no code implementations • 8 Mar 2021 • Christophe Piveteau, David Sutter, Sergey Bravyi, Jay M. Gambetta, Kristan Temme
The Eastin-Knill theorem states that no quantum error correcting code can have a universal set of transversal gates.
Quantum Physics
1 code implementation • 20 Mar 2020 • Sergey Bravyi, Dmitri Maslov
We show that any Clifford operator can be uniquely written in the canonical form $F_1HSF_2$, where $H$ is a layer of Hadamard gates, $S$ is a permutation of qubits, and $F_i$ are parameterized Hadamard-free circuits chosen from suitable subgroups of the Clifford group.
Quantum Physics Emerging Technologies
2 code implementations • 1 Aug 2018 • Sergey Bravyi, Dan Browne, Padraic Calpin, Earl Campbell, David Gosset, Mark Howard
The computational cost of such methods is directly related to the notion of stabilizer rank, which for a pure state $\psi$ is defined to be the smallest integer $\chi$ such that $\psi$ is a superposition of $\chi$ stabilizer states.
Quantum Physics
1 code implementation • 27 Jan 2017 • Sergey Bravyi, Jay M. Gambetta, Antonio Mezzacapo, Kristan Temme
Such encodings eliminate redundant degrees of freedom in a way that preserves a simple structure of the system Hamiltonian enabling quantum simulations with fewer qubits.
Quantum Physics
1 code implementation • 27 Jan 2016 • Sergey Bravyi, David Gosset
The main ingredient of both algorithms is a subroutine for approximating the norm of an n-qubit state which is given as a linear combination of $\chi$ stabilizer states.
Quantum Physics
