# Improved upper bounds on the stabilizer rank of magic states

@article{Qassim2021ImprovedUB, title={Improved upper bounds on the stabilizer rank of magic states}, author={Hammam Qassim and Hakop Pashayan and David Gosset}, journal={Quantum}, year={2021}, volume={5}, pages={606} }

<jats:p>In this work we improve the runtime of recent classical algorithms for strong simulation of quantum circuits composed of Clifford and T gates. The improvement is obtained by establishing a new upper bound on the stabilizer rank of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>m</mml:mi></mml:math> copies of the magic state <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow class="MJX-TeXAtom-ORD"><mml:mo stretchy="false">|</mml:mo></mml:mrow><mml:mi>T…

## 11 Citations

### Lower Bounds on Stabilizer Rank

- MathematicsElectron. Colloquium Comput. Complex.
- 2021

The stabilizer rank of a quantum state ψ is the minimal r such that |ψ〉 = ∑j=1 cj ∣ ∣ so that ψ ≥ 1 and r ≥ 1.

### Simulating quantum circuits with ZX-calculus reduced stabiliser decompositions

- Computer ScienceQuantum Science and Technology
- 2022

We introduce an enhanced technique for strong classical simulation of quantum circuits which combines the ‘sum-of-stabilisers’ method with an automated simplification strategy based on the…

### Classical Simulation of Quantum Circuits with Partial and Graphical Stabiliser Decompositions

- Computer ScienceTQC
- 2022

This work finds a new technique of partial stabiliser decompositions that allow us to trade magic states for stabiliser terms, and manages to reliably simulate 50-qubit 1400 T-count hidden shift circuits in a couple of minutes on a consumer laptop.

### Quantum circuit compilation and hybrid computation using Pauli-based computation

- Physics, Computer Science
- 2022

Practical ways of implementing PBC as adaptive quantum circuits, and code to do the required classical side-processing are proposed, and the practical advantage of PBC techniques for circuit compilation and hybrid computation is demonstrated.

### How to Simulate Quantum Measurement without Computing Marginals.

- Computer SciencePhysical review letters
- 2022

Algorithms for classically simulating measurement of an n-qubit quantum state in the standard basis, that is, sampling a bit string from the probability distribution determined by the Born rule are described and analyzed.

### Magic hinders quantum certification

- Computer Science
- 2022

The resource theory of magic quantifies the hardness of quantum certiﬁcation protocols, showing that the resources needed to certify the quality of the application of a given unitary U are governed by the magic in the Choi state associated with U, which is shown to possess a profound connection with out-of-time order correlators.

### Faster Born probability estimation via gate merging and frame optimisation

- Computer ScienceQuantum
- 2022

Two classical sub-routines are proposed: circuit gate merging and frame optimisation, which optimise the circuit representation to reduce the sampling overhead and show that the runtimes of both sub- routines scale polynomially in circuit size and gate depth.

### New techniques for bounding stabilizer rank

- Mathematics, Computer ScienceQuantum
- 2022

A number-theoretic theorem of Moulton is refined to exhibit an explicit sequence of product states with exponential stabilizer rank but constant approximate stabilizers rank, and alternate (and simplified) proofs of the best-known asymptotic lower bounds on stabilizerRank and approximate stabilizerrank are provided.

### Magic-state resource theory for the ground state of the transverse-field Ising model

- PhysicsPhysical Review A
- 2022

Ground states of quantum many-body systems are both entangled and possess a kind of quantum complexity as their preparation requires universal resources that go beyond the Cliﬀord group and…

### Efficient classical simulation of cluster state quantum circuits with alternative inputs

- Economics
- 2022

Sahar Atallah , Michael Garn 1,∗, Sania Jevtic , Yukuan Tao 3,†, and Shashank Virmani1,‡ Department of Mathematics, Brunel University London, Kingston Ln, Uxbridge, UB8 3PH, United Kingdom, 2…

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