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Improved Techniques for Preparing Eigenstates of Fermionic Hamiltonians

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Dominic W. Berry, Mária Kieferová, Artur Scherer, Yuval R. Sanders, Guang Hao Low, Nathan Wiebe, Craig Gidney, Ryan Babbush

Quantum Physics · Submitted 28 Nov 2017

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We present three techniques for reducing the cost of preparing fermionic Hamiltonian eigenstates using phase estimation.

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arXiv ID1711.10460 (version 3)
Pith IDPABT3FHN, Pith's permanent record of this paper and its review
CitationArtur Scherer, Craig Gidney, Dominic W. Berry, Guang Hao Low, M\'aria Kieferov\'a, Nathan Wiebe, Ryan Babbush, Yuval R. Sanders. "Improved Techniques for Preparing Eigenstates of Fermionic Hamiltonians." arXiv:1711.10460 (2017). https://pith.science/paper/PABT3FHN
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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,989 input tokens.

What the abstract itself states, as probabilities: claims first 0.14 · states limitation 0.36 · human participants 0.01 · controlled comparison 0.19 · randomized assignment 0.01 · states quantitative result 0.46 · compares with prior results 0.96 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; .

Modeling low energy eigenstates of fermionic systems can provide insight into chemical reactions and material properties and is one of the most anticipated applications of quantum computing. We present three techniques for reducing the cost of preparing fermionic Hamiltonian eigenstates using phase estimation. First, we report a polylogarithmic-depth quantum algorithm for antisymmetrizing the initial states required for simulation of fermions in first quantization. This is an exponential improvement over the previous state-of-the-art. Next, we show how to reduce the overhead due to repeated state preparation in phase estimation when the goal is to prepare the ground state to high precision and one has knowledge of an upper bound on the ground state energy that is less than the excited state energy (often the case in quantum chemistry). Finally, we explain how one can perform the time evolution necessary for the phase estimation based preparation of Hamiltonian eigenstates with exactly zero error by using the recently introduced qubitization procedure.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 Modeling low energy eigenstates of fermionic systems can provide insight into chemical reactions and material properties and is one of the most anticipated applications of quantum computing. background 1.00 0.04 0.04 asserted 0.94
s1 We present three techniques for reducing the cost of preparing fermionic Hamiltonian eigenstates using phase estimation. contribution 1.00 0.94 0.49 asserted 1.00
s2 First, we report a polylogarithmic-depth quantum algorithm for antisymmetrizing the initial states required for simulation of fermions in first quantization. contribution 0.77 0.95 0.15 asserted 1.00
s3 This is an exponential improvement over the previous state-of-the-art. result 0.56 0.75 0.12 asserted 1.00
s4 Next, we show how to reduce the overhead due to repeated state preparation in phase estimation when the goal is to prepare the ground state to high precision and one has knowledge of an upper bound on the ground state energy that is less than the excited state energy (often the case in quantum chemistry). contribution 0.68 0.90 0.08 asserted 0.99
s5 Finally, we explain how one can perform the time evolution necessary for the phase estimation based preparation of Hamiltonian eigenstates with exactly zero error by using the recently introduced qubitization procedure. contribution 0.67 0.77 0.14 asserted 0.99

What kind of paper the classifier reports this is: method or tool 1.00 · evidence from proof or derivation 0.99.

What was examined, and what was not

sources read
  • arXiv listing abstract v3
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
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  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

Modeling low energy eigenstates of fermionic systems can provide insight into chemical reactions and material properties and is one of the most anticipated applications of quantum computing. We present three techniques for reducing the cost of preparing fermionic Hamiltonian eigenstates using phase estimation. First, we report a polylogarithmic-depth quantum algorithm for antisymmetrizing the initial states required for simulation of fermions in first quantization. This is an exponential improvement over the previous state-of-the-art. Next, we show how to reduce the overhead due to repeated state preparation in phase estimation when the goal is to prepare the ground state to high precision and one has knowledge of an upper bound on the ground state energy that is less than the excited state energy (often the case in quantum chemistry). Finally, we explain how one can perform the time evolution necessary for the phase estimation based preparation of Hamiltonian eigenstates with exactly zero error by using the recently introduced qubitization procedure.

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References
How later papers used it

66 later papers cite it

Evidence: substantial. 45 of the citing papers share no author with it, and 11 of those carry a confident label from Pith's citation classifier.

Pith read 18 of the 108 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

Uses its method or tool 1 of 13 papers with this label · 1 by the same authors

By the same authors

Cites it as support 1 of 2 papers with this label
How the literature uses it

7 arXiv papers cite this in 7 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 4 sentences without a confident label

Cites it as background 3 papers
  • With the exception of [ref] , all prior papers which analyze the time-evolution of electronic structure Hamiltonians use the Trotter-Suzuki decomposition.

    Low Depth Quantum Simulation of Electronic Structure · Bounding Cost of Time-Evolution using Taylor Series Methods · 0.85

  • This is equivalent to a sum over 2 and 4-fold Majorana terms: [equation] Time evolution is performed by applying the Trotter expansion of the evolution operator $e^iHt$ [We have not discussed post-Trotter methods such as [ref] in this work.

    Majorana-based fermionic quantum computation · Introduction · 0.80

  • Recent proposals have developed new algorithms for this problem by considering simulation based on Taylor series methods as opposed to Trotterization [ref] , performing simulations in a fixed particle number manifold [ref] , and considering specialized basis functions [ref] .

    Strategies for quantum computing molecular energies using the unitary coupled cluster ansatz · Introduction · 0.97

What it cites · 7 sentences without a confident label

Uses the method or tool of 2 papers
  • In no_error we explain how qubitization [ref] provides a unitary sufficient for phase estimation purposes with exactly zero error (provided a gate set consisting of an entangling gate and arbitrary single-qubit rotations).

    Hamiltonian Simulation by Qubitization · Introduction · 0.86

  • As a concrete example, consider a calculation on the water molecule in its equilibrium geometry (bond angle of $104.5^∘$, bond length of $0.9584$ Å) in the minimal (STO-3G) basis set performed using OpenFermion [ref] and Psi4 [ref] .

    OpenFermion: The Electronic Structure Package for Quantum Computers · Fewer Phase Estimation Repetitions by Partial Eigenstate Projection Rejection · 0.96

Cites as background 7 papers

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