CLinalg: C++ Linear-algebra-based simulator

Proposed as a faster alternative to PyLinalg, CLinalg is a Linear-algebra simulator written in C++, with a python (pybind11) interface.

The quantum state is stored as a complex valued vector of length \(2^{N}\), with each element being the complex amplitude of the particular state:

\[\vert\psi\rangle = \sum_{i=0}^{2^{N}}a_{i}|i\rangle\]

where \(|i\rangle\) represents a computational basis state.

Quantum gates are manipulated as complex valued matrices. Applying a gate consists in selecting the groups of \(2^{arity}\) amplitudes in the state vector, and doing a dot product of each group with the matrix representing the gate.

Miscellanous remarks about the simulator:

• it accepts any gate, of any arity.

• it works with the entire amplitude vector. Any information is available.

• it is memory and run-time exponential in the number of qubits. This implies a hard simulation limit at around 20-30 qubits, depending on your RAM.