Resource estimations for the Hamiltonian simulation in correlated electron materials

Kanno, Shu; Endo, Suguru; Utsumi, T.; Tada, Tomofumi

doi:10.1103/physreva.106.012612

Cited by 3 publications

(3 citation statements)

References 72 publications

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“…Previous work. Qubit and gate resources required for Trotterized Hamiltonian simulation algorithms of fully local Hamiltonians have recently been investigated by Kanno et al 22 . Here, effective Hamiltonians of several unit cells of materials have been constructed starting from a classical description that accounts for the important chemistry of the active space 10 .…”

Section: Simulation Algorithmsmentioning

confidence: 99%

“…This incurs a qubit overhead proportional to the number of unit cells. Importantly, considering that the main problem of current QCs is the presence of gate errors, our approach allows us to achieve a layer depth for single Trotter step that is independent of the size of the system, in stark contrast with the OðN 2=3 cells Þ depth using JW (in a cubic system with nearest neighbour interactions) 22 . Delgado et al recently gave a detailed resource analysis of quantum algorithms for determining properties of battery materials, such as equilibrium voltages and thermal stability 25 .…”

Section: Simulation Algorithmsmentioning

confidence: 99%

“…Interactions acting on large numbers of qubits introduce large circuit overheads in quantum simulation, making them undesirable. For example, under the JW transform-which many naive methods use to estimate algorithmic costs-simulating the dynamics of one of the 2-mode hopping terms may require a quantum circuit whose depth grows with the size of the system 22 . However if the interactions are sparse such that each fermionic mode is involved in a relatively small number of interactions, then these problems may be avoided by a judicious choice of mapping 11,57,58 .…”

Section: Hybrid Fermionic Encoding and Fermionic Swap Networkmentioning

confidence: 99%

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Towards near-term quantum simulation of materials

Clinton,

Cubitt,

Flynn

et al. 2024

Nat Commun

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Determining the ground and excited state properties of materials is considered one of the most promising applications of quantum computers. On near-term hardware, the limiting constraint on such simulations is the requisite circuit depths and qubit numbers, which currently lie well beyond near-term capabilities. Here we develop a quantum algorithm which reduces the estimated cost of material simulations. For example, we obtain a circuit depth improvement by up to 6 orders of magnitude for a Trotter layer of time-dynamics simulation in the transition-metal oxide SrVO3 compared with the best previous quantum algorithms. We achieve this by introducing a collection of connected techniques, including highly localised and physically compact representations of materials Hamiltonians in the Wannier basis, a hybrid fermion-to-qubit mapping, and an efficient circuit compiler. Combined together, these methods leverage locality of materials Hamiltonians and result in a design that generates quantum circuits with depth independent of the system’s size. Although the requisite resources for the quantum simulation of materials are still beyond current hardware, our results show that realistic simulation of specific properties may be feasible without necessarily requiring fully scalable, fault-tolerant quantum computers, providing quantum algorithm design incorporates deeper understanding of the target materials and applications.

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Section: Simulation Algorithmsmentioning

confidence: 99%

Section: Simulation Algorithmsmentioning

confidence: 99%

Section: Hybrid Fermionic Encoding and Fermionic Swap Networkmentioning

confidence: 99%

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Towards near-term quantum simulation of materials

Clinton,

Cubitt,

Flynn

et al. 2024

Nat Commun

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Quantum computation for periodic solids in second quantization

Ivanov

Sünderhauf

Holzmann

et al. 2023

Phys. Rev. Research

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Variational quantum algorithm for ergotropy estimation in quantum many-body batteries

Hoang,

Metz,

Thomasen

et al. 2024

Phys. Rev. Research

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Quantum batteries are predicted to have the potential to outperform their classical counterparts and are therefore an important element in the development of quantum technologies. Of particular interest is the role of correlations in many-body quantum batteries and how these can affect the maximal work extraction, quantified by the ergotropy. In this paper we simulate the charging process and work extraction of many-body quantum batteries on noisy intermediate-scale quantum devices and devise the variational quantum ergotropy (VQErgo) algorithm, which finds the optimal unitary operation that maximizes work extraction from the battery. We test VQErgo by calculating the ergotropy of a many-body quantum battery undergoing transverse field Ising dynamics following a sudden quench. We investigate the battery for different system sizes and charging times and analyze the minimum number of ansatz circuit repetitions needed for the variational optimization using both ideal and noisy simulators. We also discuss how the growth of long-range correlations can hamper the accuracy of VQErgo in larger systems, requiring increased repetitions of the ansatz circuit to reduce error. Finally, we optimize part of the VQErgo algorithm and calculate the ergotropy on one of IBM's quantum devices. Published by the American Physical Society 2024

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Resource estimations for the Hamiltonian simulation in correlated electron materials

Cited by 3 publications

References 72 publications

Towards near-term quantum simulation of materials

Towards near-term quantum simulation of materials

Quantum computation for periodic solids in second quantization

Variational quantum algorithm for ergotropy estimation in quantum many-body batteries

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