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arxiv: 2502.15375 · v1 · submitted 2025-02-21 · 🪐 quant-ph

Digitized Counter-Diabatic Quantum Optimization for Bin Packing Problem

Ruoqian Xu , Sebasti\'an V. Romero , Jialiang Tang , Yue Ban , Xi Chen This is my paper

Pith reviewed 2026-05-23 02:47 UTC · model grok-4.3

classification 🪐 quant-ph
keywords bin packingcounter-diabatic QAOAquantum optimizationcombinatorial problemsIBM quantum hardwareansatz designdigitized counter-diabatic driving
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The pith

The CD-mixer ansatz in digitized counter-diabatic QAOA delivers more accurate solutions to the one-dimensional bin packing problem than standard QAOA variants.

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

The paper develops three ways to add counter-diabatic driving to QAOA circuits for the bin packing problem. Each variant mixes cost and mixer Hamiltonians differently with the added driving terms. The version that pairs the driving terms with the mixer Hamiltonian produces the closest results to exact solutions. This holds across changes in iteration number, circuit layers, and Hamiltonian steps. The same circuit, after simulation-based tuning, runs on IBM hardware for a ten-item case and still returns high-accuracy answers with good success probability.

Core claim

Among the DC-QAOA, CD-inspired, and CD-mixer ansatzes, the CD-mixer ansatz that incorporates counter-diabatic terms specifically into the mixer Hamiltonian yields the highest accuracy and success rate for a ten-item one-dimensional bin packing instance, both in simulation and when executed on IBM quantum hardware despite circuit-depth limits.

What carries the argument

The CD-mixer ansatz, which augments the digitized counter-diabatic QAOA circuit by adding counter-diabatic driving terms to the mixer Hamiltonian while keeping the cost Hamiltonian separate.

If this is right

  • Fewer quantum resources are needed to reach a given solution quality for this NP-hard problem.
  • The method remains stable when the number of iterations, layers, or Hamiltonian steps is varied.
  • Near-term devices can produce usable approximations for small combinatorial instances.

Where Pith is reading between the lines

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

  • The same ansatz construction could be tested on other packing or scheduling problems that share similar cost Hamiltonians.
  • Circuit-depth reduction techniques beyond those used here might allow the approach to reach instances with fifteen or more items before noise dominates.
  • Hybrid classical post-processing of the measured bit strings could further improve the reported success probability without changing the quantum circuit.

Load-bearing premise

The performance edge seen on one ten-item instance will persist for larger problems without hardware noise or circuit depth becoming dominant.

What would settle it

Execute the CD-mixer ansatz on a twenty-item bin-packing instance on the same hardware and measure whether solution accuracy falls below that of classical solvers or other QAOA variants.

Figures

Figures reproduced from arXiv: 2502.15375 by Jialiang Tang, Ruoqian Xu, Sebasti\'an V. Romero, Xi Chen, Yue Ban.

Figure 1
Figure 1. Figure 1: FIG. 1. Schematic of the procedure proposed for solving 1dBPP. Step [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. The quantum circuit structures of QAOA in (a), DC-QAOA in (b), CD-inspired ansatz in (c), and CD-mixer in (d) are illustrated. [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. State probabilities at the 5th, 50th, and 100th iterations us [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. (a)-(d) Number of partial solutions and FR in Eq. ( [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Experimental results for instance W3 [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. The number of solutions (a) and FR (b) are plotted as func [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. The circuit layout of the IBM quantum computer [PITH_FULL_IMAGE:figures/full_fig_p010_7.png] view at source ↗
read the original abstract

The bin packing problem, a classical NP-hard combinatorial optimization challenge, has emerged as a promising candidate for quantum computing applications. In this work, we address the one-dimensional bin packing problem (1dBPP) using a digitized counter-diabatic quantum algorithm (DC-QAOA), which incorporates counter-diabatic (CD) driving to reduce quantum resource requirements while maintaining high solution quality, outperforming traditional methods such as QAOA. We evaluate three ansatz schemes-DC-QAOA, a CD-inspired ansatz, and a CD-mixer ansatz-each integrating CD terms with distinct combinations of cost and mixer Hamiltonians, resulting in different DC-QAOA variants. Among these, the CD-mixer ansatz demonstrates superior performance, showing robustness across various iteration counts, layer depths, and Hamiltonian steps, while consistently producing the most accurate approximations to exact solutions. To validate our approach, we solve a 10-item 1dBPP instance on an IBM quantum computer, optimizing circuit structures through simulations. Despite constraints on circuit depth, the CD-mixer ansatz achieves high accuracy and a high likelihood of success. These findings establish DC-QAOA, particularly the CD-mixer variant, as a powerful framework for solving combinatorial optimization problems on near-term quantum devices.

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

2 major / 1 minor

Summary. The manuscript introduces digitized counter-diabatic QAOA (DC-QAOA) and three ansatz variants (DC-QAOA, CD-inspired ansatz, CD-mixer ansatz) for the one-dimensional bin packing problem. It claims the CD-mixer ansatz is robust and superior in simulations across iteration counts, layer depths and Hamiltonian steps, and that it achieves high accuracy with high success likelihood when a 10-item instance is executed on IBM hardware after simulation-based circuit optimization.

Significance. If the claimed advantages are confirmed with quantitative metrics, error bars and statistical controls, the incorporation of counter-diabatic terms into variational ansatze could reduce circuit depth requirements for combinatorial optimization on near-term devices; the hardware execution on a small instance supplies a concrete existence proof, though the work does not yet address scaling.

major comments (2)
  1. [Hardware experiment] Hardware experiment (final results section): the assertion that the CD-mixer ansatz 'achieves high accuracy and a high likelihood of success' on the 10-item 1dBPP instance rests on a single hardware execution whose shot count, success probability, variance and comparison to the other two ansatze are not reported; without these data the observed outcome cannot be distinguished from finite-shot noise or post-selection effects.
  2. [Numerical results] Numerical results (simulation section): the claim of consistent superiority and robustness across iteration counts, layer depths and Hamiltonian steps is stated without tabulated success probabilities, approximation ratios or direct head-to-head metrics against standard QAOA, so the performance ordering cannot be verified from the presented evidence.
minor comments (1)
  1. [Abstract] The abstract states that the method 'outperforms traditional methods such as QAOA' but supplies no numerical values or baseline definitions; moving the quantitative comparison into the abstract or adding a summary table would improve clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments. We address each major comment below and will revise the manuscript accordingly to improve the presentation of quantitative results.

read point-by-point responses

  1. Referee: [Hardware experiment] Hardware experiment (final results section): the assertion that the CD-mixer ansatz 'achieves high accuracy and a high likelihood of success' on the 10-item 1dBPP instance rests on a single hardware execution whose shot count, success probability, variance and comparison to the other two ansatze are not reported; without these data the observed outcome cannot be distinguished from finite-shot noise or post-selection effects.

    Authors: We agree that the hardware results would be strengthened by reporting the shot count, success probability, variance, and direct comparisons to the other ansatze. In the revised manuscript we will add these quantitative details from the 10-item execution to allow readers to assess the outcome against finite-shot statistics. revision: yes

  2. Referee: [Numerical results] Numerical results (simulation section): the claim of consistent superiority and robustness across iteration counts, layer depths and Hamiltonian steps is stated without tabulated success probabilities, approximation ratios or direct head-to-head metrics against standard QAOA, so the performance ordering cannot be verified from the presented evidence.

    Authors: The simulation comparisons are shown via figures, but we concur that tabulated success probabilities and approximation ratios would enable direct verification. We will add such tables with head-to-head metrics against QAOA in the revised manuscript. revision: yes

Circularity Check

0 steps flagged

No circularity: claims rest on simulations and hardware benchmarks, not self-referential derivations

full rationale

The paper proposes three DC-QAOA ansatz variants for the 1dBPP and reports their performance via numerical simulations across iteration counts, layer depths, and Hamiltonian steps, plus a single hardware execution on a 10-item instance. No equations, uniqueness theorems, or ansatze are derived from self-citations or fitted parameters that are then relabeled as predictions. The central claim of CD-mixer superiority is presented as an empirical outcome of the experiments rather than a mathematical reduction to prior inputs. No load-bearing self-citation chains, self-definitional constructions, or renamed known results appear in the abstract or described structure. The work is self-contained against external benchmarks (exact solutions for the small instance) and does not invoke external uniqueness results to force its conclusions.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only access prevents identification of any free parameters, axioms, or invented entities; full text would be required to audit the Hamiltonian constructions and digitization steps.

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Reference graph

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