Towards a Linear-Ramp QAOA protocol: Evidence of a scaling advantage in solving some combinatorial optimization problems

• URL: http://arxiv.org/abs/2405.09169v3
• Date: Mon, 04 Aug 2025 14:10:48 GMT
• Title: Towards a Linear-Ramp QAOA protocol: Evidence of a scaling advantage in solving some combinatorial optimization problems
• Abstract summary: We show that linear ramp QAOA can efficiently approximate optimal solutions across diverse optimization problems.<n>We show results of LR-QAOA on multiple QPUs with up to $N_q = 109$ qubits, $p=100$, and circuits requiring 21,200 CNOT gates.
• Score: 0.46040036610482665
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The Quantum Approximate Optimization Algorithm (QAOA) is a promising algorithm for solving combinatorial optimization problems (COPs), with performance governed by variational parameters $\{\gamma_i, \beta_i\}_{i=0}^{p-1}$. While most prior work has focused on classically optimizing these parameters, we demonstrate that fixed linear ramp schedules, linear ramp QAOA (LR-QAOA), can efficiently approximate optimal solutions across diverse COPs. Simulations with up to $N_q=42$ qubits and $p=400$ layers suggest that the success probability scales as $P(x^*) \approx 2^{-\eta(p) N_q + C}$, where $\eta(p)$ decreases with increasing $p$. For example, in Weighted Maxcut instances, $\eta(10) = 0.22$ improves to $\eta(100) = 0.05$. Comparisons with classical algorithms, including simulated annealing, Tabu Search, and branch-and-bound, show a scaling advantage for LR-QAOA. We show results of LR-QAOA on multiple QPUs (IonQ, Quantinuum, IBM) with up to $N_q = 109$ qubits, $p=100$, and circuits requiring 21,200 CNOT gates. Finally, we present a noise model based on two-qubit gate counts that accurately reproduces the experimental behavior of LR-QAOA.

Related papers

• Offline Channel-Independent QAOA Angles for RIS Power Aggregation: Unit-Circle Phase Dictionaries and Infinite-Size Spin-Glass Limits [0.0]
  We introduce a $2M$-phase $$ dictionary for optimizing power on reconfigurable surfaces.<n>We observe performance reaching a near-optimal multi-start single-flip local-search reference for $N!le!16$ under order-2 modeling.<n>The approach suggests a route to near-optimal large-$N$ performance on future fault-tolerant (FTQ) quantum computers.
  arXiv  Detail & Related papers  (2026-06-23T13:07:10Z)
• Near-Optimal Parameter Tuning of Level-1 QAOA for Ising Models [3.390330377512402]
  We show how to reduce the two-dimensional $(gamma, beta)$ search to a one-dimensional search over $gamma$, with $beta*$ computed analytically.<n>This approach is validated using Recursive QAOA (RQAOA), where it consistently outperforms both coarsely optimised RQAOA and semidefinite programs.
  arXiv  Detail & Related papers  (2025-01-27T19:00:00Z)
• An Adaptive Mixer Allocation Algorithm for the Quantum Alternating Operator Ansatz [2.7704630812545474]
  We propose the adaptive mixer allocation algorithm (AMA) to solve constrained optimization problems. AMA significantly reduces the resource consumption, achieving only $34.08%$ ($29.77%$) of QAOA+ circuit depth and $15.05%$ ($18.72%$) of the number of CNOT gates, respectively.
  arXiv  Detail & Related papers  (2024-12-27T12:43:36Z)
• A Multilevel Approach For Solving Large-Scale QUBO Problems With Noisy Hybrid Quantum Approximate Optimization [3.3493770627144004]
  We experimentally test how existing quantum processing units (QPUs) perform as subsolvers within a multilevel strategy. We find approximate solutions to $10$ instances of fully connected $82$-qubit Sherrington-Kirkpatrick graphs. We observe that quantum optimization results are competitive regarding the quality of solutions compared to classicals.
  arXiv  Detail & Related papers  (2024-08-14T20:06:32Z)
• Nearly Minimax Optimal Regret for Learning Linear Mixture Stochastic Shortest Path [80.60592344361073]
  We study the Shortest Path (SSP) problem with a linear mixture transition kernel. An agent repeatedly interacts with a environment and seeks to reach certain goal state while minimizing the cumulative cost. Existing works often assume a strictly positive lower bound of the iteration cost function or an upper bound of the expected length for the optimal policy.
  arXiv  Detail & Related papers  (2024-02-14T07:52:00Z)
• Transfer learning of optimal QAOA parameters in combinatorial optimization [0.46040036610482665]
  We study the transfer learning (TL) methodology to reuse pre-trained QAOA parameters of one problem instance into different COP instances. In this work, we select small cases of the traveling salesman problem (TSP), the bin packing problem (BPP), the knapsack problem (KP), the weighted maximum cut (MaxCut) problem, and portfolio optimization (PO) We show that cross-platform TL is possible using the D-Wave Advantage quantum annealer with the parameters found for BPP.
  arXiv  Detail & Related papers  (2024-02-08T10:35:23Z)
• 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)
• An Oblivious Stochastic Composite Optimization Algorithm for Eigenvalue Optimization Problems [76.2042837251496]
  We introduce two oblivious mirror descent algorithms based on a complementary composite setting. Remarkably, both algorithms work without prior knowledge of the Lipschitz constant or smoothness of the objective function. We show how to extend our framework to scale and demonstrate the efficiency and robustness of our methods on large scale semidefinite programs.
  arXiv  Detail & Related papers  (2023-06-30T08:34:29Z)
• Near-Optimal Non-Convex Stochastic Optimization under Generalized Smoothness [21.865728815935665]
  Two recent works established the $O(epsilon-3)$ sample complexity to obtain an $O(epsilon)$-stationary point. However, both require a large batch size on the order of $mathrmploy(epsilon-1)$, which is not only computationally burdensome but also unsuitable for streaming applications. In this work, we solve the prior two problems simultaneously by revisiting a simple variant of the STORM algorithm.
  arXiv  Detail & Related papers  (2023-02-13T00:22:28Z)
• Mind the gap: Achieving a super-Grover quantum speedup by jumping to the end [114.3957763744719]
  We present a quantum algorithm that has rigorous runtime guarantees for several families of binary optimization problems. We show that the algorithm finds the optimal solution in time $O*(2(0.5-c)n)$ for an $n$-independent constant $c$. We also show that for a large fraction of random instances from the $k$-spin model and for any fully satisfiable or slightly frustrated $k$-CSP formula, statement (a) is the case.
  arXiv  Detail & Related papers  (2022-12-03T02:45:23Z)
• QAOA-in-QAOA: solving large-scale MaxCut problems on small quantum machines [81.4597482536073]
  Quantum approximate optimization algorithms (QAOAs) utilize the power of quantum machines and inherit the spirit of adiabatic evolution. We propose QAOA-in-QAOA ($textQAOA2$) to solve arbitrary large-scale MaxCut problems using quantum machines. Our method can be seamlessly embedded into other advanced strategies to enhance the capability of QAOAs in large-scale optimization problems.
  arXiv  Detail & Related papers  (2022-05-24T03:49:10Z)
• Nearly Minimax Optimal Reinforcement Learning for Linear Mixture Markov Decision Processes [91.38793800392108]
  We study reinforcement learning with linear function approximation where the underlying transition probability kernel of the Markov decision process (MDP) is a linear mixture model. We propose a new, computationally efficient algorithm with linear function approximation named $textUCRL-VTR+$ for the aforementioned linear mixture MDPs. To the best of our knowledge, these are the first computationally efficient, nearly minimax optimal algorithms for RL with linear function approximation.
  arXiv  Detail & Related papers  (2020-12-15T18:56:46Z)
• Practical and Parallelizable Algorithms for Non-Monotone Submodular Maximization with Size Constraint [20.104148319012854]
  We present and parallelizable for a submodular function, not necessarily a monotone, with respect to a size constraint. We improve the best approximation factor achieved by an algorithm that has optimal adaptivity and nearly optimal complexity query to $0.193 - varepsilon$.
  arXiv  Detail & Related papers  (2020-09-03T22:43:55Z)
• Convergence of Sparse Variational Inference in Gaussian Processes Regression [29.636483122130027]
  We show that a method with an overall computational cost of $mathcalO(log N)2D(loglog N)2)$ can be used to perform inference.
  arXiv  Detail & Related papers  (2020-08-01T19:23:34Z)
• Streaming Complexity of SVMs [110.63976030971106]
  We study the space complexity of solving the bias-regularized SVM problem in the streaming model. We show that for both problems, for dimensions of $frac1lambdaepsilon$, one can obtain streaming algorithms with spacely smaller than $frac1lambdaepsilon$.
  arXiv  Detail & Related papers  (2020-07-07T17:10:00Z)
• FANOK: Knockoffs in Linear Time [73.5154025911318]
  We describe a series of algorithms that efficiently implement Gaussian model-X knockoffs to control the false discovery rate on large scale feature selection problems. We test our methods on problems with $p$ as large as $500,000$.
  arXiv  Detail & Related papers  (2020-06-15T21:55:34Z)

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.