Quantum Computers Sidestep Costly Data Readout for Faster Materials Modelling

A new quantum algorithm sharply accelerates density functional theory (DFT) calculations and overcomes limitations in electronic structure modelling. Yuansheng Zhao and colleagues from Quemix Inc, Honda R&D Co, The University of Tokyo, National Institutes for Quantum Science and Technology (QST) and Quantum Materials and Applications Research Centre, present a qubit-efficient encoding scheme alongside a quantum algorithm capable of simultaneously computing all occupied orbitals. Their approach circumvents the computationally expensive process of reading out the electronic density, potentially offering an exponential speedup when applied to the Harris functional and enabling self-consistent DFT calculations without density readout. These findings represent a key step towards realising the full potential of quantum computers for materials science and quantum chemistry.

Density-free algorithms unlock scalable quantum simulations via simultaneous orbital computation

A reduction in computational cost for Kohn-Sham density functional theory (KS-DFT) calculations has been achieved, demonstrating an order of magnitude improvement by removing the need to read out electronic density. This process previously limited the scalability of quantum simulations. The breakthrough circumvents a fundamental bottleneck, enabling self-consistent DFT calculations that were previously intractable for all but the smallest systems due to exponential scaling with system size. Traditional DFT calculations rely heavily on determining the electron density of a material, a step that becomes increasingly demanding as the number of atoms and electrons increases. The computational cost of obtaining this density scales exponentially with system size, hindering the application of DFT to larger, more complex materials. This new algorithm bypasses this bottleneck by directly calculating the occupied orbitals without explicitly determining the density, significantly reducing the computational burden.

The new algorithms, particularly effective with the Harris functional, utilise a qubit-efficient encoding scheme and simultaneous orbital computation to unlock potentially exponential speedups. Copies of wavefunctions further enable self-consistent calculations without electronic density readout, representing an advance in quantum chemistry and materials science. Further analysis revealed the number of computational steps needed to achieve a designated accuracy on per-atom energy scales independently of system size, an important factor for modelling complex materials. This independence from system size is crucial for tackling realistic materials, which often contain hundreds or even thousands of atoms. Quantum algorithms for density functional theory with minimal readout are being developed to address challenges in accelerating calculations. Employing the Harris functional, which avoids density readout, or increasing the number of bands considered in the calculation, even when level crossing occurs, maintains accuracy. The Harris functional, a non-local correlation functional, is particularly well-suited to this density-free approach as it inherently avoids the explicit calculation of the electron density. Level crossing, a phenomenon in band structure calculations, can introduce inaccuracies, but the algorithm demonstrates robustness even in these scenarios.

Qubit encoding of Kohn-Sham Slater determinants for reduced computational complexity

The core of this advancement lies in a qubit-efficient encoding scheme, a method of representing quantum information using the minimum number of qubits, much like compressing a computer file to save storage space. Specifically tailored to the single Slater determinant used within KS-DFT, this encoding differs from those designed for general wavefunctions. KS-DFT is a computational method used to calculate the electronic structure of atoms, molecules and solids. By focusing on the KS-DFT framework, the need to encode the full, complex many-body wavefunction was circumvented, dramatically reducing the computational burden. A Slater determinant is a mathematical construct used to describe the antisymmetric wavefunction of a system of fermions, such as electrons. Encoding this determinant efficiently on a quantum computer requires careful consideration of the number of qubits needed to represent the information. Traditional methods often require a many qubits, limiting the size of systems that can be simulated. This new encoding scheme minimises the qubit requirements, making it more practical for larger systems. This refinement in how quantum computers approach KS-DFT represents a significant step forward in electronic structure calculations by removing the need to directly measure electronic density, a computationally expensive step in traditional density functional theory. The algorithm leverages the properties of Slater determinants to achieve this efficiency, exploiting the inherent symmetries and constraints within the wavefunction.

The encoding scheme represents each Kohn-Sham orbital using a compact binary string, reducing the number of qubits required to be compared to conventional approaches. This is achieved by exploiting the fact that each orbital is occupied by a maximum of two electrons with opposite spins. The algorithm then efficiently maps these binary strings onto the qubits of the quantum computer. Simultaneous computation of all occupied orbitals is achieved through a carefully designed quantum circuit that operates on these encoded orbitals in parallel. This parallelisation is a key factor in the potential exponential speedup offered by the algorithm. The ability to compute all occupied orbitals simultaneously, rather than sequentially, significantly reduces the overall computation time. This is particularly advantageous for larger systems with many occupied orbitals.

Balancing computational efficiency with accuracy in molecular simulations

Despite these encouraging initial results, the algorithms’ performance remains dependent on the Harris functional, which exhibits slightly reduced accuracy compared to full KS-DFT. While exponential speedups are attractive, the trade-off between computational speed and precision introduces a tension if the resulting answers are less accurate. A variational method is proposed to mitigate this accuracy loss, though its effectiveness requires further scrutiny. The variational method involves introducing adjustable parameters into the calculation and optimising them to minimise the energy, thereby improving the accuracy of the results. However, the optimal choice of these parameters and the efficiency of the optimisation process remain open questions. Acknowledging concerns about the Harris functional’s precision is vital, as a slight reduction in accuracy is not catastrophic given the potential for substantial gains in processing speed. This new approach offers a pathway to tackle complex molecular simulations currently beyond the reach of conventional computers. Avoiding density readout unlocks the potential for exponential speedups and enables self-consistent calculations previously limited by computational cost, allowing larger and more intricate systems to be explored.

The implications of this work extend beyond fundamental materials science and quantum chemistry. Accurate modelling of molecular properties is crucial for drug discovery, materials design, and catalysis. By enabling the simulation of larger and more complex systems, this algorithm could accelerate the development of new materials with tailored properties and the design of more effective drugs. Furthermore, the qubit-efficient encoding scheme and density-free approach could be adapted to other quantum algorithms for electronic structure calculations, broadening its impact on the field. Future research will focus on improving the accuracy of the algorithm, exploring its applicability to different functionals, and scaling it up to even larger systems. The team aims to demonstrate the algorithm’s performance on benchmark materials and compare it to existing methods. The ultimate goal is to develop a practical quantum algorithm that can routinely solve electronic structure problems that are currently intractable for classical computers.

This research demonstrated a new quantum algorithm for density functional theory calculations that avoids the computationally expensive step of reading out electronic density. This is significant because it potentially allows for an exponential speedup in calculating the total energy of Kohn, Sham systems, enabling simulations of more complex molecules. The scientists achieved this through a qubit-efficient encoding scheme and a method utilising multiple copies of the wavefunction. Further work intends to refine the algorithm’s accuracy and expand its application to a wider range of materials and systems.