Stabilizer extent is not multiplicative
| Autor: | Frank Vallentin, Arne Heimendahl, Felipe Montealegre-Mora, David Gross |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Quantum Physics
Physics and Astronomy (miscellaneous) Open problem Dimension (graph theory) Multiplicative function FOS: Physical sciences State (functional analysis) 16. Peace & justice 01 natural sciences Atomic and Molecular Physics and Optics lcsh:QC1-999 010305 fluids & plasmas Superposition principle Tensor product Cover (topology) Optimization and Control (math.OC) Product (mathematics) 0103 physical sciences FOS: Mathematics Applied mathematics Quantum Physics (quant-ph) 010306 general physics Mathematics - Optimization and Control lcsh:Physics Mathematics |
| Zdroj: | Quantum, Vol 5, p 400 (2021) |
| Popis: | The Gottesman-Knill theorem states that a Clifford circuit acting on stabilizer states can be simulated efficiently on a classical computer. Recently, this result has been generalized to cover inputs that are close to a coherent superposition of logarithmically many stabilizer states. The runtime of the classical simulation is governed by the stabilizer extent, which roughly measures how many stabilizer states are needed to approximate the state. An important open problem is to decide whether the extent is multiplicative under tensor products. An affirmative answer would yield an efficient algorithm for computing the extent of product inputs, while a negative result implies the existence of more efficient classical algorithms for simulating largescale quantum circuits. Here, we answer this question in the negative. Our result follows from very general properties of the set of stabilizer states, such as having a size that scales subexponentially in the dimension, and can thus be readily adapted to similar constructions for other resource theories. 15 pages, 1 figure |
| Databáze: | OpenAIRE |
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