Spontaneous symmetry breaking in a <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>S</mml:mi> <mml:mi>O</mml:mi> <mml:mo>(</mml:mo> <mml:mn>3</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> non-Abelian lattice gauge theory in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>2</mml:mn> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> <mml:mi mathvariant="normal">D</mml:mi> </mml:mrow> </mml:math> with quantum algorithms
Bibliographic record
Abstract
The simulation of various properties of quantum field theories is rapidly becoming a testing ground for demonstrating the prowess of quantum algorithms. Some examples include the preparation of ground states, as well as the investigation of various simple wave packets relevant for scattering phenomena. In this paper, we study the ability of quantum algorithms to prepare ground states in a matter-free non-Abelian <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:mi>S</a:mi> <a:mi>O</a:mi> <a:mo>(</a:mo> <a:mn>3</a:mn> <a:mo>)</a:mo> </a:mrow> </a:math> lattice gauge theory in <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mrow> <b:mn>2</b:mn> <b:mo>+</b:mo> <b:mn>1</b:mn> <b:mi mathvariant="normal">D</b:mi> </b:mrow> </b:math> in a phase where the global charge conjugation symmetry is spontaneously broken. This is challenging for two reasons: the necessity of dealing with a large Hilbert space for gauge theories compared to that of quantum spin models, and the closing of the gap between the two ground states, which becomes exponentially small as a function of the volume. To deal with the large Hilbert space of gauge fields, we demonstrate how the exact imposition of the non-Abelian Gauss law in the rishon representation of the quantum link operator significantly reduces the degrees of freedom. Further, to resolve the gap, we introduce symmetry-guided ansätze in the Gauss-law-resolved basis for trial states as the starting point for the quantum algorithms to prepare the two lowest-energy states. In addition to simulation results for a range of two-dimensional system sizes, we also provide experimental results from the trapped-ion-based quantum hardware, IonQ, when working on systems with four quantum links. The experimental/simulation results derived from our theoretical developments indicate the role of metrics—such as the energy and the infidelity—to assess the obtained results.
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How this classification was reachedexpand
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 | 0.011 | 0.004 |
| Meta-epidemiology (narrow) | 0.003 | 0.005 |
| Meta-epidemiology (broad) | 0.002 | 0.005 |
| Bibliometrics | 0.002 | 0.006 |
| Science and technology studies | 0.004 | 0.005 |
| Scholarly communication | 0.004 | 0.004 |
| Open science | 0.008 | 0.007 |
| Research integrity | 0.004 | 0.008 |
| Insufficient payload (model declined to judge) | 0.046 | 0.008 |
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 itClassification
machine, unvalidatedMachine predicted; both teacher heads agree on what is shown here.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".