# Semiclassical formulation of the Gottesman-Knill theorem and universal quantum computation

@article{Kocia2017SemiclassicalFO, title={Semiclassical formulation of the Gottesman-Knill theorem and universal quantum computation}, author={Lucas Kocia and Yifei Huang and Peter Love}, journal={Physical Review A}, year={2017}, volume={96} }

We give a path integral formulation of the time evolution of qudits of odd dimension. This allows us to consider semiclassical evolution of discrete systems in terms of an expansion of the propagator in powers of $\hbar$. The largest power of $\hbar$ required to describe the evolution is a traditional measure of classicality. We show that the action of the Clifford operators on stabilizer states can be fully described by a single contribution of a path integral truncated at order $\hbar^0$ and… CONTINUE READING

#### Citations

##### Publications citing this paper.

SHOWING 1-6 OF 6 CITATIONS

## Stationary Phase Method in Discrete Wigner Functions and Classical Simulation of Quantum Circuits

VIEW 10 EXCERPTS

CITES METHODS & BACKGROUND

## Discrete Wigner Function Derivation of the Aaronson-Gottesman Tableau Algorithm

VIEW 8 EXCERPTS

CITES BACKGROUND & METHODS

## Discrete Wigner formalism for qubits and noncontextuality of Clifford gates on qubit stabilizer states

VIEW 10 EXCERPTS

CITES BACKGROUND, METHODS & RESULTS

## Measurement contextuality and Planck’s constant

VIEW 4 EXCERPTS

CITES BACKGROUND

#### References

##### Publications referenced by this paper.

SHOWING 1-10 OF 40 REFERENCES

## The Weyl representation in classical and quantum mechanics

VIEW 7 EXCERPTS

HIGHLY INFLUENTIAL

## The Heisenberg representation of quantum computers

VIEW 2 EXCERPTS

## Quantum circuit dynamics via path integrals: Is there a classical action for discrete-time paths?

VIEW 4 EXCERPTS

HIGHLY INFLUENTIAL

## The cat maps: quantum mechanics and classical motion

VIEW 16 EXCERPTS

HIGHLY INFLUENTIAL

## Discrete phase space based on finite fields

VIEW 2 EXCERPTS

## Improved Simulation of Stabilizer Circuits

VIEW 4 EXCERPTS

HIGHLY INFLUENTIAL

## Classicality in discrete Wigner functions

VIEW 2 EXCERPTS