Global Optimization for Parametrized Quantum Circuits

• URL: http://arxiv.org/abs/2603.21757v1
• Date: Mon, 23 Mar 2026 09:49:40 GMT
• Title: Global Optimization for Parametrized Quantum Circuits
• Abstract summary: We study the training of practical classes of quantum circuits with a constant number of trainable parameters.<n>Our main result is a fully randomized approximation scheme (FPRAS)<n>Unlike the standard hybrid quantum-classical training in variational algorithms, our approach separates the computation into two distinct stages.
• Score: 3.558201566667322
• License: http://creativecommons.org/licenses/by-sa/4.0/
• Abstract: In the absence of error correction, noisy intermediate-scale quantum devices are operated by training parametrized quantum circuits (PQCs) so as to minimize a suitable loss function. Finding the optimal parameters of those circuits is a hard optimization problem, where global guarantees are known only for highly structured cases of limited practical relevance, and first-order methods can fail to find even local minima due to the presence of barren plateaus. In this work, we study the training of practical classes of PQCs, namely polynomial-depth circuits with a constant number of trainable parameters. This captures widely used PQC families, including fixed-depth QAOA, hardware-efficient ansätze, and Fixed Parameter Count QAOA. Our main technical result is a fully polynomial randomized approximation scheme (FPRAS), which, for every $ε>0$, returns an $ε$-approximate solution to the problem's global optimum with high probability, and has runtime and query complexity polynomial in $1/ε$ and the number of qubits. Unlike the standard hybrid quantum-classical training loop in variational algorithms, where the quantum device is queried repeatedly throughout the training, our approach separates the computation into two distinct stages: (1) an initial quantum data-acquisition phase, followed by (2) a classical global-optimization phase based on the trigonometric moment/sum-of-squares hierarchies. Under a standard flat-extension condition, which can be checked numerically, the method also supports the extraction of optimal circuit parameters. The existence of an FPRAS implies that the promise problem associated with the optimization of poly-depth constant-parameter PQC is in BQP. This imposes a limitation on the expressive power of the class, namely, it cannot encode combinatorial optimization problems whose objective values are separated by an inverse-polynomial gap.

Related papers

• Quantum Approximate Optimization Algorithm with Fixed Number of Parameters [0.0]
  We introduce a novel quantum optimization paradigm: the Fixed--Count Approximate Quantum Optimization Algorithm (FPC-QAOA)<n>It is a scalable variational framework that maintains a constant number of trainable parameters regardless of the number of qubits, Hamiltonian complexity, or circuit depth.<n>We benchmark FPC-QAOA on random MaxCut instances and the Tail Assignment Problem, achieving performance comparable to or better than standard QAOA.
  arXiv  Detail & Related papers  (2025-12-24T14:02:31Z)
• Performance Guarantees for Quantum Neural Estimation of Entropies [31.955071410400947]
  Quantum neural estimators (QNEs) combine classical neural networks with parametrized quantum circuits.<n>We study formal guarantees for QNEs of measured relative entropies in the form of non-asymptotic error risk bounds.<n>Our theory aims to facilitate principled implementation of QNEs for measured relative entropies.
  arXiv  Detail & Related papers  (2025-11-24T16:36:06Z)
• Efficient QAOA Architecture for Solving Multi-Constrained Optimization Problems [3.757262277494307]
  This paper proposes a novel combination of constraint encoding methods for the Quantum Approximate Optimization Ansatz.<n>One-hot constraints are enforced through $XY$-mixers that restrict the search space to the feasible sub-space naturally.<n>Since $XY$-mixers restrict the search space, specific state vector entries are always zero and can be omitted from the simulation, saving valuable memory and computing resources.
  arXiv  Detail & Related papers  (2025-06-03T17:46:53Z)
• Interpolation-based coordinate descent method for parameterized quantum circuits [11.745089977547558]
  We propose an coordinate descent (ICD) method to address the parameter optimization problem in quantum circuits (PQCs)<n>ICD employs to approximate the PQC cost function, effectively recovering its underlying trigonometric structure, and then performs an argmin update on a single parameter in each iteration.<n>In contrast to previous studies on structure optimization, we determine the optimal nodes to mitigate statistical errors from quantum measurements.
  arXiv  Detail & Related papers  (2025-03-06T17:06:47Z)
• Characterizing randomness in parameterized quantum circuits through expressibility and average entanglement [39.58317527488534]
  Quantum Circuits (PQCs) are still not fully understood outside the scope of their principal application.<n>We analyse the generation of random states in PQCs under restrictions on the qubits connectivities.<n>We place a connection between how steep is the increase on the uniformity of the distribution of the generated states and the generation of entanglement.
  arXiv  Detail & Related papers  (2024-05-03T17:32:55Z)
• Bayesian Parameterized Quantum Circuit Optimization (BPQCO): A task and hardware-dependent approach [49.89480853499917]
  Variational quantum algorithms (VQA) have emerged as a promising quantum alternative for solving optimization and machine learning problems. In this paper, we experimentally demonstrate the influence of the circuit design on the performance obtained for two classification problems. We also study the degradation of the obtained circuits in the presence of noise when simulating real quantum computers.
  arXiv  Detail & Related papers  (2024-04-17T11:00:12Z)
• Approximate Quantum Compiling for Quantum Simulation: A Tensor Network based approach [1.237454174824584]
  We introduce AQCtensor, a novel algorithm to produce short-depth quantum circuits from Matrix Product States (MPS)<n>Our approach is specifically tailored to the preparation of quantum states generated from the time evolution of quantum many-body Hamiltonians.<n>For simulation problems on 100 qubits, we show that AQCtensor achieves at least an order of magnitude reduction in the depth of the resulting optimized circuit.
  arXiv  Detail & Related papers  (2023-01-20T14:40:29Z)
• Iteration Complexity of Variational Quantum Algorithms [5.203200173190989]
  We argue that noise makes evaluations of the objective function via quantum circuits biased. We derive the missing guarantees and find that the rate of convergence is unaffected.
  arXiv  Detail & Related papers  (2022-09-21T19:18:41Z)
• FLIP: A flexible initializer for arbitrarily-sized parametrized quantum circuits [105.54048699217668]
  We propose a FLexible Initializer for arbitrarily-sized Parametrized quantum circuits. FLIP can be applied to any family of PQCs, and instead of relying on a generic set of initial parameters, it is tailored to learn the structure of successful parameters. We illustrate the advantage of using FLIP in three scenarios: a family of problems with proven barren plateaus, PQC training to solve max-cut problem instances, and PQC training for finding the ground state energies of 1D Fermi-Hubbard models.
  arXiv  Detail & Related papers  (2021-03-15T17:38:33Z)
• Adaptive pruning-based optimization of parameterized quantum circuits [62.997667081978825]
  Variisy hybrid quantum-classical algorithms are powerful tools to maximize the use of Noisy Intermediate Scale Quantum devices. We propose a strategy for such ansatze used in variational quantum algorithms, which we call "Efficient Circuit Training" (PECT) Instead of optimizing all of the ansatz parameters at once, PECT launches a sequence of variational algorithms.
  arXiv  Detail & Related papers  (2020-10-01T18:14:11Z)
• Cross Entropy Hyperparameter Optimization for Constrained Problem Hamiltonians Applied to QAOA [68.11912614360878]
  Hybrid quantum-classical algorithms such as Quantum Approximate Optimization Algorithm (QAOA) are considered as one of the most encouraging approaches for taking advantage of near-term quantum computers in practical applications. Such algorithms are usually implemented in a variational form, combining a classical optimization method with a quantum machine to find good solutions to an optimization problem. In this study we apply a Cross-Entropy method to shape this landscape, which allows the classical parameter to find better parameters more easily and hence results in an improved performance.
  arXiv  Detail & Related papers  (2020-03-11T13:52:41Z)

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.