Stabilizer Configuration Interaction

Quantum Error Correction is essential for fault-tolerant (FT) quantum computation. However, a major hurdle in realizing FT quantum computation is the substantial overhead required to encode information into logical qubits. This resource-intensive process makes it challenging to perform reliable quantum computations, especially with current quantum devices. To address this, we need to explore alternative approaches that can enable reliable computation in the near term.

In this article, we present a framework for designing quantum algorithms tailored for reliable execution on early fault-tolerant quantum computers. Our focus is on approximating the ground states of molecules, a critical problem in chemistry and materials science.

We first develop an efficient classical algorithm to construct approximations of these ground states using stabilizer states - special types of quantum states that are computationally efficient to work with. By testing our algorithm on molecules with up to 36 qubits, we found that our approximations outperformed traditional methods, such as the Hartree-Fock approximation, which is widely used in quantum chemistry. Additionally, we introduced circuit constructions for preparing generalized stabilizer states - a class of states that offer improved approximations in certain cases. While the approximations we construct do not yet meet the accuracy required for many practical applications, they can serve as a valuable starting point for more sophisticated quantum techniques, such as quantum phase estimation and variational quantum eigensolvers.

The next step involves using the stabilizer approximations to construct quantum error detection codes. Specifically, we used codeword stabilized codes to design error detection methods that require minimal resources. These codes enable the preparation of both stabilizer and generalized stabilizer states with higher fidelity using post-selection. Using a simple noise model, we perform noisy simulations and verify the error detection properties of the codes we construct for preparing the states. These simulations suggest that our method can be useful in preparing approximate eigenstates for different molecular systems, albeit with an overhead due to increasing discard rates.

Our work represents a first step toward the design of algorithms suitable for reliable implementation on quantum devices of the near future. Future work will involve improving this approach for better approximations and developing fully fault-tolerant protocols for these approximations.