What can we do on a small quantum computer with O(10) qubits?
We propose a variational scheme to study ground state properties of quantum many-body systems on small scale near-term noisy quantum computers. One can obtain a matrix product state (MPS) representation of the variational ground state using a number of qubits smaller than the problem size. By increasing the qubits number, one can exponentially increase the bond dimension of the variational MPS on the quantum computer. To demonstrate the practical feasibility of the proposed scheme, we perform a first-principle classical simulation of differentiable circuit learning. Using only 6 qubits one can obtain the ground state of a 4 x 4 square lattice frustrated Heisenberg model with fidelity over 97%. Arbitrarily long ranged correlations can also be measured on the same circuit after variational optimization. Studying ground state of quantum magnets and quantum chemistry problems in this way will be one of few killer applications of a near-term quantum computer.
Reference: Variational Quantum Eigensolver with Fewer Qubits, Jin-Guo Liu, Yi-Hong Zhang, Yuan Wan, Lei Wang, arXiv: 1902.02663