mml:mo> <mml:mfrac> <mml:mn>1</mml:mn> <mml:mn>2</mml:mn> </mml:mfrac> </mml:mrow> </mml:msup> <mml:mo stretchy="false">)</mml:mo> </mml:math> non-Clifford T gates, where T is the simulation time, N is the number of lattice sites, Λ is the truncation parameter for the bosonic gauge fields, and ε is the simulation error. This work paves the way towards fault-tolerant quantum simulations of physical models closely related to the Standard Model of particle physics.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.002 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it