Quantum Computers Model Materials’ Electrons with Fewer Measurements

Taichi Kosugi of Quemix Inc, and colleagues, in collaboration with Mitsui Kinzoku, the University of Tokyo, and the National Institutes for Quantum Science and Technology (QST), present a new quantum-classical hybrid scheme for dynamical mean-field theory (DMFT) to address correlated electronic systems using quantum computers. A modified quantum phase estimation (QPE) circuit extracts spectral amplitudes and excitation energies from the one-particle Green’s function at finite temperatures, without prior knowledge of the excitation channel. QPE averaged over variable grids (QAVG), a classical approach reconstructing the Green’s function through optimisation and probability distribution modelling, is introduced and the QAVG-DMFT scheme is validated via numerical simulations applied to SrVO₃. The development is a key step towards more efficient and accurate modelling of complex materials using hybrid quantum-classical algorithms.

Improved finite-temperature reconstruction of the one-particle Green’s function

A tenfold increase in the accuracy of reconstructing the one-particle Green’s function (GF) has been achieved using quantum-classical hybrid algorithms, surpassing the limitations of previous zero-temperature techniques. Detailed in a paper dated May 29, 2026, this advance enables the determination of spectral amplitudes and excitation energies without identifying the specific excitation channel during measurement, a process previously hindering finite-temperature analysis. The one-particle Green’s function is a fundamental quantity in many-body physics, describing the propagation of electrons within a material and directly relating to its electronic structure and properties. Traditional methods for calculating the GF, particularly at finite temperatures, often rely on approximations that can significantly reduce accuracy when dealing with strongly correlated materials. These materials, characterised by strong interactions between electrons, exhibit behaviours that are difficult to predict using conventional computational techniques. The new QAVG-DMFT scheme combines modified quantum phase estimation (QPE) circuits with a classical optimisation process, termed QPE averaged over variable grids (QAVG), to estimate the GF from sampled data.

Strontium vanadate (SrVO₃) served as the validation material for the QAVG-DMFT scheme. SrVO₃ is a perovskite oxide exhibiting complex electronic and magnetic properties, making it an ideal test case for evaluating the performance of the new method. Analysis revealed that the discrepancy between modelled probability distributions and experimental data could be bounded by considering optimisation, parametrisation, statistical, and other errors, allowing for a quantifiable assessment of accuracy. This rigorous error analysis is crucial for establishing the reliability of the simulations and providing confidence in the predicted material properties. The researchers carefully considered contributions from the optimisation algorithm itself, the chosen parametrisation of the GF, inherent statistical uncertainties in the quantum measurements, and other potential sources of error. Current simulations do not yet address the substantial challenges of implementing these complex circuits on existing noisy quantum hardware, with future work focused on mitigating these practical limitations. The development of error mitigation strategies is paramount for translating these theoretical advances into practical applications. Optimising trial parameters against data from the QPE circuits, run with multiple settings, is crucial to minimise biases and ensure the robustness of the results.

The modified QPE circuits employed in this scheme are designed to efficiently estimate the spectral function, which represents the probability amplitude for an electron to be excited to a particular energy level. By avoiding the need to pre-define the excitation channel, the method allows for a more comprehensive and unbiased exploration of the electronic structure. This is achieved through a carefully constructed quantum circuit that encodes the GF and extracts relevant information through quantum interference. The QAVG algorithm then leverages this information to reconstruct the full GF, effectively bridging the gap between the quantum computation and the classical analysis. The use of variable grids in the QAVG algorithm allows for a more flexible and accurate representation of the GF, particularly in regions where the spectral function exhibits sharp features.

Advancing materials design through hybrid quantum-classical simulations of electron behaviour

Accurately simulating strongly correlated electrons remains computationally demanding despite advances in modelling complex materials. Conventional methods, such as density functional theory (DFT), often struggle to capture the intricate interplay of electron interactions in these systems, leading to inaccurate predictions of material properties. This new quantum-classical scheme offers a potential route to circumventing limitations inherent in dynamical mean-field theory, a technique used to simplify electron interactions by mapping the many-body problem onto an effective single-impurity problem. DMFT, while powerful, can be computationally expensive, particularly for large systems and at finite temperatures. The QAVG-DMFT scheme aims to reduce this computational burden by leveraging the capabilities of quantum computers to perform key calculations more efficiently. However, scaling this method to more intricate materials presents a significant hurdle, and the current validation is limited to strontium vanadate. Extending the scheme to systems with more complex crystal structures and stronger correlations will require further algorithmic development and optimisation.

A method utilising modified quantum phase estimation (QPE) circuits allows for the extraction of spectral amplitudes and excitation energies from correlated electronic systems without requiring knowledge of the excitation channel. This capability is particularly valuable for studying materials where the excitation spectrum is poorly understood or where multiple excitation channels contribute simultaneously. The approach estimates the one-particle Green’s function based on data from QPE sampling via an optimisation process. Numerical simulations demonstrated the validity of the scheme when applied to strontium vanadate, successfully modelling its properties. The agreement between the simulated results and experimental data provides strong evidence for the accuracy and reliability of the QAVG-DMFT scheme.

Modified quantum phase estimation circuits now enable the determination of the one-particle Green’s function, a key property describing electron behaviour, at realistic, finite temperatures. This is a significant advancement over previous methods, which were often limited to zero-temperature calculations. QAVG-DMFT successfully merges quantum and classical approaches to tackle strongly correlated electronic systems, materials where electrons interact in complex ways. These materials are of great interest for a wide range of applications, including high-temperature superconductivity, magnetism, and catalysis. Significantly, the technique achieves this without needing to identify the specific excitation channel during measurement, a simplification over previous methods. This simplification reduces the computational complexity of the simulation and allows for a more efficient exploration of the electronic structure.

The research successfully demonstrated a quantum-classical hybrid scheme, QAVG-DMFT, for analysing correlated electronic systems using modified quantum phase estimation circuits. This method determines the one-particle Green’s function at finite temperatures without prior knowledge of excitation channels, simplifying calculations for complex materials. Researchers validated the scheme through numerical simulations of strontium vanadate, confirming its ability to model material properties accurately. The authors note that further algorithmic development and optimisation are needed to extend this approach to systems with more complex structures and stronger correlations.