Quantum implementation of the unitary coupled cluster for simulating molecular electronic structure

Abstract

In classical computational chemistry, the coupled-cluster ansatz is one of the most commonly used ab initio methods, which is critically limited by its non-unitary nature. The unitary modification as an ideal solution to the problem is, however, extremely inefficient in classical conventional computation. Here, we provide the first experimental evidence that indeed the unitary version of the coupled cluster ansatz can be reliably performed in physical quantum system, a trapped ion system. We perform a simulation on the electronic structure of a molecular ion (HeH + ), where the ground-state energy surface curve is probed, energies of excited-states are studied and the bond-dissociation is simulated non-perturbatively. Our simulation takes advantages from quantum computation to overcome the intrinsic limitations in classical computation and our experimental results indicate that the method is promising for preparing molecular ground-states for quantum simulation.PACS numbers: 03.67. Ac, 31.15.Dv, 37.10.Ty, 42.50.Dv The central problem in quantum chemistry and molecular physics is to determine the electronic structure and the ground-state energy of atoms and molecules by solving the quantum many-body equations, which is generally intractable due to the exponential scaling to the size of the system. Quantum simulation [1][2][3][4][5][6] can provide the solution for such "exponential catastrophe" problem. The key ingredient of quantum molecular simulation consists of (i) ground (excited) -state preparation and (ii) energy estimation of the corresponding state [3,4]. Recently, the assessed costs for the energy estimation for a well-prepared ground-state in quantum computation have been immensely reduced [7][8][9][10][11], indicating that chemistry simulation can be one of the main applications of a quantum computer in near future. However, it is still remaining major obstacle to efficiently and reliably find the molecular ground state, which belongs to the class of extremely hard problems called Quantum Merlin Arthur, the quantum analog of NP-hard problem [12,13]. Recently various theoretical schemes for the ground-state problem have been proposed and proof-of principle experimental demonstrations have been performed including the adiabatic [14][15][16] and algorithmic preparations [17][18][19][20].For the ground-state problem, the developments of conventional quantum chemistry can be adopted to quantum computation. In computational chemistry, it has been the main focus to circumvent the problem by approximating the many-body Schrödinger equation and a series of theoretical and numerical methods have been developed. The coupled-cluster method is one of the most prominent ab initio methods for finding a molecular ground state and it is considered to be the current gold standard [21][22][23][24]. However, the coupled-cluster ansatz is built with non-unitary operation, which leads to drawbacks such as lacking a variational bound on the ground-state energy [22][23][24][25][26]. The unitary version of the coupled-clust...

Collective optimization for variational quantum eigensolvers

“…We now turn to consider Helium hydride cation, which is a more complicated molecular carrying one positive charge. Under STO-3G basis, four qubits are required to describe the Hamiltonian [17]. To capture essential quantum correlation, the UCC ansatz should include a two-particle scattering component [17].…”

“…Under STO-3G basis, four qubits are required to describe the Hamiltonian [17]. To capture essential quantum correlation, the UCC ansatz should include a two-particle scattering component [17]. The Collective optimization with the snake algorithm for molecules at different bond lengths.…”

“…The reference state is |001 . For the above two effective qubit Hamiltonians, we adopt simple unitary coupled cluster ansatz [11,17,19,45,46], which can establish entanglement between different qubits and thus take quantum correlations into account. For H 2 , the unitary operator is U (θ) = exp(−iθσ x 0 σ y 1 ) and the wavefunciton ansatz is U (θ)|01 .…”

“…It promises to solve some outstanding problems with quantum advantages [1][2][3][4][5][6], and is influencing a broad of computational intensive areas, such as quantum simulation [1,[7][8][9] and machine learning [10]. A variational approach for quantum computing sets parameters in a quantum circuit, and learn those parameters through hybrid quantum-classical optimization [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27]. Such an approach is well suited for near-term quantum processor, and receives lots of attention in recent years [28].…”

VanQver: the variational and adiabatically navigated quantum eigensolver

“…Quantum computing, for example, is a promising approach to mitigating this problem [2,3]. There has been a recent increase in the number of experiments simulating quantum systems on quantum devices [3][4][5][6][7][8][9][10][11][12]. The…”