The existing backend is "Schrodinger"-style, which means it stores the entire wavefunction, runtime is O(2^N M) and space is O(2^N) where N is the number of qubits and M the number of gates. A Feynman path integral backend would sum up all the possible paths from the input to the output through the circuit, making the runtime exponential in the circuit depth, but the memory footprint constant. This may be difficult to implement because of measurements taken midway through the circuit, but would be very helpful for certain circuit types. Furthermore there are likely mixed S-F algorithms which can optimize space/runtime tradeoffs.
The existing backend is "Schrodinger"-style, which means it stores the entire wavefunction, runtime is O(2^N M) and space is O(2^N) where N is the number of qubits and M the number of gates. A Feynman path integral backend would sum up all the possible paths from the input to the output through the circuit, making the runtime exponential in the circuit depth, but the memory footprint constant. This may be difficult to implement because of measurements taken midway through the circuit, but would be very helpful for certain circuit types. Furthermore there are likely mixed S-F algorithms which can optimize space/runtime tradeoffs.