Quantum Chemistry Breakthrough: TCAVQITE Method Promises Accurate Results, Overcomes Hardware Limitations

Quantum chemistry, which deals with the electronic structure problem, faces significant challenges due to the exponential scaling of the Schrödinger equation with system size. While quantum computers are believed to be well-suited for simulating quantum systems, noise and qubit requirements limit their practical use. However, Variational Quantum Algorithms (VQAs) can reduce quantum circuit depth by offloading non-quantum calculations to a conventional computer. Researchers have combined the Transcorrelated (TC) method with the Adaptive Variational Quantum Imaginary Time Evolution algorithm (AVQITE) to create the TCAVQITE method. This approach yields compact, noise-resilient, and easy-to-optimize quantum circuits, potentially overcoming current quantum hardware limitations.

What is the Challenge at the Heart of Quantum Chemistry?

Quantum chemistry is a field that deals with the electronic structure problem, which is encapsulated in the Schrödinger equation. This problem scales exponentially with system size, making it a significant challenge. There are numerous computational approaches to tackle this challenge, ranging from approximate mean-field theories like Hartree-Fock (HF) to more accurate but costly methods like coupled cluster (CC), density matrix renormalization group (DMRG), and quantum Monte Carlo (QMC) methods. There are also exact but exponentially-scaling full configuration interaction (FCI) and exact diagonalization (ED) methods.

In recent years, attempts have been made to circumvent the unfavorable scaling of highly accurate quantum chemistry using quantum computers. Quantum hardware is believed to be particularly well suited for simulating quantum systems like molecules and may enable a significant computational speedup. However, given the existence of conventional numerical methods that have been refined over decades, it is still uncertain if quantum algorithms can provide a genuine quantum advantage over established techniques.

Unfortunately, noise severely limits practicable circuit depths on current and near-term quantum processors. Furthermore, the number of qubits needed to encode quantum chemistry on quantum hardware is proportional to the basis set size or the number of orbitals in the case of an active space approach. Thus, the achievable accuracy on quantum hardware is severely limited as either small, often minimal basis sets have to be used, or calculations must be done with very small active spaces to fit the problem on current quantum hardware.

How Can Quantum Computers Overcome These Challenges?

Despite these constraints, quantum hardware may in the future outperform conventional computation in specialized instances such as modeling highly correlated systems. Various algorithms have been devised to advance toward practical quantum advantage in the current noisy intermediate-scale quantum (NISQ) regime. Most of these NISQ algorithms are variational, i.e., based on the variational theorem. Variational quantum algorithms (VQAs) can significantly reduce quantum circuit depth by offloading calculations that do not strictly need quantum properties to a conventional computer.

This idea follows naturally from trying to use the quantum computer as little as possible. VQAs are heuristic and rely on an ansatz circuit, which is optimized following some scheme. A considerable drawback of VQAs is that many measurements are needed for this optimization procedure, a factor that may limit or remove the chances for practical quantum advantage. Despite this drawback, for reasons related to the limitations of current hardware, VQAs are by far the most investigated type of quantum algorithm to date.

What are the Variations and Additions to VQAs?

A myriad variations of and additions to these VQAs have been made to improve them in search of practical quantum advantage. These include reducing circuit depth by gradually building the ansatz circuit to be only as deep as needed, reducing qubit requirements by similarity transforms, or post-processing. Among these additions, explicitly correlated methods like the transcorrelated (TC) method make it possible to obtain more accurate results with smaller basis sets by incorporating the problematic electronic cusp condition into the Hamiltonian.

The TC approach also has the added benefit of providing a more compact ground state wavefunctions. A consequence of this compactness is that the ground state of the TC Hamiltonian is easier to prepare with shallower quantum circuits. Explicitly correlated and TC-based approaches have also recently been applied to increase the accuracy of quantum chemistry calculations on quantum hardware.

How Can Variants of VQAs be Combined?

Many variants of and additions to VQAs can be combined, leading to composite methods that may perform better. For the TC method, the compactness of the ground state wavefunction gives merit to combining the TC method with adaptive algorithms. Inspired by these possibilities, the researchers present in this work a combination of Gomes et al.’s Adaptive variational quantum imaginary time evolution algorithm (AVQITE) with the TC method.

The capability and strength of the resulting algorithm, Transcorrelated adaptive variational quantum imaginary time evolution (TCAVQITE), is then evaluated through simulations. The combined TCAVQITE method is used to calculate ground state energies across the potential energy surfaces of H4, LiH, and H2O. In particular, H4 is a notoriously difficult case where unitary coupled cluster theory, including singles and doubles excitations, fails to provide accurate results. Adding TC yields energies close to the complete basis set (CBS) limit while reducing the number of necessary operators, and thus circuit depth, in the adaptive ansätze.

What are the Benefits of the TCAVQITE Method?

The reduced circuit depth furthermore makes the algorithm more noise-resilient and accelerates convergence. The study demonstrates that combining the TC method with adaptive ansätze yields compact, noise-resilient, and easy-to-optimize quantum circuits that yield accurate quantum chemistry results close to the CBS limit. This approach could potentially overcome the limitations of current quantum hardware and provide a practical quantum advantage in the field of quantum chemistry.