Abstract
We propose a qubit efficient scheme to study ground state properties of quantum many-body systems on near-term noisy intermediate scale quantum computers. One can obtain a tensor network representation of the ground state using a number of qubits smaller than the physical degrees of freedom. By increasing the qubits number, one can exponentially increase the bond dimension of the tensor network variational ansatz on a quantum computer. Moreover, we construct circuits blocks which respect U(1) and SU(2) symmetries of the physical system and show that they can significantly speed up the training process and alleviate the gradient vanishing problem. To demonstrate the feasibility of the qubit efficient variational quantum eigensolver in a practical setting, we perform first principle classical simulation of differentiable programming of the circuits. Using only $6$ qubits one can obtain the ground state of a $4\times 4$ square lattice frustrated Heisenberg model with fidelity over 97%. Arbitrarily long ranged correlations can also be measured on the same circuit after variational optimization.
Highlights
Studying ground-state properties of quantum many-body systems is a promising native application of quantum computers
Given limited qubit resources and noisy realizations of near-term quantum devices [1,2], a practical approach is to employ the variational quantum eigensolver (VQE) [3,4,5,6,7,8], which runs in a classical quantum hybrid mode
We address these problems by adopting the qubit efficient circuit architecture [29,37] for the variational quantum eigensolver
Summary
Studying ground-state properties of quantum many-body systems is a promising native application of quantum computers. Since the number of required qubits is the same as the problem size in the standard VQE applications, one has to push up the number of controllable qubits way beyond the current technology to convincingly surpass the classical simulation approach in finding the ground states of quantum many-body systems Related approaches such as the quantum approximate optimization algorithm [35] and related field such as quantum machine learning [15,16,36] suffer from the same problem. Codes and pretrained circuit parameters can be found in the Github repository [50]
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