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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]
Experimental — accuracy not yet measuredIn the citing paper
“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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Ouyang, Y., White, D. R., & Campbell, E. T. (2020) · Quantum · doi:10.22331/q-2020-02-27-235 · Cited by 66
Fast Multiqubit Gates through Simultaneous Two-Qubit Gates
Gu, X. Q., Fernández-Pendás, J., Vikstål, P., Abad, T., Warren, C., Bengtsson, A., Tancredi, G., Shumeiko, V. S., Bylander, J., Johansson, G., et al. (2021) · PRX Quantum · doi:10.1103/prxquantum.2.040348 · Cited by 49
Linear-depth quantum circuits for multiqubit controlled gates
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Subsystem codes with high thresholds by gauge fixing and reduced qubit overhead
Higgott, O., & Breuckmann, N. P. (2021) · Physical Review X · doi:10.1103/physrevx.11.031039 · Cited by 48
Block-encoding structured matrices for data input in quantum computing
Sünderhauf, C., Campbell, E. T., & Camps, J. (2024) · Quantum · doi:10.22331/q-2024-01-11-1226 · Cited by 86
Hybridized Methods for Quantum Simulation in the Interaction Picture
Rajput, A., Roggero, A., & Wiebe, N. (2022) · Quantum · doi:10.22331/q-2022-08-17-780 · Cited by 62
Self-citationNear- and long-term quantum algorithmic approaches for vibrational spectroscopy
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Concrete quantum cryptanalysis of binary elliptic curves
Banegas, G., Bernstein, D. J., van Hoof, I., & Lange, T. (2020) · IACR Transactions on Cryptographic Hardware and Embedded Systems · doi:10.46586/tches.v2021.i1.451-472 · Cited by 50
Quantum unary approach to option pricing
Ramos-Calderer, S., Pérez-Salinas, A., García-Martín, D., Bravo-Prieto, C., Cortada, J., Planagumà, J., & Latorre, J. I. (2021) · Physical Review A · doi:10.1103/physreva.103.032414 · Cited by 58
Analyzing Prospects for Quantum Advantage in Topological Data Analysis
Berry, D. W., Su, Y., Gyurik, C., King, R., Basso, J., Barba, A. D. T., Rajput, A., Wiebe, N., Dunjko, V., & Babbush, R. (2024) · PRX Quantum · doi:10.1103/prxquantum.5.010319 · Cited by 74
Self-citationNam, Y., & Maslov, D. A. (2019) · npj Quantum Information · doi:10.1038/s41534-019-0152-0 · Cited by 46
Warren, C., Fernández-Pendás, J., Ahmed, S., Abad, T., Bengtsson, A., Biznárová, J., Debnath, K., Gu, X. Q., Križan, C., Osman, A., et al. (2023) · npj Quantum Information · doi:10.1038/s41534-023-00711-x · Cited by 42
Compilation by stochastic Hamiltonian sparsification
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Preparing Bethe Ansatz Eigenstates on a Quantum Computer
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Rapid Initial-State Preparation for the Quantum Simulation of Strongly Correlated Molecules
Berry, D. W., Tong, Y., Khattar, T., White, A. F., Kim, T. I., Low, G. H., Boixo, S., Ding, Z., Lin, L., Lee, S., et al. (2025) · PRX Quantum · doi:10.1103/prxquantum.6.020327 · Cited by 65
Self-citationNo-Go Theorems for Quantum Resource Purification: New Approach and Channel Theory
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Estimating Quantum Speedups for Lattice Sieves
Albrecht, M. R., Gheorghiu, V., Postlethwaite, E. W., & Schanck, J. M. (2020) · International Conference on the Theory and Application of Cryptology and Information Security · doi:10.1007/978-3-030-64834-3_20 · Cited by 58
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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