Improved simulation of stabilizer circuits
Why is this work in the frame?
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Machine scores (provisional)
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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.
- Teacher spread
- 0.282 · how far apart the two teachers sit on this one work
- Validation status
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
Abstract
The Gottesman-Knill theorem says that a stabilizer circuit---that is, a quantum circuit consisting solely of controlled-NOT (CNOT), Hadamard, and phase gates---can be simulated efficiently on a classical computer. This paper improves that theorem in several directions. First, by removing the need for Gaussian elimination, we make the simulation algorithm much faster at the cost of a factor of 2 increase in the number of bits needed to represent a state. We have implemented the improved algorithm in a freely available program called CHP (CNOT-Hadamard-phase), which can handle thousands of qubits easily. Second, we show that the problem of simulating stabilizer circuits is complete for the classical complexity class $\ensuremath{\bigoplus}\mathsf{L}$, which means that stabilizer circuits are probably not even universal for classical computation. Third, we give efficient algorithms for computing the inner product between two stabilizer states, putting any $n$-qubit stabilizer circuit into a ``canonical form'' that requires at most $O({n}^{2}∕\mathrm{log}\phantom{\rule{0.2em}{0ex}}n)$ gates, and other useful tasks. Fourth, we extend our simulation algorithm to circuits acting on mixed states, circuits containing a limited number of nonstabilizer gates, and circuits acting on general tensor-product initial states but containing only a limited number of measurements.
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.
The record
- Venue
- Physical Review A
- Topic
- Quantum Computing Algorithms and Architecture
- Field
- Computer Science
- Canadian institutions
- Perimeter Institute
- Funders
- —
- Keywords
- Controlled NOT gateQuantum computerElectronic circuitComputer scienceQuantum gateQubitHadamard transformTensor productAlgorithmQuantum circuitMathematicsQuantumQuantum mechanicsQuantum error correctionPhysicsPure mathematics
- Has abstract in OpenAlex
- yes