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REVIEW 4 major objections 8 minor 51 references

Warehouse optimization using a trapped-ion quantum processor

T0 review · 4 major / 8 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read A trapped-ion quantum processor identifies an optimal warehouse layout in a small test.

desk verdict A legitimate small trapped-ion QAOA demo with a conclusion that overclaims: the reported energies are far above the true ground state. read the letter →

arxiv 2411.17575 v1 pith:4OYURJTM submitted 2024-11-26 quant-ph

Alexandre C. Ricardo , Gabriel P.L.M. Fernandes , Amanda G. Valério , Tiago de S. Farias , Matheus da S. Fonseca , Nicolás A. C. Carpio , Paulo C. C. Bezerra , Christine Maier
show 3 more authors
Juris Ulmanis Thomas Monz Celso J. Villas-Boas
This is my paper · ORCID
classification quant-ph
keywords warehouseoptimizationQAOAtrapped-ionquantumprocessorQUBOcombinatorialinventorymanagementvariationalalgorithms
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

Warehouse managers want to place products on gravity shelves so that items requested together are stored together, reducing costly reinsertions. This paper adapts that allocation problem into a quadratic unconstrained binary optimization (QUBO) instance and solves it with the Quantum Approximate Optimization Algorithm (QAOA) on a trapped-ion quantum processor. The central claim is that the QAOA implementation, using ten qubits for a three-product, two-shelf, capacity-two warehouse, found the optimal configuration both in noiseless simulation and on real hardware. The paper also shows that a recursive parameter-initialization scheme lowers the average expected energy much faster than random multi-start as the circuit depth grows. If correct, this is a concrete demonstration that near-term trapped-ion devices can tackle practical logistics problems encoded as QUBO.

What carries the argument

The central object is the mapping of the warehouse allocation variables $x^m_\alpha$ (product $\alpha$ placed on shelf $m$) into spin operators $x^m_\alpha \to \frac{1}{2}(I - \hat\sigma_x)$, which converts the QUBO cost $f = A f_A + B f_B + C f_C$ into an Ising Hamiltonian $\hat H = \sum_{i\neq j} J_{ij} \hat\sigma_x^i \hat\sigma_x^j + \sum_i h_i \hat\sigma_x^i$. Because only $\hat\sigma_x$ and $hat\sigma_x\hat\sigma_x$ terms appear, the time evolution factorizes into rotations native to trapped-ion hardware via the Mølmer–Sørensen gate. The QAOA circuit alternates evolution under this problem Hamiltonian with a mixer $\hat H_M = -\sum_i \hat\sigma_z^i$, and the parameters are classically optimized. Capacity limits are enforced by adding 'virtual products' terms $\langle 2|a^m \rangle$, so empty shelf slots are treated as fillers; in this work the capacity is fixed at $L=2$.

What would settle it

Run a brute-force enumeration of all 1024 assignments for the three-product, two-shelf, capacity-two instance and compare the true ground state of Eq. (3) against the state most frequently sampled from the hardware; a mismatch would disprove the claim that the optimal warehouse configuration was identified.

Watch

Extended reading notes

Core claim

The paper claims that the implemented QAOA algorithm identified the optimal warehouse configuration in both simulation and execution on real quantum hardware. For the instance studied—three products distributed over two shelves of capacity two, with an interproduct cost matrix chosen so that products 1 and 3 are cheaper to store together—the most populated output states in both simulation and hardware correspond to the two global minima of the problem Hamiltonian. The hardware run reached an expected energy of $\bar E_{\mathrm{hardware}} = 2.23$, slightly lower than the simulated $\bar E_{\mathrm{sim}} = 2.40$, a difference the authors attribute to shot noise and device imperfections. Beyond the single run, the paper establishes that a recursive strategy, which fixes earlier-layer parameters based on previous runs, drives the average expected energy from $\bar E = 15.24$ at one layer down to $\bar E = 2.03$ at five layers, approaching the global minimum, while a random multi-start strategy improves only linearly with depth.

Load-bearing premise

The cost function's fidelity to the real warehouse operation is inherited from the authors' earlier work (ref. [18]) and is not rederived or validated here, so the hardware result optimizes that QUBO objective rather than a directly measured reinsertion cost.

Editorial extensions

If this is right

  • For the ten-qubit instance tested, the QAOA output on real trapped-ion hardware is consistent with the optimal assignment found in simulation, indicating that current NISQ devices can run this QUBO encoding.
  • The recursive parameter-fixing strategy reduces the average expected energy from about 15.2 to 2.0 with five layers, offering a practical recipe for improving convergence in low-depth QAOA.
  • The resource scaling of about $M(P+1+\log_2 L)$ qubits and $O(p M P (M+P+\log_2 L))$ two-qubit gates sets a concrete target for scaling to realistic warehouses, such as the 1900 qubits estimated for 15 products on 100 shelves.
  • The same QUBO-to-Ising mapping with $\hat\sigma_x$ interactions could be applied to other allocation problems on trapped-ion processors.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the QUBO formulation faithfully represents reinsertion cost, the approach could be extended to larger JIS gravity-shelf warehouses, but the exponential state space and hardware noise will require error mitigation or error correction before practical advantage appears.
  • The recursive parameter initialization could be tested on other QUBO problems, such as portfolio optimization or scheduling, to see whether the convergence speedup is general or specific to this cost landscape.
  • A direct benchmark against classical exact solvers for the same instance would quantify the quantum overhead; the paper does not provide such a comparison.
  • The capacity constraint's virtual-product encoding is only exercised for $L=2$; checking $L=4$ or $L=8$ against brute-force enumeration would validate or invalidate the generalization to arbitrary shelf capacities.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 8 minor

Summary. The paper presents a QAOA implementation for a warehouse allocation problem formulated as a QUBO. The authors consider a JIS gravity-shelf warehouse instance with P=3 products, M=2 shelves of capacity L=2, map the QUBO to a 10-qubit Hamiltonian using a Pauli-X encoding that is compatible with trapped-ion MS gates, and run the algorithm both in noiseless simulation and on AQT's IBEX trapped-ion processor. Simulation results include an energy landscape, a random multi-start strategy, and a recursive parameter-fixing strategy; hardware results report a mean expected energy of 2.23 compared with 2.40 in simulation. The paper concludes that the QAOA identified the optimal warehouse configuration in both simulation and hardware execution.

Significance. If the central claim were properly supported, the paper would be a useful proof-of-principle demonstration of QAOA for a small industrial logistics problem on trapped-ion hardware, with a native MS-gate-friendly Hamiltonian mapping and explicit resource estimates. The strengths include the clear presentation of the Hamiltonian construction, the resource scaling table, and the direct simulation-to-hardware comparison. However, the significance is currently limited by the very small instance size, the absence of any classical baseline or success-probability metric, and the reliance on an unvalidated QUBO model inherited from prior work.

major comments (4)
  1. [Sec. V and Sec. IV C] The concluding claim that 'the implemented QAOA algorithm identified the optimal warehouse configuration in both simulation and execution on real quantum computing hardware' is not supported by the reported data. The hardware run (Sec. IV C) reports only the mean expected energy (E_hardware = 2.23) and does not report the probability of measuring a ground state or the frequency of the optimal feasible configuration among the 200 shots. The simulation results in Sec. IV B show at most 5.60% probability of the ground states at the global minimum of the energy landscape, and the recursive strategy reports only mean energies without reporting the ground-state energy or the success probability. To support the optimality claim, the paper must report the ground-state fidelity or the sampling probability of the optimal solution, and ideally the constraint-violation rate.
  2. [Sec. II A, Eq. (1b)] The QUBO objective f_B in Eq. (1b) is presented as the cost to be minimized for the warehouse problem, but the paper defers the derivation of this objective to ref. [18] and does not provide any validation linking the pairwise interproduct cost matrix λ to the reinsertion frequency in a JIS gravity-shelf system. The binary variables x_m^α encode only shelf assignment, not the within-shelf position or retrieval order, so the objective may not capture the cost mechanism illustrated in Fig. 1(a), where reinsertion depends on the position of items on the shelf. Because the central claim is about the optimal warehouse configuration, the manuscript must either derive the mapping from the operational cost to Eq. (1b) or limit the claim to optimality with respect to the adopted QUBO model.
  3. [Sec. II A, Eq. (1c) and Sec. II B] The virtual-product encoding in Eq. (1c) is only exercised for the case L = 2, yet the paper states that the formulation 'is very general and can be applied to arbitrary number of objects to be allocated and arbitrary number of positions on the shelves.' For general L (or non-power-of-two capacities), the encoding requires proof that the penalty term exactly enforces the capacity constraint and does not introduce spurious low-energy states. This is particularly relevant because the number of virtual-product qubits is log2 L, which presumes binary encoding of the empty-space count; the manuscript does not discuss how the encoding behaves for general L. The generalization claim should be either proven or explicitly scoped to the power-of-two case demonstrated.
  4. [Sec. IV B] The values of the penalty weights A = 10, B = A/20, and C = B/2 are chosen heuristically, and the paper does not report whether the final sampled states satisfy the constraints in Eqs. (1a) and (1c). If the reported mean energies include states that violate the 'one shelf per product' or capacity constraints, then the comparison to the ground state of the QUBO is not meaningful. The authors should report the fraction of samples that are feasible (e.g., no product assigned to two shelves, capacity respected) and ideally show that the infeasible states have energies sufficiently penalized.
minor comments (8)
  1. [Sec. III] The gate error rates are given, but the paper does not state the number of shots used for the final energy estimation separately from the 200 shots per optimization step; no error bars or standard deviation for the hardware mean energy are reported.
  2. [Sec. IV B] The description of the recursive strategy is terse; it is not clear how the parameters of the first p-1 layers are fixed from a previous execution and whether the optimization is re-run for the last layer only. A precise algorithm pseudocode would improve reproducibility.
  3. [Sec. IV A] The resource table reports only asymptotic scalings; it would be useful to state the constant factors and the number of classical optimization parameters (2p) that dominate the classical optimization cost.
  4. [Sec. IV B] The sentence 'The algorithm yielded a 1.40% probability of identifying the possible ground states' for a single random start is useful, but the paper should also state how the ground states are defined (the two global minima) and how the probability is computed (sum over both states).
  5. [Sec. V] The phrase 'global maximum probability of 5.60%' is ambiguous; it should be 'probability of measuring one of the two ground states.'
  6. [Sec. IV C] The validation of the claim that lower expected energy corresponds to a more organized warehouse is deferred to ref. [50], a patent; this source is not accessible for verification, so the paper should either include a direct argument or cite a peer-reviewed reference.
  7. [Fig. 3] The comparison of simulation and hardware would be more informative if the panels used the same vertical scale and if a quantitative distance (e.g., total variation distance) were reported.
  8. [Eq. (2b)] The notation a_m is not defined explicitly; clarify that a_m is the m-th shelf's virtual-product binary string and specify the range of the summation index i in the definition of ⟨2|a_m⟩.

Circularity Check

2 steps flagged · score 4.0 of 10

QUBO-to-warehouse link and energy-organization relation are imported from the authors' own prior work and patent; the QAOA hardware demonstration itself is self-contained.

  1. self citation load bearing [Section II A (Eqs. 1) and Section V Conclusions]
    "Following the prior work modeling the warehouse problem as a QUBO Hamiltonian [18], in this study we consider a warehouse comprised of M gravitational shelves, each with a capacity limit Lm associated with the shelf m, which could be a quantity of weight, number of items or space."

    The only support for identifying the minimum of the QUBO f = AfA + BfB + CfC with the real warehouse goal (minimizing reinsertion frequency) is the citation to [18], whose author list overlaps heavily with the present paper. No derivation connects Eq. (1b) to reinsertion frequency, and the binary variables encode shelf assignment, not within-shelf position. Therefore the conclusion 'the implemented QAOA algorithm identified the optimal warehouse configuration' rests on a self-citation rather than on an independently established model.

  2. ansatz smuggled in via citation [Section IV C, final paragraph]
    "A quantitative analysis demonstrating that the lower the expected energy obtained by this strategy, the more organized a warehouse is can be found in [50]."

    [50] is a patent by the same group (Fernandes, Valério, Fonseca, Ricardo, Carpio, Bezerra, Villas-Boas). The monotonic relation between expected energy and warehouse organization is asserted to be established there, not shown here. Since this relation is exactly what turns the QAOA energy minimum into a warehouse-optimization result, the central interpretation is smuggled in via a self-citation rather than demonstrated in the present work.

full rationale

The paper's own technical contribution—encoding the QUBO into a trapped-ion QAOA circuit, running it, and comparing simulated and hardware energy landscapes—is self-contained: the Hamiltonian is defined from the binary variables and λ, the parameters A, B, and C are fixed before optimization, and the optimizer minimizes that Hamiltonian. No fitted parameter is relabeled as a prediction. However, the claim that the minimized energy corresponds to an 'optimal warehouse configuration' is not derived in this paper. It is imported from the authors' own prior work [18] (the QUBO formulation) and their own patent [50] (the energy-organization monotonicity). These are load-bearing self-citations: without them, the hardware result optimizes an artificial objective that is merely named 'warehouse'. The QAOA-versus-simulation agreement still has independent content, so the circularity is partial and scored 4.

Assumptions & free parameters 4 free parameters · 5 assumptions · 1 invented entities

The central claim rests on a hand-built QUBO instance (weights A, B, C and cost matrix λ), a self-cited warehouse formulation, and a capacity-encoding trick that is only tested for L=2. These are not fitted to external data, but they are chosen by hand and unvalidated.

free parameters (4)
  • Penalty weight A = 10
    Hand-chosen weight for the assignment constraint fA; the paper states A must be larger than B and C but does not justify the specific value.
  • Penalty weight B = 0.5 (A/20)
    Hand-chosen weight for the interproduct cost fB; set as A/20 in Section IV.B.
  • Penalty weight C = 0.25 (B/2)
    Hand-chosen weight for the capacity penalty fC; set as B/2 because fC grows faster than fB.
  • Interproduct cost matrix lambda = lambda_12=0.4, lambda_13=0.2, lambda_23=0.6
    Hand-chosen interproduct costs to make products 1 and 3 preferentially co-located; no real warehouse data.
assumptions (5)
  • standard math QAOA with p layers converges toward the ground state of the problem Hamiltonian as p increases.
    Invoked in Section II.B without proof; standard result from the QAOA literature.
  • standard math The mapping x -> (I - σx)/2 correctly translates the QUBO objective into a Hamiltonian whose ground states correspond to the QUBO minima.
    Used in Section II.B, Eq. (2).
  • domain assumption The warehouse model (gravity shelves, JIS, FIFO) and the cost matrix λ faithfully represent real warehouse operations.
    Stated in Section II.A; no empirical validation provided.
  • ad hoc to paper The penalty weights A, B, C can be chosen independently to enforce constraints.
    The chosen values A=10, B=0.5, C=0.25 are not derived from the problem data.
  • ad hoc to paper The 'virtual products' encoding in Eq. (1c) enforces shelf capacity for all L.
    Validated only for L=2 in this work; generality is assumed.
invented entities (1)
  • Virtual products a_m
    purpose: Binary slack variables that fill empty shelf positions to enforce the capacity constraint in Eq. (1c).
    Mathematical construct; no operational meaning beyond capacity filling.

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Cite this review

Pith. "Pith review of Warehouse optimization using a trapped-ion quantum processor." pith.science (2026). https://pith.science/paper/4OYURJTM

@misc{pith2026241117575,
  author       = {Pith},
  title        = {Pith review of: Warehouse optimization using a trapped-ion quantum processor},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/4OYURJTM}},
  note         = {Machine review of arXiv:2411.17575}
}
read the original abstract

Warehouse optimization stands as a critical component for enhancing operational efficiency within the industrial sector. By strategically streamlining warehouse operations, organizations can achieve significant reductions in logistical costs such as the necessary footprint or traveled path, and markedly improve overall workflow efficiency including retrieval times or storage time. Despite the availability of numerous algorithms designed to identify optimal solutions for such optimization challenges, certain scenarios demand computational resources that exceed the capacities of conventional computing systems. In this context, we adapt a formulation of a warehouse optimization problem specifically tailored as a binary optimization problem and implement it in a trapped-ion quantum computer.

Figures

Figures reproduced from arXiv: 2411.17575 by the authors.

Figure 1
Figure 1. Schematic representation of the problem: ( [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. a illustrates the energy landscape obtained in the simu￾lation. During the execution of the algorithm, this is the func￾tion that should be subjected to optimization by the classical optimizer to identify its global minimum. The simulated out￾comes of the quantum algorithm indicate that there is a proba￾bility of 5.60% to find either of the two potential ground states of the problem Hamiltonian in the global minimum… view at source ↗
Figure 3
Figure 3. Complete energy spectrum of the problem hamil [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

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Reference graph

Works this paper leans on

51 extracted references · 37 canonical work pages

  1. [18]

    Boulebnane and A

    S. Boulebnane and A. Montanaro, Solving boolean satisfiabil- ity problems with the quantum approximate optimization algo- rithm (2022), arXiv:2208.06909 [quant-ph]

    arXiv 2022

  2. [50]

    Xue, Z.-Y

    C. Xue, Z.-Y . Chen, Y .-C. Wu, and G.-P. Guo, Effects of quan- tum noise on quantum approximate optimization algorithm, Chinese Physics Letters 38, 030302 (2021)

    work page 2021

  3. [1]

    139701/2023-0 and 141909/2023-4, CNPq 131088/2022- 0 and CNPq 140467/2022-0

    This work is also part of the MAI/DAI–CNPq Grants No. 139701/2023-0 and 141909/2023-4, CNPq 131088/2022- 0 and CNPq 140467/2022-0

    work page 2023

  4. [2]

    Schrijver, Combinatorial Optimization: Polyhedra and Ef- ficiency, Algorithms and Combinatorics No

    A. Schrijver, Combinatorial Optimization: Polyhedra and Ef- ficiency, Algorithms and Combinatorics No. v. 1 (Springer, 2003)

    work page 2003

  5. [3]

    Fan and P

    N. Fan and P. M. Pardalos, Linear and quadratic programming approaches for the general graph partitioning problem (2010)

    work page 2010

  6. [4]

    Laporte, The traveling salesman problem: An overview of exact and approximate algorithms, European Journal of Opera- tional Research 59, 231 (1992)

    G. Laporte, The traveling salesman problem: An overview of exact and approximate algorithms, European Journal of Opera- tional Research 59, 231 (1992)

    work page 1992

  7. [5]

    A. P. Punnen, The Traveling Salesman Problem and Its Varia- tions, Combinatorial Optimization (Springer US, 2007)

    work page 2007

  8. [6]

    Kellerer, U

    H. Kellerer, U. Pferschy, and D. Pisinger, Knapsack Problems (Springer Berlin Heidelberg, 2004)

    2004

Show all 51 references
  1. [7]

    Cacchiani, M

    V . Cacchiani, M. Iori, A. Locatelli, and S. Martello, Knapsack problems — an overview of recent advances. part i: Single knapsack problems, Computers & Operations Research 143, 105692 (2022)

    2022

  2. [8]

    Cacchiani, M

    V . Cacchiani, M. Iori, A. Locatelli, and S. Martello, Knapsack problems — an overview of recent advances. part ii: Multiple, multidimensional, and quadratic knapsack problems, Comput- ers & Operations Research 143, 105693 (2022)

    2022

  3. [9]

    W. H. Press, Numerical recipes 3rd ed.: The art of scientific computing (Cambridge university press, 2007)

    2007

  4. [10]

    Potvin, Genetic algorithms for the traveling salesman problem, Ann

    J.-Y . Potvin, Genetic algorithms for the traveling salesman problem, Ann. Oper. Res. 63, 337 (1996)

    1996

  5. [11]

    Farhi, J

    E. Farhi, J. Goldstone, and S. Gutmann, A quantum approxi- mate optimization algorithm (2014), arXiv:1411.4028 [quant- ph]

    2014 arXiv

  6. [12]

    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, Nat. Com- mun. 5, 4213 (2014)

    2014

  7. [13]

    N. N. Hegade, X. Chen, and E. Solano, Digitized counter- diabatic quantum optimization, Phys. Rev. Res. 4, L042030 (2022)

    2022

  8. [14]

    Mukherjee and B

    S. Mukherjee and B. K. Chakrabarti, Multivariable optimiza- tion: Quantum annealing and computation, The European Phys- ical Journal Special Topics 224, 17 (2015)

    2015

  9. [15]

    Zhang, R

    Z. Zhang, R. Paredes, B. Sundar, D. Quiroga, A. Kyrillidis, L. Duenas-Osorio, G. Pagano, and K. R. A. Hazzard, Grover- qaoa for 3-sat: Quadratic speedup, fair-sampling, and parame- ter clustering (2024), arXiv:2402.02585 [quant-ph]

    2024 arXiv

  10. [16]

    Shaydulin, C

    R. Shaydulin, C. Li, S. Chakrabarti, M. DeCross, D. Her- man, N. Kumar, J. Larson, D. Lykov, P. Minssen, Y . Sun, Y . Alexeev, J. M. Dreiling, J. P. Gaebler, T. M. Gatter- man, J. A. Gerber, K. Gilmore, D. Gresh, N. Hewitt, C. V . Horst, S. Hu, J. Johansen, M. Matheny, T. Meng...

    2024

  11. [17]

    Golden, A

    J. Golden, A. B ¨artschi, D. O’Malley, and S. Eidenbenz, Numer- ical evidence for exponential speed-up of qaoa over unstruc- tured search for approximate constrained optimization, in 2023 IEEE International Conference on Quantum Computing and Engineering (QCE) (IEEE, 2023). 8

    2023

  12. [19]

    G. P. L. M. Fernandes, M. S. Fonseca, A. G. Val ´erio, A. C. Ricardo, N. A. C. Carpio, P. C. C. Bezerra, and C. J. Villas-Boas, Optimization algorithm for inventory management on classical, quantum and quantum-hybrid hardware (2024), arXiv:2411.11756 [quant-ph]

    2024

  13. [20]

    Nastasi, V

    G. Nastasi, V . Colla, S. Cateni, and S. Campigli, Implementa- tion and comparison of algorithms for multi-objective optimiza- tion based on genetic algorithms applied to the management of an automated warehouse, Journal of Intelligent Manufacturing 29, 1545 (2018)

    2018

  14. [21]

    Satori and N

    K. Satori and N. Yoshikawa, Quantum optimization for loca- tion assignment problem in assr, in PHM Society Asia-Pacific Conference, V ol. 4 (2023)

    2023

  15. [22]

    Y . Wang, S. Mou, and Y . Wu, Storage assignment optimization in a multi-tier shuttle warehousing system, Chinese journal of mechanical engineering 29, 421 (2016)

    2016

  16. [23]

    Lesch, P

    V . Lesch, P. B. M. M ¨uller, M. Kr ¨amer, S. Kounev, and C. Krupitzer, A case study on optimization of warehouses (2021), arXiv:2112.12058 [cs.NE]

    2021 arXiv

  17. [24]

    Huang, J

    T. Huang, J. Xu, T. Luo, X. Gu, R. Goh, and W.-F. Wong, Benchmarking quantum(-inspired) annealing hardware on prac- tical use cases, IEEE Transactions on Computers 72, 1692 (2023)

    2023

  18. [25]

    J. A. Tompkins and J. D. Smith, eds., The warehouse manage- ment handbook, 2nd ed. (Tompkins Press, 1998)

    1998

  19. [26]

    Sazvar, S

    Z. Sazvar, S. M. J. Mirzapour Al-e hashem, K. Govindan, and B. Bahli, A novel mathematical model for a multi-period, multi- product optimal ordering problem considering expiry dates in a FEFO system, Transp. Res. Part E: Logist. Trans. Rev. 93, 232 (2016)

    2016

  20. [27]

    ¨Onal, H

    M. ¨Onal, H. E. Romeijn, A. Sapra, and W. van den Heuvel, The economic lot-sizing problem with perishable items and con- sumption order preference, Eur. J. Oper. Res. 244, 881 (2015)

    2015

  21. [28]

    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 algorithms, Nature Reviews Physics 3, 625–644 (2021)

    2021

  22. [29]

    Preskill, Quantum computing in the nisq era and beyond, Quantum 2, 79 (2018)

    J. Preskill, Quantum computing in the nisq era and beyond, Quantum 2, 79 (2018)

    2018

  23. [30]

    A. P. Punnen, The Quadratic Unconstrained Binary Optimiza- tion Problem (Springer, 2022)

    2022

  24. [31]

    M. Suzuki, Generalized trotter’s formula and systematic ap- proximants of exponential operators and inner derivations with applications to many-body problems, Communications in Mathematical Physics 51, 183 (1976)

    1976

  25. [32]

    Suzuki, On the convergence of exponential operators—the zassenhaus formula, bch formula and systematic approximants, Communications in Mathematical Physics 57, 193 (1977)

    M. Suzuki, On the convergence of exponential operators—the zassenhaus formula, bch formula and systematic approximants, Communications in Mathematical Physics 57, 193 (1977)

    1977

  26. [33]

    Bittel, S

    L. Bittel, S. Gharibian, and M. Kliesch, The Optimal Depth of Variational Quantum Algorithms Is QCMA-Hard to Ap- proximate, in 38th Computational Complexity Conference (CCC 2023), Leibniz International Proceedings in Informatics (LIPIcs), V ol. 264, edited by A. Ta-Shma (Schlo...

    2023

  27. [34]

    Sørensen and K

    A. Sørensen and K. Mølmer, Entanglement and quantum com- putation with ions in thermal motion, Phys. Rev. A 62, 022311 (2000)

    2000

  28. [35]

    Mølmer and A

    K. Mølmer and A. Sørensen, Multiparticle entanglement of hot trapped ions, Phys. Rev. Lett. 82, 1835 (1999)

    1999

  29. [36]

    Sørensen and K

    A. Sørensen and K. Mølmer, Quantum computation with ions in thermal motion, Phys. Rev. Lett. 82, 1971 (1999)

    1999

  30. [37]

    Maslov, Basic circuit compilation techniques for an ion-trap quantum machine, New Journal of Physics 19, 023035 (2017)

    D. Maslov, Basic circuit compilation techniques for an ion-trap quantum machine, New Journal of Physics 19, 023035 (2017)

    2017

  31. [38]

    A. W. Cross, L. S. Bishop, J. A. Smolin, and J. M. Gambetta, Open quantum assembly language (2017), arXiv:1707.03429 [quant-ph]

    2017 arXiv

  32. [39]

    Cartis, J

    C. Cartis, J. Fiala, B. Marteau, and L. Roberts, Improv- ing the flexibility and robustness of model-based derivative- free optimization solvers, ACM Trans. Math. Softw. 45, 10.1145/3338517 (2019)

    2019 doi

  33. [40]

    Shaydulin, I

    R. Shaydulin, I. Safro, and J. Larson, Multistart methods for quantum approximate optimization, in 2019 IEEE High Per- formance Extreme Computing Conference (HPEC) (2019) pp. 1–8

    2019

  34. [41]

    https://www

    AQT, Alpine Quantum Technologies, AQT. https://www. aqt.eu/ (), (accessed 2024-09-1)

    2024

  35. [42]

    https://qiskit.org/, (accessed 2024-09-1)

    Qiskit contributors, Qiskit: An open-source framework for quantum computing. https://qiskit.org/, (accessed 2024-09-1)

    2024

  36. [43]

    https:// www.aqt.eu/qc-systems/ (), (accessed 2024-09-1)

    AQT, IBEX Quantum Computer System, AQT. https:// www.aqt.eu/qc-systems/ (), (accessed 2024-09-1)

    2024

  37. [44]

    Qiskit contributors, Qiskit: An open-source framework for quantum computing (2023)

    2023

  38. [45]

    X. Lee, Y . Saito, D. Cai, and N. Asai, Parameters fixing strat- egy for quantum approximate optimization algorithm, in 2021 IEEE International Conference on Quantum Computing and Engineering (QCE) (IEEE, 2021)

    2021

  39. [46]

    S. H. Sack and M. Serbyn, Quantum annealing initialization of the quantum approximate optimization algorithm, Quantum 5, 491 (2021)

    2021

  40. [47]

    S. H. Sack, R. A. Medina, R. Kueng, and M. Serbyn, Recur- sive greedy initialization of the quantum approximate optimiza- tion algorithm with guaranteed improvement, Phys. Rev. A107, 062404 (2023)

    2023

  41. [48]

    S. Wang, E. Fontana, M. Cerezo, K. Sharma, A. Sone, L. Cin- cio, and P. J. Coles, Noise-induced barren plateaus in variational quantum algorithms, Nature Communications 12, 6961 (2021)

    2021

  42. [49]

    Sweke, F

    R. Sweke, F. Wilde, J. Meyer, M. Schuld, P. K. Faehrmann, B. Meynard-Piganeau, and J. Eisert, Stochastic gradient de- scent for hybrid quantum-classical optimization, Quantum 4, 314 (2020)

    2020

  43. [51]

    G. P. L. M. Fernandes, A. G. Val ´erio, M. S. Fonseca, A. C. Ri- cardo, N. A. C. Carpio, P. C. C. Bezerra, and C. J. Villas-Boas, Method and system for optimizing inventory management on gravitational shelves (portuguese version only), BR Patent 10 2024 018867 5. Sep, 9th. (2024)

    2024

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.