Distributed Simulation of Statevectors and Density Matrices

Tyson Jones, Balint Koczor, Simon C. Benjamin

• Department of Materials, University of Oxford
• Quantum Motion Technologies Ltd

This repository contains C++ implementations of the multithreaded, distributed algorithms presented in this manuscript, and unit tests using Catch2. If the code is useful to you, feel free to cite

@misc{jones2023distributed,
      title={Distributed Simulation of Statevectors and Density Matrices}, 
      author={Tyson Jones and Bálint Koczor and Simon C. Benjamin},
      year={2023},
      eprint={2311.01512},
      archivePrefix={arXiv},
      primaryClass={quant-ph}
}

Types

The below API makes use of the following custom types defined in types.hpp, wherein you can vary their precision.

Type	Use	Default
Real	A real scalar	double
Nat	A natural scalar	unsigned int
Index	A state index	long long unsigned int
Amp	A complex scalar	std::complex<Real>

We also define arrays and matrices of these types, such as NatArray, which are merely eye-candy for std::vector<Nat>.

API

Before calling any of the below functions, you should initialise MPI with comm_init(), and before exiting, finalise with comm_end().

Instantiate a quantum state via:

StateVector psi = StateVector(numQubits);
DensityMatrix rho = DensityMatrix(numQubits);

Statevectors can be passed to the below unitary functions, prefixed with distributed_statevector_.

• oneTargGate(StateVector psi, Nat target, AmpMatrix gate)

• manyCtrlOneTargGate(StateVector psi, NatArray controls, Nat target, AmpMatrix gate)

• swapGate(StateVector psi, Nat qb1, Nat qb2)

• manyTargGate(StateVector psi, NatArray targets, AmpMatrix gate)

• pauliTensor(StateVector psi, NatArray targets, NatArray paulis)

• pauliGadget(StateVector psi, NatArray targets, NatArray paulis, Real theta)

• phaseGadget(StateVector psi, NatArray targets, Real theta)

Density matrices can be passed to the below functions, prefixed with distributed_densitymatrix_.

• manyTargGate(DensityMatrix rho, NatArray targets, AmpMatrix gate)

• swapGate(DensityMatrix rho, Nat qb1, Nat qb2)

• pauliTensor(DensityMatrix rho, NatArray targets, NatArray paulis)

• pauliGadget(DensityMatrix rho, NatArray targets, NatArray paulis, Real theta)

• phaseGadget(DensityMatrix rho, NatArray targets, Real theta)

• phaseGadget(DensityMatrix rho, NatArray targets, Real theta)

• oneQubitDephasing(DensityMatrix rho, Nat qb, Real prob)

• twoQubitDephasing(DensityMatrix rho, Nat qb1, Nat qb2, Real prob)

• oneQubitDepolarising(DensityMatrix rho, Nat qb, Real prob)

• twoQubitDepolarising(DensityMatrix rho, Nat qb1, Nat qb2, Real prob)

• damping(DensityMatrix rho, Nat qb, Real prob)

• expecPauliString(DensityMatrix rho, RealArray coeffs, NatArray allPaulis)

• partialTrace(DensityMatrix inRho, NatArray targets)

View the definition of these functions in the src folder.

See an example in main.cpp.

Compiling

To compile both main.cpp and the unit tests, simply call

source ./compile

Additionally, set the number of threads (per node) via

export OMP_NUM_THREADS=24

and launch the executables between (e.g.) 16 nodes via

mpirun -np 16 ./main

mpirun -np 16 ./test

You must use a power-of-2 number of nodes.

License

This repository is licensed under the terms of the MIT license.