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arxiv: 2507.23679 · v3 · submitted 2025-07-31 · 🪐 quant-ph

Swap Network Augmented Ans\"atze on Arbitrary Connectivity

Teodor Parella-Dilm\'e , Jakob S. Kottmann , Antonio Ac\'in This is my paper

Pith reviewed 2026-05-19 02:01 UTC · model grok-4.3

classification 🪐 quant-ph
keywords quantum computingvariational algorithmsqubit connectivityswap networksansatz designground state simulationspin glassmolecular electronic structure
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The pith

Embedding optimized swap networks into layered quantum ansatze yields lower energy errors with fewer gates and parameters on arbitrary qubit connectivities.

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

The paper introduces an algorithm that finds efficient qubit routing for any connectivity graph and produces a swap network allowing direct interactions between any pair of qubits. It then embeds these networks into layered, connectivity-aware variational ansatze for hybrid quantum-classical algorithms. The resulting circuits are shown to reach better accuracy in ground-state simulations of spin glasses and molecular systems while using shallower depths, fewer entangling gates, and fewer parameters than standard baselines. A sympathetic reader would care because real quantum processors have fixed, often sparse, qubit connections that normally force expensive routing or limit correlation capture.

Core claim

By first computing an optimized swap network for a given connectivity graph and then co-designing circuit layers around it, the ansatz captures complex correlations more efficiently. Across tested connectivities the swap-augmented construction consistently outperforms conventional layered ansatze in energy error while requiring fewer resources.

What carries the argument

The optimized swap network obtained from a routing algorithm for arbitrary graphs, embedded inside layered ansatze to enable direct long-range interactions without extra overhead.

If this is right

  • The same swap-network construction can be applied to any hardware graph without requiring hand-crafted layer redesigns.
  • Ground-state searches for spin-glass and molecular Hamiltonians become feasible with reduced circuit resources on constrained devices.
  • The co-design principle directly lowers the gate count needed to generate distant qubit correlations.
  • Trainability gains appear across multiple exemplified connectivities rather than being limited to a single topology.

Where Pith is reading between the lines

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

  • The routing optimization step could be reused as a modular preprocessing tool for other variational algorithms that need long-range entanglement.
  • Similar swap-augmented layering might reduce resources in quantum machine-learning or optimization tasks that also suffer from connectivity limits.

Load-bearing premise

That the routing optimization produces ansatze whose improved trainability and lower resource use are not offset by new optimization difficulties or hidden costs.

What would settle it

On a chosen connectivity graph, implement both the swap-augmented ansatz and a standard layered ansatz, run the variational optimization for the same number of iterations, and check whether the swap version reaches a lower energy error with measurably fewer gates, shallower depth, and fewer parameters.

Figures

Figures reproduced from arXiv: 2507.23679 by Antonio Ac\'in, Jakob S. Kottmann, Teodor Parella-Dilm\'e.

Figure 1
Figure 1. Figure 1: Diagram of the proposed algorithm for designing a layered ansatz embedded within a swap network with optimized [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 1
Figure 1. Figure 1: Fig.1. The algorithm takes the qubit connectivity graph [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Exemplified algorithm step with k = 2, that op￾timizes an initial graph G0 into G1. The initial history ma￾trix Ht=0 equals G0 adjacency matrix, where dark blue values (Ht=0 i,j = 1) indicate that indices i, j have yet to become ad￾jacent, and white values (Ht=0 i,j = 0) indicate prior adjacency. A simulated annealing optimization modifies the graph by adding or removing swap gates, with up to k = 2 swap l… view at source ↗
Figure 3
Figure 3. Figure 3: VQE energy error statistics for 100 random 7-spin glass instances, evaluated across varying qubit connectivities and [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Example of connectivity graph coarsening from the [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: VQE energy error for the π orbital system of p-benzyne birradical (Appendix.B) on the qubit connectivity of [ [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Entangling gate (EG) from the CRy-HEA ansatz used in the simulation of spin systems. Decomposition into single [PITH_FULL_IMAGE:figures/full_fig_p013_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Entangling layers in the CRy-HEA ansatz on the exemplified 7-qubit connectivities for the simulation of spin systems. [PITH_FULL_IMAGE:figures/full_fig_p013_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Decomposition of single excitation gate (SE) used in excitation-based circuits for electronic structure simulation, [PITH_FULL_IMAGE:figures/full_fig_p013_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Decomposition of a double excitation gate (DE) used in excitation-based circuits for electronic structure simulation, [PITH_FULL_IMAGE:figures/full_fig_p014_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Decomposition of an entangling gate (EG’) used in excitation-based circuits for electronic structure simulation. It [PITH_FULL_IMAGE:figures/full_fig_p014_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Entangling layer in the excitation-based ansatz used for electronic structure simulation in the exemplified connec [PITH_FULL_IMAGE:figures/full_fig_p014_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: SWAP gate and its equivalent decompositions into CNOT gates, and CZ + Hadamard gates. [PITH_FULL_IMAGE:figures/full_fig_p015_12.png] view at source ↗
Figure 14
Figure 14. Figure 14: Fermionic Swap gate (Fswap) and its standard decomposition. [PITH_FULL_IMAGE:figures/full_fig_p015_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Decomposition of the Orbital Swap (Oswap) gate using Fswap gates. The Oswap gate exchanges the orbitals [PITH_FULL_IMAGE:figures/full_fig_p015_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: Active space of π molecular orbitals of p-benzyne, in the basis of canonical orbitals [PITH_FULL_IMAGE:figures/full_fig_p016_16.png] view at source ↗
read the original abstract

Efficient parametrizations of quantum states are essential for trainable hybrid classical-quantum algorithms. A key challenge in their design consists in adapting to the available qubit connectivity of the quantum processor, which limits the capacity to generate correlations between distant qubits in a resource-efficient and trainable manner. In this work we first introduce an algorithm that optimizes qubit routing for arbitrary connectivity graphs, resulting in a swap network that enables direct interactions between any pair of qubits. We then propose a co-design of circuit layers and qubit routing by embedding the derived swap networks within layered, connectivity-aware ans\"atze. This construction significantly improves the trainability of the ansatz, leading to enhanced performance with reduced resources. We showcase these improvements through ground-state simulations of strongly correlated systems, including spin-glass and molecular electronic structure models. Across exemplified connectivities, the swap-enhanced ansatz consistently achieves lower energy errors using fewer entangling gates, shallower circuits, and fewer parameters than standard layered-structured baselines. Our results indicate that swap network augmented ans\"atze provide enhanced trainability and resource-efficient design to capture complex correlations on devices with constrained qubit connectivity.

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.

Referee Report

1 major / 0 minor

Summary. The manuscript introduces an algorithm to optimize qubit routing on arbitrary connectivity graphs, yielding swap networks that enable direct interactions between any qubit pair. It then embeds these networks into layered, connectivity-aware ansatze via a co-design approach. The central claim is that the resulting swap-augmented ansatze improve trainability and achieve lower energy errors with fewer entangling gates, shallower circuits, and fewer parameters than standard layered baselines, as demonstrated in ground-state simulations of spin-glass and molecular electronic structure models across exemplified connectivities.

Significance. If the empirical results hold under detailed scrutiny, the work would offer a practical route to adapting variational quantum algorithms to hardware with limited connectivity, potentially reducing resource overhead while enhancing expressivity for correlated systems.

major comments (1)
  1. [Abstract] The abstract states that swap-enhanced ansatze achieve lower energy errors using fewer entangling gates, shallower circuits, and fewer parameters than baselines, but provides no specifics on the numerical experiments (graphs, Hamiltonians, baseline constructions, whether swap depths are counted in resources, or convergence statistics). This absence is load-bearing for the central performance claim and prevents verification that gains survive proper accounting for routing overhead.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We are grateful to the referee for their insightful comments on our work. We respond to the major comment as follows and indicate the changes we will implement in the revised manuscript.

read point-by-point responses

  1. Referee: [Abstract] The abstract states that swap-enhanced ansatze achieve lower energy errors using fewer entangling gates, shallower circuits, and fewer parameters than baselines, but provides no specifics on the numerical experiments (graphs, Hamiltonians, baseline constructions, whether swap depths are counted in resources, or convergence statistics). This absence is load-bearing for the central performance claim and prevents verification that gains survive proper accounting for routing overhead.

    Authors: We thank the referee for pointing out the need for greater specificity in the abstract. The detailed numerical experiments are described in the main text, including the use of specific connectivity graphs (e.g., linear, ring, and arbitrary topologies), Hamiltonians for spin-glass models and molecular electronic structures, layered baseline ansatze without swap augmentation, and explicit inclusion of swap network depths in the circuit depth and entangling gate counts. Convergence is assessed over multiple random initializations with reported statistics. To address the referee's concern directly and make the abstract more informative, we will revise it to include brief mentions of the exemplified connectivities and confirm that routing overhead is accounted for in the resource comparisons. This will strengthen the presentation of our central claims. revision: yes

Circularity Check

0 steps flagged

No circularity: empirical claims rest on external simulations, not self-referential derivations

full rationale

The abstract describes an algorithm for optimizing qubit routing on arbitrary connectivity graphs to produce swap networks, followed by a co-design embedding those networks into layered ansatze. Performance claims (lower energy errors, fewer gates/parameters, shallower circuits) are presented as outcomes of ground-state simulations on spin-glass and molecular Hamiltonians across exemplified connectivities. These are external numerical benchmarks, not derivations that reduce by construction to fitted inputs or prior self-citations. No equations, parameter-fitting steps, uniqueness theorems, or ansatz smuggling via citation appear in the provided text. The construction is therefore self-contained against the reported simulations.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 1 invented entities

Information is limited to the abstract; no specific free parameters, axioms, or additional invented entities are detailed beyond the high-level description of the new construction.

invented entities (1)
  • swap network augmented ansatz no independent evidence
    purpose: Enhance trainability and resource efficiency for quantum state preparation on limited connectivity
    New construction proposed in the work to co-design routing and circuit layers.

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Reference graph

Works this paper leans on

55 extracted references · 55 canonical work pages · 4 internal anchors

  1. [1]

    Specifically: R1 =S m ◦ Sm−1 ◦

    This function consists of a concatenation of commut- ing label-swapping functions{Si}m i=1, each acting on dif- ferent vertices. Specifically: R1 =S m ◦ Sm−1 ◦. . .◦ S 2 ◦ S1, EachS i represents a distinct label-swapping operation, ensuring that two different operations do not act on the same vertex. This means each node is either swapped once with a neig...

    work page

  2. [2]

    Maximize the number of new direct connections be- tween labels

    work page

  3. [3]

    In this scenario, rings, rather than stars, are the dominant structure

    Minimize the distance between labels that have yet to connect in forthcoming steps. Letd ij denote the shortest path distance between labels iandjin the graphG t. We can then define the following cost function on the graphGt with history matrixH t: C(G t, Ht) = X i,j H t ijd2 ij (1) The minimization of this cost function addresses the two key requirements...

    work page doi:10.13039/501100011033

  4. [4]

    M.Cerezoetal.,Variationalquantumalgorithms,Nature Reviews Physics3, 625–644 (2021)

    work page 2021

  5. [5]

    J. R. McClean, J. Romero, R. Babbush and A. Aspuru- Guzik, The theory of variational hybrid quantum- classical algorithms, New Journal of Physics18, 023023 (2016)

    work page 2016

  6. [6]

    Tilly et al., The variational Quantum Eigensolver: A review of methods and best practices, Physics Reports 986, 1–128 (2022)

    J. Tilly et al., The variational Quantum Eigensolver: A review of methods and best practices, Physics Reports 986, 1–128 (2022)

    work page 2022

  7. [7]

    S. Sim, P. D. Johnson and A. Aspuru-Guzik, Ex- pressibility and entangling capability of parameter- ized quantum circuits for hybrid quantum-classical algorithms, Advanced Quantum Technologies2, 10.1002/qute.201900070 (2019)

    work page doi:10.1002/qute.201900070 2019

  8. [8]

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

    J. Romero et al., Strategies for quantum computing molecular energies using the unitary coupled cluster ansatz (2018), arXiv:1701.02691 [quant-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  9. [9]

    Kandala et al., Hardware-efficient variational quan- tum eigensolver for small molecules and quantum mag- nets, Nature549, 242 (2017)

    A. Kandala et al., Hardware-efficient variational quan- tum eigensolver for small molecules and quantum mag- nets, Nature549, 242 (2017)

    work page 2017

  10. [10]

    G. Li, Y. Ding and Y. Xie, Tackling the Qubit Map- ping Problem for NISQ-Era Quantum Devices (2019), arXiv:1809.02573 [cs.ET]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  11. [11]

    A.Cowtanetal.,OntheQubitRoutingProblem(Schloss Dagstuhl – Leibniz-Zentrum für Informatik, 2019)

    work page 2019

  12. [12]

    Noise-Adaptive Compiler Mappings for Noisy Intermediate-Scale Quantum Computers

    P. Murali, J. M. Baker, A. J. Abhari, F. T. Chong and M. Martonosi, Noise-Adaptive Compiler Mappings for Noisy Intermediate-Scale Quantum Computers (2019), arXiv:1901.11054 [quant-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  13. [13]

    C. Zhu et al., Quantum Compiler Design for Qubit Map- ping and Routing: A Cross-Architectural Survey of Su- perconducting, Trapped-Ion, and Neutral Atom Systems (2025), arXiv:2505.16891 [quant-ph]

    work page arXiv 2025

  14. [14]

    Holmes, S

    A. Holmes, S. Johri, G. G. Guerreschi, J. S. Clarke and A. Y. Matsuura, Impact of qubit connectivity on quan- tum algorithm performance, Quantum Science and Tech- nology5, 025009 (2020)

    work page 2020

  15. [15]

    J. R. McClean, S. Boixo, V. N. Smelyanskiy, R. Bab- bush and H. Neven, Barren plateaus in quantum neural network training landscapes, Nature Communications9, 10.1038/s41467-018-07090-4 (2018)

    work page doi:10.1038/s41467-018-07090-4 2018

  16. [16]

    I. D. Kivlichan et al., Quantum Simulation of Electronic Structure with Linear Depth and Connectivity, Phys. Rev. Lett.120, 110501 (2018)

    work page 2018

  17. [17]

    Generalized swap networks for near-term quantum computing

    B. O’Gorman, W. J. Huggins, E. G. Rieffel and K. B. Whaley, Generalized swap networks for near-term quan- tum computing (2019), arXiv:1905.05118 [quant-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  18. [18]

    G.-L. R. Anselmetti, D. Wierichs, C. Gogolin and R. M. Parrish, Local, expressive, quantum-number-preserving VQE Ansätze for Fermionic Systems, New Journal of Physics23, 113010 (2021)

    work page 2021

  19. [19]

    Hagge, Optimal fermionic swap networks for Hubbard models (2022), arXiv:2001.08324 [quant-ph]

    T. Hagge, Optimal fermionic swap networks for Hubbard models (2022), arXiv:2001.08324 [quant-ph]

    work page arXiv 2022

  20. [20]

    Hashim et al., Optimized SWAP networks with equiv- alent circuit averaging for QAOA, Phys

    A. Hashim et al., Optimized SWAP networks with equiv- alent circuit averaging for QAOA, Phys. Rev. Res.4, 033028 (2022)

    work page 2022

  21. [21]

    Barberà-Rodríguez, N

    J. Barberà-Rodríguez, N. Gama, A. K. Narayanan and D. Joseph, Finding dense sublattices as low energy states of a Hamiltonian, Phys. Rev. Res.6, 043279 (2024)

    work page 2024

  22. [22]

    H. R. Grimsley, S. E. Economou, E. Barnes and N. J. Mayhall, An adaptive variational algorithm for exact molecular simulations on a quantum computer (2019)

    work page 2019

  23. [23]

    H. L. Tang et al., Qubit-ADAPT-VQE: An Adaptive Al- gorithm for Constructing Hardware-Efficient Ansätze on 10 a Quantum Processor, PRX Quantum2, 020310 (2021)

    work page 2021

  24. [24]

    Y. S. Yordanov, V. Armaos, C. H. Barnes and D. R. Arvidsson-Shukur, Qubit-excitation-based adaptive vari- ational quantum eigensolver, Communications Physics4, 10.1038/s42005-021-00730-0 (2021)

    work page doi:10.1038/s42005-021-00730-0 2021

  25. [25]

    Leone, S

    L. Leone, S. F. Oliviero, L. Cincio and M. Cerezo, On the practical usefulness of the Hardware Efficient Ansatz, Quantum8, 1395 (2024)

    work page 2024

  26. [26]

    M.Laroccaetal.,Barrenplateausinvariationalquantum computing, Nature Reviews Physics7, 174–189 (2025)

    work page 2025

  27. [27]

    J. S. Kottmann et al., Tequila: A platform for rapid de- velopment of quantum algorithms, Quantum Science and Technology6, 024009 (2021)

    work page 2021

  28. [28]

    Suzuki et al., Qulacs: a fast and versatile quantum circuit simulator for research purpose, Quantum5, 559 (2021)

    Y. Suzuki et al., Qulacs: a fast and versatile quantum circuit simulator for research purpose, Quantum5, 559 (2021)

    work page 2021

  29. [29]

    N. S. Blunt et al., Perspective on the Current State-of- the-Art of Quantum Computing for Drug Discovery Ap- plications, Journal of Chemical Theory and Computation 18, 7001 (2022)

    work page 2022

  30. [30]

    Y. Cao, J. Romero and A. Aspuru-Guzik, Potential of quantum computing for drug discovery, IBM Journal of Research and Development62, 6:1 (2018)

    work page 2018

  31. [31]

    von Burg et al., Quantum computing enhanced com- putational catalysis, Physical Review Research3(2021)

    V. von Burg et al., Quantum computing enhanced com- putational catalysis, Physical Review Research3(2021)

    work page 2021

  32. [32]

    Lordi and J

    V. Lordi and J. M. Nichol, Advances and opportunities in materials science for scalable quantum computing, MRS Bulletin46, 589–595 (2021)

    work page 2021

  33. [33]

    Zimborás et al., Myths around quantum computation before full fault tolerance: What no-go theorems rule out and what they don’t (2025), arXiv:2501.05694 [quant- ph]

    Z. Zimborás et al., Myths around quantum computation before full fault tolerance: What no-go theorems rule out and what they don’t (2025), arXiv:2501.05694 [quant- ph]

    work page arXiv 2025

  34. [34]

    S. B. Bravyi and A. Y. Kitaev, Fermionic Quantum Com- putation, Annals of Physics298, 210 (2002)

    work page 2002

  35. [35]

    Parella-Dilmé et al., Reducing Entanglement with Physically Inspired Fermion-To-Qubit Mappings, PRX Quantum5, 030333 (2024)

    T. Parella-Dilmé et al., Reducing Entanglement with Physically Inspired Fermion-To-Qubit Mappings, PRX Quantum5, 030333 (2024)

    work page 2024

  36. [36]

    M. G. Algaba, M. Papič, I. de Vega, A. Calzona and F. Šimkovic IV, Fermion-to-qubit encodings with arbi- trary code distance (2025), arXiv:2505.02916 [quant-ph]

    work page arXiv 2025

  37. [37]

    A. Y. Vlasov, Clifford Algebras, Spin Groups and Qubit Trees, Quanta11, 97–114 (2022)

    work page 2022

  38. [38]

    Miller, Z

    A. Miller, Z. Zimborás, S. Knecht, S. Maniscalco and G. García-Pérez, Bonsai Algorithm: Grow Your Own Fermion-to-Qubit Mappings, PRX Quantum4, 030314 (2023)

    work page 2023

  39. [39]

    Miller, A

    A. Miller, A. Glos and Z. Zimborás, Treespilation: Architecture- and State-Optimised Fermion-to-Qubit Mappings (2024), arXiv:2403.03992 [quant-ph]

    work page arXiv 2024

  40. [40]

    Chiew, C

    M. Chiew, C. Ibrahim, I. Safro and S. Strelchuk, Optimal fermion-qubitmappingsviaquadraticassignment(2025), arXiv:2504.21636 [quant-ph]

    work page arXiv 2025

  41. [41]

    Chiew, B

    M. Chiew, B. Harrison and S. Strelchuk, Ternary tree transformations are equivalent to linear encodings of the Fock basis (2024), arXiv:2412.07578 [quant-ph]

    work page arXiv 2024

  42. [42]

    Harrison et al., A Sierpinski Triangle Fermion-to- Qubit Transform (2024), arXiv:2409.04348 [quant-ph]

    B. Harrison et al., A Sierpinski Triangle Fermion-to- Qubit Transform (2024), arXiv:2409.04348 [quant-ph]

    work page arXiv 2024

  43. [43]

    Jordan and E

    P. Jordan and E. Wigner, Über das Paulische Äquivalen- zverbot, Zeitschrift für Physik47, 631 (1928)

    work page 1928

  44. [44]

    Coester and H

    F. Coester and H. Kümmel, Short-range correlations in nuclear wave functions, Nuclear Physics17, 477–485 (1960)

    work page 1960

  45. [45]

    J. Lee, W. J. Huggins, M. Head-Gordon and K. B. Wha- ley, Generalized unitary coupled cluster wave functions for quantum computation, Journal of Chemical Theory and Computation15, 311–324 (2018)

    work page 2018

  46. [46]

    Anand et al., A quantum computing view on uni- tary coupled cluster theory, Chemical Society Reviews 51, 1659–1684 (2022)

    A. Anand et al., A quantum computing view on uni- tary coupled cluster theory, Chemical Society Reviews 51, 1659–1684 (2022)

    work page 2022

  47. [47]

    J. S. Kottmann, Molecular quantum circuit design: A graph-based approach, Quantum7, 1073 (2023)

    work page 2023

  48. [48]

    R. H. Byrd, P. Lu, J. Nocedal and C. Zhu, A Limited MemoryAlgorithmforBoundConstrainedOptimization, SIAM Journal on Scientific Computing16, 1190 (1995), https://doi.org/10.1137/0916069

    work page doi:10.1137/0916069 1995

  49. [49]

    Hibat-Allah, M

    M. Hibat-Allah, M. Mauri, J. Carrasquilla and A. Perdomo-Ortiz, A Framework for Demonstrating Practical Quantum Advantage: Racing Quantum against Classical Generative Models (2023), arXiv:2303.15626 [quant-ph]

    work page arXiv 2023

  50. [50]

    Grant, L

    E. Grant, L. Wossnig, M. Ostaszewski and M. Benedetti, An initialization strategy for addressing barren plateaus in parametrized quantum circuits, Quantum3, 214 (2019)

    work page 2019

  51. [51]

    Tranter, P

    A. Tranter, P. J. Love, F. Mintert, N. Wiebe and P. V. Coveney, Ordering of Trotterization: Impact on Errors in Quantum Simulation of Electronic Structure, Entropy 21, 1218 (2019)

    work page 2019

  52. [52]

    Barnes, Efficient quantum circuits for quantum compu- tational chemistry, Phys

    Y.S.Yordanov, D.R.M.Arvidsson-ShukurandC.H.W. Barnes, Efficient quantum circuits for quantum compu- tational chemistry, Phys. Rev. A102, 062612 (2020). 11 Appendix A: Approximate Implementation of Fermionic Excitations In the UCC theory [41], a reference state is parametrized in the form: |ψU CC⟩=e T−T † |ψref. ⟩(A1) with the cluster operator: T= X i,j tj...

    work page 2020

  53. [53]

    Entangling gate (EG) from the CRy-HEA ansatz used in the simulation of spin systems

    Entangling Gates Implementation EG = Ry(θ1) • Ry(θ2) Ry(θ3) Figure 6. Entangling gate (EG) from the CRy-HEA ansatz used in the simulation of spin systems. Decomposition into single- qubit rotationsR y(θ1)andR y(θ2), followed by a controlled-Ry(θ3)gate. 0 1 2 3 4 5 6 0 5 6 1 2 3 4 1 2 3 4 5 60 EG EG EG EG EG EG EG EG EG EG EG EG EG EG EG EG EG EG EG EG EG ...

    work page

  54. [54]

    SWAP gate and its equivalent decompositions into CNOT gates, and CZ + Hadamard gates

    Swap Networks Implementation SWAP = • • • = • H • H • H • H • H • H Figure 12. SWAP gate and its equivalent decompositions into CNOT gates, and CZ + Hadamard gates. Fswap = • • • • • Figure 14. Fermionic Swap gate (Fswap) and its standard decomposition. |ϕi, α⟩ Oswap |ϕi, β⟩ |ϕj, α⟩ |ϕj, β⟩ = |ϕi, α⟩ Fswap |ϕi, β⟩ Fswap Fswap |ϕj, α⟩ Fswap |ϕj, β⟩ = |ϕj, ...

    work page

  55. [55]

    Initialization details for theπactive space system of p-benzyne birradical

    Electronic Structure Initialization Molecule Basis Ecorr.(kcal/mol) Cartesian Geometry (Å) p-benzyne cc-pVDZ 76.7520 C -0.7396 -1.1953 0.0000 C 0.7396 -1.1953 0.0000 C 1.3620 0.0000 0.0000 C 0.7396 1.1953 0.0000 C -0.7396 1.1953 0.0000 C -1.3620 0.0000 0.0000 H 1.1999 -2.1824 0.0000 H -1.1999 2.1824 0.0000 H 1.1999 2.1824 0.0000 H -1.1999 -2.1824 0.0000 T...

    work page 1953