Trading Classical and Quantum Computational Resources
Sergey Bravyi, Graeme Smith, John A. Smolin · Physical Review X · 2016
We propose examples of a hybrid quantum-classical simulation where a classical computer assisted by a small quantum processor can efficiently simulate a larger quantum system.First, we consider sparse quantum circuits such that each qubit participates in Oð1Þ two-qubit gates.It is shown that any sparse circuit on n þ k qubits can be simulated by sparse circuits on n qubits and a classical processing that takes time 2 OðkÞ polyðnÞ.Second, we study Pauli-based computation (PBC), where allowed operations are nondestructive eigenvalue measurements of n-qubit Pauli operators.The computation begins by initializing each qubit in the so-called magic state.This model is known to be equivalent to the universal quantum computer.We show that any PBC on n þ k qubits can be simulated by PBCs on n qubits and a classical processing that takes time 2 OðkÞ polyðnÞ.Finally, we propose a purely classical algorithm that can simulate a PBC on n qubits in a time 2 αn polyðnÞ, where α ≈ 0.94.This improves upon the brute-force simulation method, which takes time 2 n polyðnÞ.Our algorithm exploits the fact that n-fold tensor products of magic states admit a low-rank decomposition into n-qubit stabilizer states.