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Quantum simulations of materials on near-term quantum computers
He Ma, Marco Govoni, Giulia Galli
TL;DR
Realistic materials are too large for direct near-term quantum simulation, while strongly correlated active regions require methods beyond ordinary DFT. The paper develops a DFT-based quantum embedding theory that treats such regions with quantum methods and the environment classically. Quantum and classical calculations agree within relatively small error despite hardware noise, and the approach predicts previously unobserved singlet states.
Problem
Limited qubit counts prevent direct simulation of realistic materials, while DFT is often inadequate for strongly correlated electronic states.
Method
The paper develops a first-principles DFT-based quantum embedding theory that treats appropriate active regions quantum mechanically and their environments through embedding.
Results
Quantum and classical calculations agree within a relatively small error despite noise in the quantum hardware, while the study predicts previously unobserved excited singlet states for SiV and Cr.
Takeaways & Limitations
The approach supports near-term quantum-computer investigations of realistic materials and provides first theoretical predictions of singlet states for SiV in diamond and Cr in SiC.
Takeaways & Limitations
DFT requires approximations in practice, and prior DMET and DMFT materials calculations were limited to unit cells containing a few tens of atoms.
Abstract
from arXiv · showhide
Quantum computers hold promise to enable efficient simulations of the properties of molecules and materials; however, at present they only permit ab initio calculations of a few atoms, due to a limited number of qubits. In order to harness the power of near-term quantum computers for simulations of larger systems, it is desirable to develop hybrid quantum-classical methods where the quantum computation is restricted to a small portion of the system. This is of particular relevance for molecules and solids where an active region requires a higher level of theoretical accuracy than its environment. Here we present a quantum embedding theory for the calculation of strongly-correlated electronic states of active regions, with the rest of the system described within density functional theory. We demonstrate the accuracy and effectiveness of the approach by investigating several defect quantum bits in semiconductors that are of great interest for quantum information technologies. We perform calculations on quantum computers and show that they yield results in agreement with those obtained with exact diagonalization on classical architectures, paving the way to simulations of realistic materials on near-term quantum computers.
Introduction
Near-term quantum computers could improve simulations of correlated materials, but limited qubit counts restrict realistic systems. The paper addresses this gap with DFT-based quantum embedding for active regions and demonstrates it on semiconductor spin defects.
- Motivation: Existing correlated-electron methods are computationally demanding and remain difficult to apply to complex materials containing defects and interfaces.The challenge persists even with high-performance computing architectures.
- Motivation: Quantum computers promise efficient simulations of weakly and strongly correlated molecules and materials, but current devices have only about 100 qubits.This limits straightforward simulations of realistic systems requiring hundreds of atoms and many electronic degrees of freedom.
- Approach: The proposed strategy treats a strongly correlated active region accurately while describing its surrounding environment with mean-field theory.This reduces the number of electrons treated explicitly at the highest accuracy level.
- Approach: The work presents a DFT-based quantum embedding theory that scales to large systems and includes environmental exchange-correlation effects on active regions.The theory is demonstrated on NV, SiV, and Cr spin defects in diamond and 4H-SiC.
- Results: Embedding calculations agree with measurements and classical FCI results, while quantum-computer simulations of the NV center agree with classical FCI calculations.The study also predicts previously unobserved singlet-state positions and ordering for SiV and Cr.
- Results: These results support using near-term quantum computers to investigate realistic heterogeneous materials with first-principles theories.The quantum calculations use phase estimation and variational quantum eigensolver approaches.
Results
The embedding theory describes strongly correlated active regions within heterogeneous materials while treating their environments at the DFT level. It incorporates dielectric screening and exchange-correlation effects, scales to systems with hundreds of atoms and potentially thousands of electrons, and agrees with classical and experimental results for semiconductor defects.
- Scalability: The approach applies to systems with hundreds of atoms and is designed to scale to materials containing thousands of electrons without explicitly evaluating virtual electronic states.Earlier DMET and DMFT calculations were limited to relatively small unit cells because of computational cost.
- Embedding framework: Effective interactions combine bare Coulomb interactions with polarization from the environment and explicitly include exchange-correlation effects beyond RPA.The exchange-correlation contribution is evaluated using a finite-field algorithm.
- Embedding framework: The method constructs an effective Hamiltonian for an active space, with environmental electrons represented at the DFT mean-field level.Active spaces can target defect states within semiconductor or insulator gaps.
- Defect applications: Calculations successfully describe many-body electronic structures of multiple defects, confirm experimental observations, and provide new descriptions of defect optical cycles.The reported applications include defects involving transition-metal atoms.
- Quantum calculations: On quantum hardware, the calculations converge toward classical FCI results as ancilla qubits increase, while noisy quantum-computer energies converge within 0.2 eV of the ground-state energy.The quantum simulator correctly converged for both MS = 1 and MS = 0 cases.
Discussion
The paper presents a first-principles quantum embedding framework that treats active regions and environments at different accuracy levels, enabling strongly correlated simulations in large heterogeneous materials. Classical and quantum calculations for semiconductor spin defects agree closely, while the method predicts previously unobserved states and supports extensions beyond static screening.
- Framework: The proposed embedding theory treats appropriate active regions with high-level many-body methods and their environments with DFT, targeting complex materials on NISQ computers.The framework is designed for materials with hundreds of atoms and different accuracy levels across regions.
- Framework: Effective electron-electron interactions include dielectric screening and exchange-correlation effects from the DFT environment.This goes beyond the commonly used random phase approximation, which neglects exchange-correlation effects.
- Framework: The approach is scalable to heterogeneous materials and large systems because its response-function procedure avoids explicitly evaluating virtual electronic states.The paper states that this supports materials containing thousands of atoms.
- Scope: The framework can incorporate dynamical screening, electron-phonon coupling, and self-consistent environmental response, and is not restricted to strongly correlated active regions.The authors also identify applications to molecules, catalysts, drugs, aqueous solutions, and weakly correlated systems.
- Results: Classical and quantum algorithms produced excellent agreement for semiconductor spin-defect calculations, including selected noisy quantum-hardware results.The comparison involved classical calculations, quantum simulators, and a quantum computer.
- Results: The study predicts previously unobserved excited states, including singlet-state ordering for SiV in diamond and Cr in SiC, informing their optical cycles.These are presented as the first theoretical predictions of the singlet states for those systems.
- Scope: The method enables quantum simulations of strongly correlated electronic states in systems with hundreds of atoms, extending beyond earlier quantum-embedding studies of pristine materials.The paper emphasizes defect-containing solids relevant to quantum technologies and broader applicability to materials simulations.
Methods
The calculations combine hybrid-functional DFT for host and defect structures with response-function construction of effective Hamiltonians for active spaces. These Hamiltonians are solved using classical FCI and selected PEA or VQE quantum simulations on simulators and IBM hardware.
- Effective Hamiltonians: The WEST-based construction starts from wavefunctions, diagonalizes χ0 iteratively, and represents response functions and fxc using the first 512 χ0 eigenpotentials.Finite-field fxc calculations couple WEST with Qbox.
- Density Functional Theory: Hybrid DFT, specifically a dielectric-dependent hybrid functional, provides the mean-field defect description and self-consistently determines exact-exchange fractions from the host dielectric constant.The hybrid functional is used for accurate defect levels, while PBE geometries are considered adequate.
- Effective Hamiltonians: The active-space Hamiltonian includes environment-screened interactions, with FCI calculations performed using PySCF and quantum simulations using PEA or VQE.The minimum NV model contains a1 and e orbitals treated beyond the RPA.
- Quantum Algorithms: PEA maps the fermionic Hamiltonian with Jordan-Wigner, omits Pauli terms below 10^-6 a.u., and changes eigenvalues by less than 10^-4 a.u. (0.003 eV).The Hamiltonian is scaled so 0 and 2.5 eV correspond to ancilla phases 0 and 1, with first-order Trotter evolution split into 4 slices.
- Quantum Algorithms: VQE uses parity mapping and UCCSD-based ansätze, with 4 qubits and 2 variational parameters for MS = 1 and 2 qubits for MS = 0.The MS = 0 ansatz uses two replicated excitation operators and 6 optimized parameters.
- Quantum Algorithms: Quantum simulations run on the QASM simulator and IBM Q 5 Yorktown, executing each circuit 8192 times for statistically reliable measurement sampling.The implementation uses IBM Qiskit.
Figures and tables
The figures and table present a DFT-based quantum-embedding workflow, defect electronic structures, excitation-energy comparisons, and quantum simulations benchmarked against classical FCI.
- Figure 1: Quantum embedding separates an active space from its environment and constructs an effective Hamiltonian including exchange-correlation interactions.The active-space interaction combines bare Coulomb interactions with dielectric-screening polarization from the environment.
- Figure 2: The defect calculations examine NV and SiV centers in diamond and Cr(4+) in 4H-SiC using spin densities, defect levels, and selected active spaces.The figures organize these ingredients across left, middle, and active-space panels.
- Figure 2: The electronic-structure analysis reports many-body state ordering from exact diagonalization of effective Hamiltonians with exchange-correlation interactions included.The resulting low-lying states are used to analyze the defect systems shown in the figures.
- Table 1: Table 1 compares vertical excitation energies from RPA, beyond-RPA calculations including exchange-correlation interactions, experimental ZPL measurements, and reference estimates.Reference vertical energies are derived from experimental ZPL values when Stokes energies are available.
- Figure 3: Figure 3 compares PEA and VQE quantum simulations of an NV-center minimum model with classical FCI results.PEA results converge toward classical FCI as the number of ancilla qubits increases, while VQE estimates ground-state energies from specified initial states.