A four-player potential game for barren-plateau-aware quantum ansatz design

• URL: http://arxiv.org/abs/2604.21955v1
• Date: Thu, 23 Apr 2026 07:58:46 GMT
• Title: A four-player potential game for barren-plateau-aware quantum ansatz design
• Abstract summary: We cast the design of parameterized quantum circuits as a four-player potential game whose state is a circuit directed acyclic graph (DAG)<n>Per-player restricted action sets factorize the move space into append, remove, retype, and rewire operations; a block-coordinate $varepsilon-Nash residual $_textNash$ certifies that no single player can improve unilaterally.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We cast the design of parameterized quantum circuits as a four-player potential game whose state is a circuit directed acyclic graph (DAG) and whose players encode trainability, non-stabilizerness, task performance, and hardware cost. Per-player restricted action sets factorize the move space into append, remove, retype, and rewire operations; a block-coordinate $\varepsilon$-Nash residual $δ_\text{Nash}$ certifies that no single player can improve unilaterally. A single weight sweep on MaxCut $K_4$ traces a Pareto frontier from a Clifford endpoint $(M_2/n,\langle H\rangle)=(0,4.00)$ to a non-Clifford endpoint $(0.48,3.30)$. On three four-qubit hardware topologies (heavy-hex, $2\times 2$ grid, Rydberg all-to-all), Nash search achieves the highest mean potential; on the $2\times 2$ grid Nash reaches the theoretical ceiling $Φ_\text{max}=4.10$ on two of five seeds while the simulated-annealing baseline does so on one; paired Wilcoxon tests over five seeds cannot reject the null on any single topology ($p\ge 0.22$). On LiH/STO-3G, seeding Nash from a 58-gate Givens-doubles ansatz produces a 48-operation, depth-25 circuit retaining $97.7\%$ of the correlation energy while simultaneously reducing gate count, increasing non-stabilizerness, and controlling trainability. The framework is complementary to energy-only searches such as ADAPT-VQE and k-UpCCGSD, which reach chemical accuracy with fewer operations but do not optimize the other three axes.

Related papers

• Quantum Circuit for General Unitary: Improved T-count via Block Flattening and Dilation [9.242453412591354]
  We present a Clifford+$T$ quantum circuit construction that implements any classically specified unitary to within error $$.<n>The key innovation lies in treating the target unitary as a single block-encoded object rather than a long product of simpler operations.
  arXiv  Detail & Related papers  (2026-08-18T14:43:22Z)
• Analytical Landscape of Maximal Magic for Two-Qutrit States and Beyond [39.447454043481464]
  We investigate entanglement and magic in systems of two qutrits and two ququints.<n>For the lower frontier, we recast the minimal magic as a compact function of concurrence and negativity.<n>For the upper frontier, we determine the maximal stabilizer Rényi to be $M = ln(81/17) approx 1.561$.<n>The maximum magic is achieved eighteen distinct maxima categorized into three families of six permutation-equivalent spectra.
  arXiv  Detail & Related papers  (2026-07-08T09:31:18Z)
• Expressibility, Noise, and Error Mitigation in VQE Ansatz Selection [0.0]
  Expressibility, a metric quantifying a circuit's ability to explore the Hilbert space, has been proposed as a guide for ansatz selection.<n>We extend this investigation to cover both $H$ and $H_3+$ under four execution scenarios: ideal, noisy, and noisy with zero-noise extrapolation (ZNE) or error cancellation (PEC)<n>ZNE reduces error for only 4 of 12 $H$ circuits and 4 of 6 $H_3+$ circuits, while PEC actually increases error in 11 of 12 $H$ circuits and all 6 $H_3+$
  arXiv  Detail & Related papers  (2026-06-03T14:43:24Z)
• Toward Magnetic-Field-Free Quantum Computing and Quantum Reservoir Computing in Engineered Organic Materials: A Unified Framework from the 3-Layer Quantum Brain Hypothesis [0.0]
  We extend the spin-vortex-induced loop-current (SVILC) qubit to engineered organic materials operated without any applied magnetic field.<n>Four paths are proposed: (P1) a flavin--nitroxide radical-pair reservoir, (P2) a perchlorotriphenylmethyl (PTM) radical array in a covalent organic framework, and (P4) a Su-Schrieffer--Heeger soliton on trans-polyacetylene.
  arXiv  Detail & Related papers  (2026-04-22T09:12:12Z)
• Quantum-Enhanced Single-Parameter Phase Estimation with Adaptive NOON States [0.0]
  NOON states-maximally path-entangled $N$-photon superpositions $(|N,0rangle + |0,Nrangle)/sqrt2$.<n>We present an end-to-end differentiable quantum-optical framework.
  arXiv  Detail & Related papers  (2026-04-14T05:55:58Z)
• Blind Catalytic Quantum Error Correction: Target-State Estimation and Fidelity Recovery Without \textit{A Priori} Knowledge [0.0]
  We introduce emphblind CQEC, which estimates the target from the noisy output alone before catalytic recovery.<n>Five estimation strategies are benchmarked across three noise models.
  arXiv  Detail & Related papers  (2026-04-13T08:27:08Z)
• IsoQuant: Hardware-Aligned SO(4) Isoclinic Rotations for LLM KV Cache Compression [0.4496256885343706]
  We propose a blockwise rotation framework based on quaternion algebra and the isoclinic decomposition of $SO(4)$.<n>IsoQuant achieves mean kernel-level speedups of $4.5times$--$4.7times$ over RotorQuant with peak speedups above $6times$.
  arXiv  Detail & Related papers  (2026-03-30T13:37:45Z)
• Reducing T Gates with Unitary Synthesis [0.41873449350124814]
  This work presents a novel FT synthesis algorithm that directly synthesizes arbitrary single-qubit unitaries.<n>By leveraging tensor network-based search, our approach enables native $U3$ synthesis, reducing the $T$ count, Clifford gate count, and approximation error.
  arXiv  Detail & Related papers  (2025-03-20T04:53:54Z)
• Far from Perfect: Quantum Error Correction with (Hyperinvariant) Evenbly Codes [38.729065908701585]
  We introduce a new class of qubit codes that we call Evenbly codes.<n>Our work indicates that Evenbly codes may show promise for practical quantum computing applications.
  arXiv  Detail & Related papers  (2024-07-16T17:18:13Z)
• Towards large-scale quantum optimization solvers with few qubits [59.63282173947468]
  We introduce a variational quantum solver for optimizations over $m=mathcalO(nk)$ binary variables using only $n$ qubits, with tunable $k>1$. We analytically prove that the specific qubit-efficient encoding brings in a super-polynomial mitigation of barren plateaus as a built-in feature.
  arXiv  Detail & Related papers  (2024-01-17T18:59:38Z)
• Can We Find Nash Equilibria at a Linear Rate in Markov Games? [95.10091348976779]
  We study decentralized learning in two-player zero-sum discounted Markov games. The goal is to design a policy optimization algorithm for either agent satisfying two properties.
  arXiv  Detail & Related papers  (2023-03-03T02:40:26Z)
• Minimax-Optimal Multi-Agent RL in Zero-Sum Markov Games With a Generative Model [50.38446482252857]
  Two-player zero-sum Markov games are arguably the most basic setting in multi-agent reinforcement learning. We develop a learning algorithm that learns an $varepsilon$-approximate Markov NE policy using $$ widetildeObigg. We derive a refined regret bound for FTRL that makes explicit the role of variance-type quantities.
  arXiv  Detail & Related papers  (2022-08-22T17:24:55Z)
• Quantum double aspects of surface code models [77.34726150561087]
  We revisit the Kitaev model for fault tolerant quantum computing on a square lattice with underlying quantum double $D(G)$ symmetry. We show how our constructions generalise to $D(H)$ models based on a finite-dimensional Hopf algebra $H$.
  arXiv  Detail & Related papers  (2021-06-25T17:03:38Z)
• Almost Optimal Algorithms for Two-player Markov Games with Linear Function Approximation [92.99933928528797]
  We study reinforcement learning for two-player zero-sum Markov games with simultaneous moves. We propose an algorithm Nash-UCRL-VTR based on the principle "Optimism-in-Face-of-Uncertainty" We show that Nash-UCRL-VTR can provably achieve an $tildeO(dHsqrtT)$ regret, where $d$ is the linear function dimension.
  arXiv  Detail & Related papers  (2021-02-15T09:09:16Z)
• Quantum Algorithms for Simulating the Lattice Schwinger Model [63.18141027763459]
  We give scalable, explicit digital quantum algorithms to simulate the lattice Schwinger model in both NISQ and fault-tolerant settings. In lattice units, we find a Schwinger model on $N/2$ physical sites with coupling constant $x-1/2$ and electric field cutoff $x-1/2Lambda$. We estimate observables which we cost in both the NISQ and fault-tolerant settings by assuming a simple target observable---the mean pair density.
  arXiv  Detail & Related papers  (2020-02-25T19:18:36Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.