arxiv: 2604.23555 · v1 · submitted 2026-04-26 · 🪐 quant-ph

Recognition: unknown

Calibrating the Role of Entanglement in Variational Quantum Algorithms from a Geometric Perspective

Chunxiao Du (1) , Yang Zhou (1) , Zhichen Huang (1) , Rui Li (2) , Zheng Qin (3) , Shikun Zhang (4) , Zhisong Xiao (1 , 5) ((1) School of Physics

show 15 more authors

Beihang University Beijing 100191 China (2) School of Applied Science Beijing Information Science Technology University. Beijing 100192 China (3) Shenzhen Institute of Beihang University. Shenzhen 518063 China (4) School of Future Technology Henan University Kaifeng (5) School of Instrument Science Opto-Electronics Engineering Technology University Beijing 100192 China)

Authors on Pith no claims yet

Pith reviewed 2026-05-08 06:15 UTC · model grok-4.3

classification 🪐 quant-ph

keywords entanglementvariational quantum algorithmsgeometric phasehardware-efficient ansatzhamiltonian variational ansatzquantum dynamicshilbert space

0 comments

The pith

In variational quantum algorithms, quantum state evolution is primarily governed by the geometric phase determined by the parameter-dependent Hilbert space geometry.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper investigates the dynamical role of entanglement in variational quantum algorithms by analyzing quantum state evolution through a geometric lens. It contrasts this with conventional Hamiltonian dynamics, where dynamical phase dominates, showing instead that geometric phase controls the trajectory in these algorithms. The analysis reveals that in hardware-efficient ansatzes, entanglement changes are decoupled from the evolution process, while in Hamiltonian variational ansatzes, entanglement serves as a resource where increased consumption leads to quicker state evolution. This distinction is important for understanding how to design ansatzes that effectively use entanglement for algorithm performance.

Core claim

Quantum state evolution in quantum algorithms is primarily governed by the geometric phase with the trajectory determined by the parameter-dependent Hilbert space geometry. In the Hardware-Efficient Ansatz, entanglement dynamics and state evolution are decoupled. In the Hamiltonian Variational Ansatz, the dynamical phase contribution is enhanced, allowing entanglement to function as a dynamical resource where more entanglement consumption correlates directly with faster quantum state evolution.

What carries the argument

The geometric phase in the parameter-dependent Hilbert space geometry that dictates the path of quantum state evolution in variational quantum algorithms.

If this is right

In hardware-efficient ansatzes, entanglement can vary without affecting the speed of quantum state evolution.
In Hamiltonian variational ansatzes, higher entanglement consumption directly speeds up the quantum state evolution process.
The choice of ansatz determines whether entanglement acts as a decoupled feature or an active dynamical resource.
Variational quantum algorithms can be calibrated by considering the geometric properties of the ansatz space rather than traditional phase dynamics.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Problem-inspired ansatzes like HVA may be more suitable for tasks where leveraging entanglement can accelerate optimization.
Quantifying the exact relationship between entanglement consumption and evolution speed could lead to better resource management in quantum computing.
This geometric view might extend to analyzing other quantum processes where parameterization plays a key role.

Load-bearing premise

The geometric phase dominates state evolution in variational quantum algorithms and that entanglement consumption can be directly correlated with faster evolution in the Hamiltonian variational ansatz.

What would settle it

A simulation of the Hamiltonian variational ansatz where varying the entanglement levels does not change the rate of state evolution toward the solution.

Figures

Figures reproduced from arXiv: 2604.23555 by (2) School of Applied Science, (3) Shenzhen Institute of Beihang University. Shenzhen 518063 China, (4) School of Future Technology, 5) ((1) School of Physics, (5) School of Instrument Science, Beihang University, Beijing 100191, Beijing 100192, Beijing Information Science, China, China), Chunxiao Du (1), Henan University, Kaifeng, Opto-Electronics Engineering, Rui Li (2), Shikun Zhang (4), Technology University, Technology University. Beijing 100192 China, Yang Zhou (1), Zheng Qin (3), Zhichen Huang (1), Zhisong Xiao (1.

**Figure 2.** Figure 2: FIG. 2. The HEA quantum circuit structure with view at source ↗

**Figure 4.** Figure 4: FIG. 4. Statistical correlations between changes of entan view at source ↗

**Figure 6.** Figure 6: (a) demonstrates that, for both HVA and HEA circuits, the entanglement entropy initially increases with circuit depth, reaches a maximum at intermediate layers, and then gradually decreases, eventually approaching the entanglement entropy of the ground state. Besides, the maximum value of entanglement entropy doesn’t attain the saturation value and exhibits a slower growth. This indicates that the optimiza… view at source ↗

**Figure 7.** Figure 7: FIG. 7. Statistical correlations between changes of entan view at source ↗

**Figure 8.** Figure 8: FIG. 8. Statistical correlations between changes of entangle view at source ↗

read the original abstract

Calibrating the role of entanglement in quantum algorithms is a crucial task in the development of quantum computing. Most existing studies have primarily focused on how the static properties of entanglement-such as its magnitude and phase-affect key performance metrics. In this work, we instead explore the relationship between the dynamical behaviors of entanglement and the execution of variational quantum algorithms from a geometric perspective. We find that, in contrast to conventional Hamiltonian dynamics where the evolution process is dominated by the dynamical phase, quantum state evolution in quantum algorithms is primarily governed by the geometric phase with the trajectory determined by the parameter-dependent Hilbert space geometry. In the problem-agnostic Hardware-Efficient Ansatz (HEA), entanglement dynamics and state evolution are decoupled. Conversely, in the problem-inspired Hamiltonian Variational Ansatz (HVA), the dynamical phase contribution is enhanced, allowing entanglement to function as a dynamical resource: more entanglement consumption correlates directly with faster quantum state evolution.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper claims geometric phase dominates VQA evolution and entanglement acts as a dynamical resource only in HVA, but the phase split and correlation metrics look under-specified for parameterized circuits.

read the letter

The main takeaway is that this work frames entanglement dynamics geometrically in variational quantum algorithms, arguing that state evolution follows the parameter-dependent Hilbert space geometry rather than conventional dynamical phase, with HEA showing decoupled entanglement and evolution while HVA ties higher entanglement consumption to faster progress. That distinction between problem-agnostic and problem-inspired ansatzes is the clearest new angle here. It builds on existing geometric quantum mechanics and VQA comparisons without reinventing the wheel, but it does give a practical lens for treating entanglement as tunable rather than fixed overhead in ansatz choice. The abstract at least lays out the contrast cleanly, which could help readers thinking about near-term device performance. The soft spot is the central mechanism. The claim that geometric phase governs the trajectory requires a clean decomposition of phases for discrete parameterized unitaries, not just continuous Schrödinger evolution, and the paper needs to show how they extract the geometric contribution independently of total fidelity or circuit depth. The reported correlation between entanglement consumption and evolution speed in HVA also needs quantitative, non-circular measures—otherwise it risks being an interpretive restatement of the ansatz structure itself. If the full text supplies explicit Berry connection calculations or controlled simulations with separate metrics, that would shore it up; from the given material the evidence looks thin. This is for people already working on VQA ansatz engineering and entanglement resource analysis. A reader who knows the geometric phase literature might extract a useful design heuristic, but anyone expecting rigorous derivations or falsifiable predictions will want to see the methods section first. I would send it to peer review so referees can test whether the phase split and correlation hold up with proper definitions and controls.

Referee Report

2 major / 2 minor

Summary. The manuscript claims that, unlike conventional Hamiltonian dynamics dominated by the dynamical phase, quantum state evolution in variational quantum algorithms (VQAs) is primarily governed by the geometric phase, with the trajectory set by the parameter-dependent Hilbert space geometry. In the problem-agnostic Hardware-Efficient Ansatz (HEA), entanglement dynamics and state evolution are decoupled. In the problem-inspired Hamiltonian Variational Ansatz (HVA), the dynamical phase contribution is enhanced, allowing entanglement to act as a dynamical resource such that greater entanglement consumption correlates directly with faster quantum state evolution.

Significance. If the central claims are rigorously established, the work supplies a geometric framework for distinguishing the dynamical roles of entanglement across ansatz families, which could inform ansatz selection and resource allocation in near-term quantum algorithms. The shift from static entanglement metrics to dynamical behaviors is a constructive contribution. No machine-checked proofs, reproducible code, or parameter-free derivations are evident from the provided text, limiting the immediate strength of the assessment.

major comments (2)

[Abstract] The assertion that geometric phase dominates VQA evolution (in contrast to dynamical-phase dominance in Hamiltonian dynamics) rests on an unstated decomposition of the total phase for discrete parameterized unitaries U(θ). Without an explicit construction of the geometric phase (e.g., via Berry connection on the ansatz manifold or Pancharatnam phase) that is independent of the circuit parameterization itself, the dominance claim cannot be verified and is load-bearing for the paper's central thesis.
[Abstract] The HVA claim that 'more entanglement consumption correlates directly with faster quantum state evolution' requires quantitative, independent metrics for both consumption (e.g., change in entanglement entropy per layer) and evolution speed (e.g., fidelity improvement rate or circuit-depth scaling). If these quantities are defined only within the same geometric construction used to identify the phase split, the correlation is at risk of circularity and undermines the assertion that entanglement functions as a dynamical resource.

minor comments (2)

The abstract is concise but would benefit from one sentence outlining the concrete measures or simulation protocol used to separate phases and quantify the claimed correlation.
Ensure that all abstract-level statements are directly supported by explicit derivations, figures, or tables in the main text rather than interpretive summary.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the thoughtful and constructive report. We address the two major comments point by point below, providing clarifications on our geometric construction and committing to revisions that strengthen the explicitness of the phase decomposition and metric definitions.

read point-by-point responses

Referee: [Abstract] The assertion that geometric phase dominates VQA evolution (in contrast to dynamical-phase dominance in Hamiltonian dynamics) rests on an unstated decomposition of the total phase for discrete parameterized unitaries U(θ). Without an explicit construction of the geometric phase (e.g., via Berry connection on the ansatz manifold or Pancharatnam phase) that is independent of the circuit parameterization itself, the dominance claim cannot be verified and is load-bearing for the paper's central thesis.

Authors: We agree that an explicit, verifiable construction is required. Our geometric phase is defined on the ansatz manifold via the Berry connection A = i ⟨ψ(θ)|∇_θ|ψ(θ)⟩, with the total phase split as φ_total = φ_dynamical + φ_geometric where φ_dynamical incorporates the expectation value of the layer-wise effective Hamiltonian. This construction depends on the reachable state manifold induced by the ansatz family rather than on the internal gate decomposition of any single layer. To make the dominance claim directly verifiable, we will add a dedicated subsection with the explicit integral formulas, a discrete-layer Pancharatnam-phase comparison, and numerical verification that the geometric contribution exceeds the dynamical one across the HEA and HVA trajectories. revision: yes
Referee: [Abstract] The HVA claim that 'more entanglement consumption correlates directly with faster quantum state evolution' requires quantitative, independent metrics for both consumption (e.g., change in entanglement entropy per layer) and evolution speed (e.g., fidelity improvement rate or circuit-depth scaling). If these quantities are defined only within the same geometric construction used to identify the phase split, the correlation is at risk of circularity and undermines the assertion that entanglement functions as a dynamical resource.

Authors: We share the concern about potential circularity. Entanglement consumption is quantified by the layer-wise change in von Neumann entropy of the reduced density matrix for a fixed bipartition, while evolution speed is measured by the per-layer increase in target-state fidelity and the Fubini-Study distance on the projective Hilbert space; both quantities are computed directly from the generated quantum states and are independent of the subsequent phase decomposition. The geometric framework is used only for post-hoc interpretation. In the revision we will insert explicit definitions of these two metrics, report the raw numerical values for multiple random instances, and add a statistical test confirming that the observed correlation in HVA is not an artifact of the phase split. revision: yes

Circularity Check

0 steps flagged

No circularity: geometric-phase dominance and entanglement-evolution correlation presented as empirical findings without reduction to self-defined inputs or self-citation chains in the abstract.

full rationale

The abstract states interpretive findings on phase dominance and entanglement as a resource in HVA versus HEA but provides no equations, parameter fits, or derivation steps that reduce the claimed geometric governance or consumption-speed correlation to quantities defined by the same construction. No self-citation load-bearing steps, ansatz smuggling, or renaming of known results are visible. The derivation chain cannot be walked to a circular reduction from the given text; the claims remain non-reducible to their inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review yields no explicit free parameters, axioms, or invented entities; the geometric perspective and phase dominance are invoked without stated assumptions or supporting derivations.

pith-pipeline@v0.9.0 · 5586 in / 1219 out tokens · 52874 ms · 2026-05-08T06:15:53.730639+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

58 extracted references · 7 canonical work pages · 1 internal anchor

[1]

R. P. Feynman, Simulating physics with computers, In- ternational Journal of Theoretical Physics21(1982)

1982
[2]

Palacios-Berraquero, L

C. Palacios-Berraquero, L. Mueck, and D. M. Persaud, Instead of ’supremacy’ use ’quantum advantage’, Nature 576, 213 (2019)

2019
[3]

Einstein, B

A. Einstein, B. Podolsky, and N. Rosen, Can quantum- mechanical description of physical reality be considered complete?, Phys Rev47, 696 (1935)

1935
[4]

Bravyi and A

S. Bravyi and A. Kitaev, Universal quantum computa- tion with ideal clifford gates and noisy ancillas, Physical Review A (2005)

2005
[5]

Kochen and E

S. Kochen and E. P. Specker, The problem of hidden vari- ables in quantum mechanics, Review of Modern Physics 5a, 293 (1967)

1967
[6]

Schr¨ odinger, Discussion of probability relations be- tween separated systems, Mathematical Proceedings of the Cambridge Philosophical Society31, 555 (1935)

E. Schr¨ odinger, Discussion of probability relations be- tween separated systems, Mathematical Proceedings of the Cambridge Philosophical Society31, 555 (1935)

1935
[7]

Hayden, D

P. Hayden, D. Leung, P. W. Shor, and A. Winter, Ran- domizing quantum states: Constructions and applica- tions, Communications in Mathematical Physics250, 371–391 (2004)

2004
[8]

Hayden, D

P. Hayden, D. W. Leung, and A. Winter, Aspects of generic entanglement, Communications in mathematical physics265, 95 (2006)

2006
[9]

Gross, S

D. Gross, S. T. Flammia, and J. Eisert, Most quantum states are too entangled to be useful as computational resources, Physical review letters102, 190501 (2009)

2009
[10]

M. V. D. Nest, Universal quantum computation with lit- tle entanglement, Physical Review Letters110, 060504 (2013)

2013
[11]

J. Chen, E. M. Stoudenmire, and S. R. White, Quantum fourier transform has small entanglement, PRX Quan- tum4(2023)

2023
[12]

Wiersema, C

R. Wiersema, C. Zhou, Y. de Sereville, J. F. Carrasquilla, Y. B. Kim, and H. Yuen, Exploring entanglement and optimization within the hamiltonian variational ansatz, PRX quantum1, 020319 (2020)

2020
[13]

Ortiz Marrero, M

C. Ortiz Marrero, M. Kieferov´ a, and N. Wiebe, Entanglement-induced barren plateaus, PRX Quantum 2, 040316 (2021)

2021
[14]

Patti, K

T. Patti, K. Najafi, X. Gao, and S. Yelin, Entanglement devised barren plateau mitigation, Physical Review Re- search (2020)

2020
[15]

Zhang, S

H.-K. Zhang, S. Liu, and S.-X. Zhang, Absence of barren plateaus in finite local-depth circuits with long-range en- tanglement, Physical Review Letters132, 150603 (2024)

2024
[16]

Zhang, Z

S. Zhang, Z. Qin, Y. Zhou, R. Li, C. Du, and Z. Xiao, Sin- gle entanglement connection architecture between multi- layer bipartite hardware efficient ansatz, New Journal of Physics26, 073042 (2024)

2024
[17]

Zhang, Y

S. Zhang, Y. Zhou, Z. Qin, R. Li, C. Du, Z. Xiao, and Y. Zhang, Machine-learning insights into the entanglement-trainability correlation of parametrized quantum circuits, Physical Review A: Atomic,Molecular,and Optical Physics111, 052403 (2025)

2025
[18]

Dupont, N

M. Dupont, N. Didier, M. J. Hodson, J. E. Moore, and M. J. Reagor, Entanglement perspective on the quantum approximate optimization algorithm, Physical Review A 106, 10.1103/physreva.106.022423 (2022)

work page doi:10.1103/physreva.106.022423 2022
[19]

Dupont, N

M. Dupont, N. Didier, M. J. Hodson, J. E. Moore, and M. J. Reagor, Calibrating the classical hardness of the quantum approximate optimization algorithm, PRX Quantum3, 10.1103/prxquantum.3.040339 (2022)

work page doi:10.1103/prxquantum.3.040339 2022
[20]

A. C. Nakhl, T. Quella, and M. Usman, Calibrating the role of entanglement in variational quantum circuits, Physical Review A109, 032413 (2024)

2024
[21]

D. L. Deng, X. Li, and S. Das Sarma, Quantum entan- glement in neural network states, Physical Review X7, 021021 (2017)

2017
[22]

Cerezo, A

M. Cerezo, A. Arrasmith, R. Babbush, S. C. Benjamin, S. Endo, K. Fujii, J. R. McClean, K. Mitarai, X. Yuan, L. Cincio, and P. J. Coles, Variational quantum algo- rithms, Nature Reviews Physics3, 625–644 (2021)

2021
[23]

Q. Zhao, Y. Zhou, and A. M. Childs, Entanglement ac- celerates quantum simulation, Nature Physics21, 1338 (2025)

2025
[24]

D´ ıez-Valle, D

P. D´ ıez-Valle, D. Porras, and J. J. Garc´ ıa-Ripoll, Quan- tum variational optimization: The role of entangle- ment and problem hardness, Physical Review A104, 10.1103/physreva.104.062426 (2021)

work page doi:10.1103/physreva.104.062426 2021
[25]

Peruzzo, J

A. Peruzzo, J. McClean, P. Shadbolt, M.-H. Yung, X.-Q. Zhou, P. J. Love, A. Aspuru-Guzik, and J. L. O’brien, A variational eigenvalue solver on a photonic quantum processor, Nature communications5, 4213 (2014)

2014
[26]

Kandala, A

A. Kandala, A. Mezzacapo, K. Temme, M. Takita, M. Brink, J. M. Chow, and J. M. Gambetta, Hardware- efficient variational quantum eigensolver for small molecules and quantum magnets, nature549, 242 (2017)

2017
[27]

Wecker, M

D. Wecker, M. B. Hastings, and M. Troyer, Progress to- wards practical quantum variational algorithms, Physical Review A92, 042303 (2015)

2015
[28]

A. K. Pati, V. Vedral, and E. Sjoqvist, Fractional con- tribution of dynamical and geometric phases in quantum evolution (2025), arXiv:2511.13090 [quant-ph]

work page arXiv 2025
[29]

Vidal, Efficient simulation of one-dimensional quan- tum many-body systems, Physical review letters93, 040502 (2004)

G. Vidal, Efficient simulation of one-dimensional quan- tum many-body systems, Physical review letters93, 040502 (2004)

2004
[30]

Schollw¨ ock, The density-matrix renormalization group in the age of matrix product states, Annals of physics 326, 96 (2011)

U. Schollw¨ ock, The density-matrix renormalization group in the age of matrix product states, Annals of physics 326, 96 (2011)

2011
[31]

Or´ us, A practical introduction to tensor networks: Matrix product states and projected entangled pair states, Annals of physics349, 117 (2014)

R. Or´ us, A practical introduction to tensor networks: Matrix product states and projected entangled pair states, Annals of physics349, 117 (2014)

2014
[32]

W. K. Wootters, Statistical distance and hilbert space, Physical Review D23, 357 (1981)

1981
[33]

Anandan and Y

J. Anandan and Y. Aharonov, Geometry of quantum evo- lution, Physical review letters65, 1697 (1990)

1990
[34]

Kr¨ uger and W

T. Kr¨ uger and W. Mauerer, Quantum dark magic effi- ciency of intermediate non-stabiliserness, in2025 IEEE International Conference on Quantum Computing and Engineering (QCE), Vol. 2 (IEEE, 2025) pp. 592–593

2025
[35]

Kingma and J

D. Kingma and J. Ba, Adam: A method for stochastic optimization, Computer Science (2014)

2014
[36]

P. Shor, Algorithms for quantum computation: discrete logarithms and factoring, In Proceedings of 35th Annual Symposium on the Foundations of Computer Science, IEEE Computer Society Press, Los Alamitos, CA , 124 (1994)

1994
[37]

L. K. Grover, A fast quantum mechanical algorithm for database search, Phys. Rev. Lett79(1997)

1997
[38]

Horodecki, P

R. Horodecki, P. Horodecki, M. Horodecki, and 10 K. Horodecki, Quantum entanglement, Reviews of mod- ern physics81, 865 (2009)

2009
[39]

Preskill, Quantum computing and the entanglement frontier, arXiv preprint arXiv:1203.5813 (2012)

J. Preskill, Quantum computing and the entanglement frontier, arXiv preprint arXiv:1203.5813 (2012)

work page arXiv 2012
[40]

S. Sim, P. D. Johnson, and A. Aspuru-Guzik, Express- ibility and entangling capability of parameterized quan- tum circuits for hybrid quantum-classical algorithms, Ad- vanced Quantum Technologies2, 1900070 (2019)

2019
[41]

Abbas, D

A. Abbas, D. Sutter, C. Zoufal, A. Lucchi, A. Figalli, and S. Woerner, The power of quantum neural networks, Nature Computational Science1, 403 (2021)

2021
[42]

Larocca, N

M. Larocca, N. Ju, D. Garc´ ıa-Mart´ ın, P. J. Coles, and M. Cerezo, Theory of overparametrization in quantum neural networks, Nature Computational Science3, 542 (2023)

2023
[43]

Jozsa and N

R. Jozsa and N. Linden, On the role of entanglement in quantum-computational speed-up, Proceedings of the Royal Society of London. Series A: Mathematical, Phys- ical and Engineering Sciences459, 2011 (2003)

2011
[44]

Passarelli, R

G. Passarelli, R. Fazio, and P. Lucignano, Nonstabilizer- ness of permutationally invariant systems, Physical Re- view A110, 022436 (2024)

2024
[45]

Qian and J

D. Qian and J. Wang, Quantum nonlocal nonstabilizer- ness, Physical Review A111, 052443 (2025)

2025
[46]

Li, Y.-R

H.-Z. Li, Y.-R. Zhang, Y.-J. Zhao, X. Huang, and J.- X. Zhong, Nonstabilizerness in stark many-body local- ization, arXiv preprint arXiv:2512.16859 (2025)

work page arXiv 2025
[47]

Passarelli, A

G. Passarelli, A. Russomanno, and P. Lucignano, Nonsta- bilizerness of a boundary time crystal, Physical Review A111, 062417 (2025)

2025
[48]

Rise and fall of nonstabilizerness via random measurements

A. Scocco, W.-K. Mok, L. Aolita, M. Collura, and T. Haug, Rise and fall of nonstabilizerness via random measurements, arXiv preprint arXiv:2507.11619 (2025)

work page internal anchor Pith review Pith/arXiv arXiv 2025
[49]

Howard, J

M. Howard, J. Wallman, V. Veitch, and J. Emerson, Con- textuality supplies the ‘magic’for quantum computation, Nature510, 351 (2014)

2014
[50]

M. G. Genoni, M. G. Paris, and K. Banaszek, Measure of the non-gaussian character of a quantum state, Physical Review A—Atomic, Molecular, and Optical Physics76, 042327 (2007)

2007
[51]

Wiersema, C

R. Wiersema, C. Zhou, J. F. Carrasquilla, and Y. B. Kim, Measurement-induced entanglement phase transi- tions in variational quantum circuits, SciPost Physics14, 147 (2023)

2023
[52]

A. Joch, G. S. Uhrig, and B. Fauseweh, Entanglement- informed construction of variational quantum circuits, Quantum Science and Technology10, 035032 (2025)

2025
[53]

Friedrich, M

L. Friedrich, M. L. Basso, A. B. Junior, J. M. Varela, L. Morais, R. Chaves, and J. Maziero, Variational quan- tum algorithm for entanglement quantification, Physical Review A112, 052452 (2025)

2025
[54]

P. C. Azado, G. I. Correr, A. Drinko, I. Medina, A. Canabarro, and D. O. Soares-Pinto, Expressibility, entangling power, and quantum average causal effect for causally indefinite circuits, Physical Review A111, 042620 (2025)

2025
[55]

S. E. Rasmussen, N. J. S. Loft, T. Bækkegaard, M. Kues, and N. T. Zinner, Reducing the amount of single-qubit rotations in vqe and related algorithms, Advanced Quan- tum Technologies3, 2000063 (2020)

2020
[56]

Qian, W.-F

C. Qian, W.-F. Zhuang, R.-C. Guo, M.-J. Hu, and D. E. Liu, Information scrambling and entanglement in quan- tum approximate optimization algorithm circuits, The European Physical Journal Plus139, 14 (2024)

2024
[57]

G. I. Correr, I. Medina, P. C. Azado, A. Drinko, and D. O. Soares-Pinto, Characterizing randomness in pa- rameterized quantum circuits through expressibility and average entanglement, Quantum Science and Technology 10, 015008 (2024)

2024
[58]

Bermejo-Vega, N

J. Bermejo-Vega, N. Delfosse, D. E. Browne, C. Okay, and R. Raussendorf, Contextuality as a resource for mod- els of quantum computation with qubits, Physical review letters119, 120505 (2017)

2017