#Clifford group quantum error correction full
#Clifford group quantum error correction code
#Clifford group quantum error correction simulator

Answer to 'how many n-qubit stabilizer states are there?'. Https:///generating-random-numbers-using-c-standard-library-the-problems/ https:///generating-random-numbers-using-c-standard-library-the-problems/, 2020. 'generating random numbers using c++ standard library: the problems'. 'response times: The 3 important limits'.

#Clifford group quantum error correction code

Surface code quantum computing by lattice surgery. Clare Horsman, Austin G Fowler, Simon Devitt, and Rodney Van Meter. Hudson’s theorem for finite-dimensional quantum systems. Stabilizer codes and quantum error correction.

Informal private conversations about simulation bottlenecks, 2021. Craig Gidney, Austin Fowler, and Michael Newman. Efficient magic state factories with a catalyzed $|ccz angle$ to $2|t angle $ transformation. Surface codes: Towards practical large-scale quantum computation. Qiskit: An open-source framework for quantum computing. Optimization of the surface code design for majorana-based qubits. Rui Chao, Michael E Beverland, Nicolas Delfosse, and Jeongwan Haah. Efficient classical simulation of clifford circuits with nonstabilizer input states. Simulation of quantum circuits by low-rank stabilizer decompositions. Sergey Bravyi, Dan Browne, Padraic Calpin, Earl Campbell, David Gosset, and Mark Howard. Hadamard-free circuits expose the structure of the clifford group. Operator quantum error-correcting subsystems for self-correcting quantum memories. Fast simulation of stabilizer circuits using a graph-state representation. 'a new openqasm for a new era of dynamic circuits'. Thomas Alexander, Lev Bishop, Andrew Cross, Jay Gambetta, Ali Javadi-Abhari, Blake Johnson, and John Smolin. Improved simulation of stabilizer circuits. Further samples are collected in bulk by using that sample as a reference for batches of Pauli frames propagating through the circuit. Third, Stim only uses expensive stabilizer tableau simulation to create an initial reference sample. Second, Stim improves the constant factors of the algorithm by using a cache-friendly data layout and 256 bit wide SIMD instructions. First, Stim improves the asymptotic complexity of deterministic measurement from quadratic to linear by tracking the $inverse$ of the circuit's stabilizer tableau. Stim uses a stabilizer tableau representation, similar to Aaronson and Gottesman's CHP simulator, but with three main improvements.

#Clifford group quantum error correction full

With no foreknowledge, Stim can analyze a distance 100 surface code circuit (20 thousand qubits, 8 million gates, 1 million measurements) in 15 seconds and then begin sampling full circuit shots at a rate of 1 kHz. The paper explains how Stim works and compares it to existing tools.

#Clifford group quantum error correction simulator

This paper presents “Stim', a fast simulator for quantum stabilizer circuits.