We present a quantum information-inspired ansatz for the variational quantum eigensolver and demonstrate its efficacy in calculating ground-state energies of atomic systems. Instead of adopting a heuristic approach, we start with an approximate multiqubit target state and utilize two quantum information-theoretic quantities, i.e., von Neumann entropy and quantum mutual information, to construct our ansatz. The quantum information encoded in the target state helps us design unique blocks and identify qubit pairs that exhibit maximal quantum correlations within the multi-qubit system, thereby enabling us to deterministically place two-qubit entanglers in the suitably constructed parametrized quantum circuit. We find that our approach offers the advantage of reduced circuit depth compared to the physics-inspired unitary coupled-cluster (UCC) ansatz, while yielding accurate results. To test the performance of our ansatz, we apply it to compute ground-state energies of atomic systems in the relativistic regime. Our results show that for up to 12-qubits (12-spinorbitals) noiseless calculations, our ansatz yields energies within chemical accuracy ( ∼ 1.6 mhartree) relative to the complete active space configuration interaction values, while utilizing only a few blocks that contain in the best case 98 % fewer two-qubit gates when compared with the UCC ansatz in the singles and doubles approximation.
We present a quantum information-inspired ansatz for the variational quantum eigensolver and demonstrate its efficacy in calculating ground-state energies of atomic systems. Instead of adopting a heuristic approach, we start with an approximate multiqubit target state and utilize two quantum information-theoretic quantities, i.e., von Neumann entropy and quantum mutual information, to construct our ansatz. The quantum information encoded in the target state helps us design unique blocks and identify qubit pairs that exhibit maximal quantum correlations within the multi-qubit system, thereby enabling us to deterministically place two-qubit entanglers in the suitably constructed parametrized quantum circuit. We find that our approach offers the advantage of reduced circuit depth compared to the physics-inspired unitary coupled-cluster (UCC) ansatz, while yielding accurate results. To test the performance of our ansatz, we apply it to compute ground-state energies of atomic systems in the relativistic regime. Our results show that for up to 12-qubits (12-spinorbitals) noiseless calculations, our ansatz yields energies within chemical accuracy ( ∼ 1.6 mhartree) relative to the complete active space configuration interaction values, while utilizing only a few blocks that contain in the best case 98 % fewer two-qubit gates when compared with the UCC ansatz in the singles and doubles approximation.
Abstract The variational quantum eigensolver (VQE) algorithm combines the ability of quantum computers to efficiently compute expectation values with a classical optimization routine in order to approximate ground state energies of quantum systems. In this paper, we study the application of VQE to the simulation of molecular energies using the unitary coupled cluster (UCC) ansatz. We introduce new strategies to reduce the circuit depth for the implementation of UCC and improve the optimization of the wavefunction based on efficient classical approximations of the cluster amplitudes. Additionally, we propose an analytical method to compute the energy gradient that reduces the sampling cost for gradient estimation by several orders of magnitude compared to numerical gradients. We illustrate our methodology with numerical simulations for a system of four hydrogen atoms that exhibit strong correlation and show that the circuit depth of VQE using a UCC ansatz can be reduced without introducing significant loss of accuracy in the final wavefunctions and energies.
High Resolution Image Download MS PowerPoint Slide Quantum computers have the potential to efficiently solve the electronic structure problem but are currently limited by noise and shallow circuits. We present an enhanced Variational Quantum Eigensolver (VQE) ansatz based on the Qubit Coupled Cluster (QCC) approach that requires optimization of only n parameters, where n is the number of Pauli string generators, rather than the typical n + 2 m parameters, where m is the number of qubits. We evaluate the ground state energies and molecular dissociation curves of strongly correlated molecules, namely O 3 and Li 4, using active spaces of varying sizes in conjunction with our enhanced QCC ansatz, Unitary Coupled Cluster Single–Double (UCCSD) ansatz, and the classical Coupled Cluster Singles and Doubles (CCSD) method. Compared to UCCSD, our approach significantly reduces the number of parameters while maintaining high accuracy. Numerical simulations demonstrate the effectiveness of our approach, and experiments on superconducting and trapped-ion quantum computers showcase its practicality on real hardware. By eliminating the need for symmetry-restoring gates and reducing the number of parameters, our enhanced QCC ansatz enables accurate quantum chemistry calculations on near-term quantum devices for strongly correlated systems.
Hardware-efficient empirical variational ansätze for Variational Quantum Eigensolver (VQE) simulations of quantum chemistry often lack a direct connection to classical quantum chemistry methods. In this work, we propose a method to bridge this gap by introducing a novel approach to constructing a starting point for variational quantum circuits, leveraging quantum mutual information from classical quantum chemistry states to design simple yet effective heuristic ansätze with a topology reflecting the molecular system’s correlations. As a first step, we make use of quantum chemistry calculations, such as Mo̷ller–Plesset (MP2) perturbation theory, to initially provide approximate Natural Orbitals, which have been shown to be the best candidate one-electron basis for developing compact empirical wave functions. 1 Second, we evaluate the quantum mutual information matrix, which provides insights about the main correlations between qubits of the quantum circuit, and enables a direct design of entangling blocks for the circuit. The resulting ansatz is then used with a VQE to obtain a short-depth variational ground state of the electronic Hamiltonian. To validate our approach, we perform a comprehensive statistical analysis through simulations of various molecular systems ( H 2, LiH, H 2 O ) and apply it to the more complex NH 3 molecule. The reported results demonstrate that the proposed methodology gives rise to highly effective ansätze, outperforming the standard empirical ladder-entangler ansatz. Overall, our approach can be used as an effective state preparation, providing a promising route for designing efficient variational quantum circuits for large molecular systems.
The variational quantum eigensolver (VQE) is a method of choice to solve the electronic structure problem for molecules on near-term gate-based quantum computers.However, the circuit depth is expected to grow significantly with the problem size.Increased depth can both degrade the accuracy of the results and reduce trainability.In this work, we propose an approach to reduce ansatz circuit depth.Our approach, called "PermVQE," adds an additional optimization loop to the VQE that permutes qubits in order to solve for the qubit Hamiltonian that maximally localizes correlations in the ground state.The choice of permutations is based on mutual information, which is a measure of interaction between electrons and/or holes in spin-orbitals.Encoding strongly entangled spin-orbitals into proximal qubits on a quantum chip naturally reduces the circuit depth needed to prepare the ground state.For representative molecular systems, LiH, H 2 , (H 2 ) 2 , H = 4 , H + 3 , and N 2 , we demonstrate that placing entangled qubits in close proximity leads to shallower depth circuits required to reach a given eigenvalue-eigenvector accuracy.The approach is designed for hardware-efficient ansatz of any qubit connectivity, and examples are demonstrated for linear and twodimensional grid architectures.The main ideas can also be applied to simulate molecules with other ansatz as well as variational quantum algorithms beyond the VQE.In particular, we demonstrate the beneficial effect of qubit permutations to build fermionic-adaptive derivative assembled pseudo-Trotter ansatz on a linear qubit connectivity architecture with nearly a twofold reduction of the number of controlled NOT gates.
Development of resource-friendly quantum algorithms remains highly desirable for noisy intermediate-scale quantum computing. Based on the variational quantum eigensolver (VQE) with unitary coupled-cluster Ansatz, we demonstrate that partitioning of the Hilbert space made possible by the point-group symmetry of the molecular systems greatly reduces the number of variational operators by confining the variational search within a subspace. In addition, we found that instead of including all subterms for each excitation operator, a single-term representation suffices to reach required accuracy for various molecules tested, resulting in an additional shortening of the quantum circuit by a factor of 4–8. With these strategies, VQE calculations on a noise-free quantum simulator achieve energies within a few meVs of those obtained with the full unitary coupled-cluster Ansatz with single and double excitations for the H4-square, H4-chain, and H6-hexagon molecules, while the number of cnot gates, a measure of the quantum-circuit depth, is reduced by a factor of as large as 35. Furthermore, we introduced an efficient “score” parameter to rank the excitation operators, so that the operators causing larger energy reduction can be applied first. Using the H4 square and H4 chain as examples, We demonstrated on noisy quantum simulators that the first few variational operators can bring the energy within the chemical accuracy, while additional operators do not improve the energy since the accumulative noise outweighs the gain from the expansion of the variational Ansatz.
In recent years, the Variational Quantum Eigensolver (VQE) has emerged as one of the most popular algorithms for solving the electronic structure problem on near-term quantum computers. The utility of VQE is often hindered by the limitations of current quantum hardware, including, but not limited to, short qubit coherence times and low gate fidelities. These limitations become particularly pronounced when VQE is used along with deep quantum circuits, such as those required by the ”Unitary Coupled Cluster Singles and Doubles” (UCCSD) ansatz, often resulting in significant errors. To address these issues, we propose a low-depth ansatz based on parallelized Givens rotations, which can recover substantial correlation energy while drastically reducing circuit depth and two-qubit gate counts for an arbitrary active space (AS). Also, considering the current hardware architectures with low qubit counts, we introduce a systematic way to select molecular orbitals to define active spaces (ASs) that retain significant electron correlation. We validate our approach by computing bond dissociation profiles of water and strongly correlated systems, such as molecular nitrogen and oxygen, across various ASs. Noiseless simulations using the new ansatz yield ground-state energies comparable to those from the UCCSD ansatz while reducing circuit depth by 50–70%. Moreover, in noisy simulations, our approach achieves energy error rates an order of magnitude lower than that of UCCSD. Considering the efficiency and practical usage of our ansatz, we hope that it becomes a potential choice for performing quantum chemistry calculations on near-term quantum devices.