Sample-Based Krylov Diagonalization Approximates Ground-State Wave Functions for Many-Body Systems

Calculating the ground state energy of complex molecules remains a significant challenge in quantum chemistry, often requiring computational resources that quickly become intractable. Samuele Watson, Javier Robledo-Moreno, and William Kirby, all from IBM Quantum, alongside their colleagues, address this limitation with a new approach to approximating molecular ground states on near-term quantum computers. Their research introduces SqDRIFT, an algorithm that combines sample-based Krylov diagonalization with randomized Hamiltonian compilation, effectively reducing the computational demands of these calculations. This innovation allows researchers to tackle larger and more complex molecules, such as polycyclic aromatic hydrocarbons, extending the reach of quantum simulations beyond the capabilities of traditional methods and opening new avenues for materials discovery and chemical design.

Sample-based quantum diagonalization (SQD) represents a recently proposed algorithm designed to approximate the ground-state wave function of many-body quantum systems on near-term and early-fault-tolerant quantum devices. The method leverages a quantum computer as a sampling engine to generate data crucial for determining the ground state. Current approaches to simulating quantum many-body systems face significant challenges, particularly as system size increases, due to the exponential growth in computational resources required by traditional methods. SQD offers a potential pathway to overcome these limitations by reformulating the problem as a sampling task, which is naturally suited to quantum computation, and by reducing the demands on quantum coherence and gate fidelity. This allows researchers to explore systems currently inaccessible to classical computation and provides a means to benchmark the capabilities of emerging quantum hardware.

Randomized SqDRIFT for Molecular Ground State Finding

Researchers are improving the accuracy of finding the ground state, the lowest energy state, of quantum systems, specifically molecules like naphthalene and coronene. Determining the ground state is crucial for understanding a molecule’s properties and behavior, but traditional calculation methods become computationally expensive for larger molecules. This research explores a hybrid quantum-classical approach using a technique called randomized SqDRIFT to leverage the power of quantum computers. The team utilizes a hybrid quantum-classical algorithm, combining the strengths of both types of computers.

The quantum computer performs a specific task, while the classical computer processes the results and guides the quantum computation. SqDRIFT, a type of variational quantum eigensolver, is used to find the ground state of a Hamiltonian, a mathematical representation of the system’s energy. Randomization is introduced to improve the algorithm’s performance and robustness by randomly selecting which parts of the quantum system to operate on. In simpler terms, the researchers are using quantum computers to help find the lowest energy state of molecules. They’ve developed a method that combines the strengths of both quantum and classical computers and have shown it can work on real quantum hardware, though challenges remain before it can solve really complex problems.

SqDRIFT Algorithm Accelerates Molecular Energy Calculations

Researchers have developed a new quantum algorithm, SqDRIFT, that significantly improves the ability to calculate the ground-state energy of complex molecular systems. This advancement addresses a key limitation in current quantum computing approaches, which struggle with the depth of calculations required for accurate molecular modeling. SqDRIFT builds upon existing methods by combining sample-based quantum diagonalization with a technique called qDRIFT, allowing for more efficient use of available quantum hardware. The core of SqDRIFT lies in its ability to intelligently sample potential solutions to the complex equations governing molecular behavior.

Instead of exhaustively searching all possibilities, the algorithm focuses on the most promising areas of the solution space, dramatically reducing the computational burden. This is achieved by generating a series of quantum circuits that produce a range of potential solutions, then efficiently identifying the most relevant ones through a classical diagonalization process. The algorithm’s effectiveness relies on the principle of “concentration,” meaning the ground-state wave function, a description of the molecule’s lowest energy state, is largely confined to a relatively small subset of all possible configurations. Importantly, SqDRIFT overcomes limitations of previous methods by requiring shallower quantum circuits, meaning fewer computational steps are needed.

This is crucial because current quantum computers are prone to errors, and the probability of error increases with circuit depth. Demonstrations on simulated systems and actual IBM quantum processors show that SqDRIFT can accurately calculate the ground-state energy of polycyclic aromatic hydrocarbons, molecules that are challenging for traditional computational methods. Specifically, the team successfully modeled coronene, a complex molecule requiring up to 48 qubits, demonstrating the algorithm’s scalability. This advancement has the potential to accelerate the discovery of new materials, design more efficient catalysts, and improve our understanding of fundamental chemical processes. The algorithm’s ability to trade circuit complexity for sampling overhead provides a practical pathway toward achieving accurate quantum simulations on near-term quantum hardware.

SqDRIFT Improves Energy Calculations for Complex Systems

Researchers have presented a new algorithm, termed SqDRIFT, designed to calculate the ground-state energy of complex many-body systems using near-term quantum computers. Building upon the Sample-based Krylov Diagonalization (SKQD) method, SqDRIFT combines SKQD with a randomized compilation technique to enable calculations on larger chemical systems than previously possible. The team successfully applied SqDRIFT to determine the electronic ground-state energy of polycyclic aromatic hydrocarbons, achieving results for systems beyond the reach of traditional exact diagonalization methods. Notably, the researchers observed that the combination of hardware noise and error mitigation techniques appeared to enhance the exploration of relevant computational subspaces, leading to improved energy estimates for the tested systems.

While this effect was prominent in their experiments, the authors acknowledge that it may not hold true as system size increases due to the exponential growth in the number of determinants affected by noise. Future work will need to investigate the limits of this noise-assisted sampling and explore methods to maintain accuracy as systems become more complex. The study demonstrates a promising approach to tackling challenging quantum chemistry problems with current and near-future quantum hardware, while also highlighting the potential, and limitations, of leveraging noise as a computational resource.