Quantum Advantage from Measurement-Induced Entanglement in Random Shallow Circuits
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Bibliographic record
Abstract
We study random constant-depth quantum circuits in a two-dimensional (2D) architecture. While these circuits only produce entanglement between nearby qubits on the lattice, long-range entanglement can be generated by measuring a subset of the qubits of the output state. It is conjectured that this (MIE) proliferates when the circuit depth is at least a constant critical value <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <a:msup> <a:mi>d</a:mi> <a:mo>∗</a:mo> </a:msup> </a:math> . For circuits composed of Haar-random two-qubit gates, it is also believed that this coincides with a in the classical hardness of sampling from the output distribution. Here, we provide evidence for a quantum advantage phase transition in the setting of random circuits. Our work extends the scope of recent separations between the computational power of constant-depth quantum and classical circuits, demonstrating that this kind of advantage is present in canonical random circuit sampling tasks. In particular, we show that in any architecture of random shallow Clifford circuits, the presence of long-range MIE gives rise to an unconditional quantum advantage. In contrast, any depth- <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <d:mi>d</d:mi> </d:math> 2D quantum circuit that satisfies a short-range MIE property can be classically simulated efficiently and with depth <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <g:mi>O</g:mi> <g:mo stretchy="false">(</g:mo> <g:mi>d</g:mi> <g:mo stretchy="false">)</g:mo> </g:math> . Finally, we introduce a 2D depth- <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <l:mn>2</l:mn> </l:math> “coarse-grained” circuit architecture, composed of random Clifford gates acting on <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <o:mi>O</o:mi> <o:mo stretchy="false">(</o:mo> <o:mi>log</o:mi> <o:mo></o:mo> <o:mo stretchy="false">(</o:mo> <o:mi>n</o:mi> <o:mo stretchy="false">)</o:mo> <o:mo stretchy="false">)</o:mo> </o:math> qubits, for which we prove the existence of long-range MIE and establish an unconditional quantum advantage.
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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) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.002 | 0.001 |
| 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