Quantum Phase Estimation by Compressed Sensing
Bibliographic record
Abstract
As a signal recovery algorithm, compressed sensing is particularly effective when the data has low complexity and samples are scarce, which aligns natually with the task of quantum phase estimation (QPE) on early fault-tolerant quantum computers. In this work, we present a new Heisenberg-limited, robust QPE algorithm based on compressed sensing, which requires only sparse and discrete sampling of times. Specifically, given multiple copies of a suitable initial state and queries to a specific unitary matrix, our algorithm can recover the phase with a total runtime of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow class="MJX-TeXAtom-ORD"><mml:mi class="MJX-tex-caligraphic" mathvariant="script">O</mml:mi></mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:msup><mml:mi>&#x03F5;</mml:mi><mml:mrow class="MJX-TeXAtom-ORD"><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup><mml:mtext>poly</mml:mtext><mml:mi>log</mml:mi><mml:mo>&#x2061;</mml:mo><mml:mo stretchy="false">(</mml:mo><mml:msup><mml:mi>&#x03F5;</mml:mi><mml:mrow class="MJX-TeXAtom-ORD"><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup><mml:mo stretchy="false">)</mml:mo><mml:mo stretchy="false">)</mml:mo></mml:math>, where <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>&#x03F5;</mml:mi></mml:math> is the desired accuracy. Additionally, the maximum runtime satisfies <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>T</mml:mi><mml:mrow class="MJX-TeXAtom-ORD"><mml:mo movablelimits="true" form="prefix">max</mml:mo></mml:mrow></mml:msub><mml:mi>&#x03F5;</mml:mi><mml:mo>&#x226A;</mml:mo><mml:mi>&#x03C0;</mml:mi></mml:math>, making it comparable to state-of-the-art algorithms. Furthermore, our result resolves the basis mismatch problem in certain cases by introducing an additional parameter to the traditional compressed sensing framework.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.001 |
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; a candidate call from one teacher head, not a consensus.
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".