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Encoding Electronic Spectra in Quantum Circuits with Linear T Complexity
Open accessAbstract
We construct quantum circuits that exactly encode the spectra of correlated electron models up to errors from rotation synthesis.By invoking these circuits as oracles within the recently introduced "qubitization" framework, one can use quantum phase estimation to sample states in the Hamiltonian eigenbasis with optimal query complexity Oðλ=ϵÞ, where λ is an absolute sum of Hamiltonian coefficients and ϵ is the target precision.For both the Hubbard model and electronic structure Hamiltonian in a second quantized basis diagonalizing the Coulomb operator, our circuits have T-gate complexity O(N þ logð1=ϵÞ), where N is the number of orbitals in the basis.This scenario enables sampling in the eigenbasis of electronic structure Hamiltonians with T complexity O(N 3 =ϵ þ N 2 logð1=ϵÞ=ϵ).Compared to prior approaches, our algorithms are asymptotically more efficient in gate complexity and require fewer T gates near the classically intractable regime.Compiling to surface code fault-tolerant gates and assuming per-gate error rates of one part in a thousand reveals that one can error correct phase estimation on interesting instances of these problems beyond the current capabilities of classical methods using only about a million superconducting qubits in a matter of hours.
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“Using Babbush et al.'s QROM read (section 3A of [2]), each table lookup has a Toffoli count and measurement depth of 2 c mul + c exp and uses a negligible O ( c mul + c exp ) ancillae.”
From How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits (2021) · cites this paper as [2]
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“Crosson et al. 298 demonstrated that this effect is common even for instances that do not exhibit noticeable symmetries.”
From Quantum Chemistry in the Age of Quantum Computing (2019) · cites this paper as [298]
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“Note that it is not always necessary to reach the adiabatic regime to achieve a significant overlap with the ground state.”
From Quantum Chemistry in the Age of Quantum Computing (2019) · cites this paper as [298]
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Self-citation
Metadata
- Authors
- Babbush, R., Gidney, C., Berry, D. W., Wiebe, N., McClean, J., Paler, A., Fowler, A., & Neven, H.
- Affiliations
- Google (United States) (US)
- Macquarie University (AU)
- Microsoft (United States) (US)
- ORCID
- Venue
- Physical Review X
- Publisher
- American Physical Society (APS)
- Published
- 2018-10-23
- Volume
- 8
- Issue
- 4
- ISSN
- 2160-3308 (ISSN-L)
- OpenAlex
- W2801305581
- Cited by
- 383
- References
- 118
- Citations by year
- 2026: 45 · 2025: 82 · 2024: 52 · 2023: 49 · 2022: 43 · 2021: 41 · 2020: 35 · 2019: 32 · 2018: 4
- FWCI
- 15.90
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Licence
- Locations
- Physical Review X (publishedVersion, cc-by)
- arXiv (Cornell University) (submittedVersion)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
- arXiv (Cornell University)
- Funders
- Australian Research Council (DP160102426)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Information and Cryptography
- Keywords
- quantum circuits, qubitization, quantum phase estimation, Hubbard model, superconducting qubits, query complexity, correlated electrons
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