Variational quantum eigensolver with fewer qubits

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 × 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.

Collective optimization for variational quantum eigensolvers

“…We have applied the unitary coupled cluster ansatz for quantum chemistry problem, and only consider a small number of variational parameters. For many quantum chemistry/many-body problems, more variational parameters are required and also other wavefunction ansatzes may be more suitable [29]. The snake algorithm can be studied for such high dimensional optimization problem.…”

“…Optimization methods for updating parameters θ in general can be categorized as gradient free [19,23], such as Nelder-Mead method, and gradient descent [18,27,29]. Gradient descent methods update parameters using information of gradients.…”

“…Such an approach is well suited for near-term quantum processor, and receives lots of attention in recent years [28]. Among them, variational quantum eigensolver (VQE) aims to solve eigenvalues and eigenstates for quantum systems [11,13,18,19,29]. The power of representing exponentially large wavefunction on quantum processors and effective hybrid quantum-classical optimization of VQE enhances the ability to solve hard quantum problems.…”

Yao.jl: Extensible, Efficient Framework for Quantum Algorithm Design

“…• Solve ground state of a 6 × 6 lattice spin model with a tensor network inspired quantum circuit on GPU [28].…”

“…The tensor network inspired quantum circuits described in [28,66] allow the study of large systems with a reduced number of qubits. For example, one can solve the ground state of a 6 × 6 frustrated Heisenberg lattice model with only 12 qubits.…”