Classical algorithms for measurement-adaptive Gaussian circuits

• URL: http://arxiv.org/abs/2509.00746v1
• Date: Sun, 31 Aug 2025 08:39:58 GMT
• Title: Classical algorithms for measurement-adaptive Gaussian circuits
• Authors: Changhun Oh, Youngrong Lim,
• Abstract summary: We study the quantum mean-value problem, estimating observable expectation values that underpin simulation and variational algorithms.<n>We analyze bosonic circuits with adaptivity and prove that when the number of adaptive measurements is small, the mean-value problem admits efficient classical algorithms.
• Score: 0.1909808926064466
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Gaussian building blocks are essential for photonic quantum information processing, and universality can be practically achieved by equipping Gaussian circuits with adaptive measurement and feedforward. The number of adaptive steps then provides a natural parameter for computational power. Rather than assessing power only through sampling problems -- the usual benchmark -- we follow the ongoing shift toward tasks of practical relevance and study the quantum mean-value problem, i.e., estimating observable expectation values that underpin simulation and variational algorithms. More specifically, we analyze bosonic circuits with adaptivity and prove that when the number of adaptive measurements is small, the mean-value problem admits efficient classical algorithms even if a large amount of non-Gaussian resources are present in the input state, whereas less constrained regimes are computationally hard. This yields a task-level contrast with sampling, where non-Gaussian ingredients alone often induce hardness, and provides a clean complexity boundary parameterized by the number of adaptive measurement-and-feedforward steps between classical simulability and quantum advantage. Beyond the main result, we introduce classical techniques -- including a generalization of Gurvits's second algorithm to arbitrary product inputs and Gaussian circuits -- for computing the marginal quantities needed by our estimators, which may be of independent interest.

Related papers

• A Posteriori Certification Framework for Generalized Quantum Arimoto-Blahut Algorithms [41.15017547767954]
  We introduce an a posteriori certification viewpoint for the generalized quantum Arimoto-Blahut (QAB) algorithm.<n>We prove a global convergence theorem showing that, under convexity and a substantially weaker numerically verifiable condition, the QAB iteration converges to the global minimizer.<n>As an application, we develop a certified iterative scheme for computing the quantum relative entropy of channels.
  arXiv  Detail & Related papers  (2026-01-14T09:10:41Z)
• Measurement-driven Quantum Approximate Optimization [2.5514179157254877]
  A recently proposed method makes use of ancilla qubits and controlled unitary operators to implement weak measurements related to imaginary-time evolution.<n>We first generalize the algorithm from exact to approximate optimization, taking advantage of several properties unique to classical problems.<n>We show how to adapt our paradigm to the setting of constrained optimization for a number of important classes of hard problem constraints.
  arXiv  Detail & Related papers  (2025-12-24T08:27:32Z)
• Quantum Approximate Optimization Algorithm for MIMO with Quantized b-bit Beamforming [47.98440449939344]
  Multiple-input multiple-output (MIMO) is critical for 6G communication, offering improved spectral efficiency and reliability.<n>This paper explores the use of the Quantum Approximate Optimization Algorithm (QAOA) and alternating optimization to address the problem of b-bit quantized phase shifters both at the transmitter and the receiver.<n>We demonstrate that the structure of this quantized beamforming problem aligns naturally with hybrid-classical methods like QAOA, as the phase shifts used in beamforming can be directly mapped to rotation gates in a quantum circuit.
  arXiv  Detail & Related papers  (2025-10-07T17:53:02Z)
• Universal Quantum Error Mitigation via Random Inverse Depolarizing Approximation [45.88028371034407]
  We introduce RIDA (Random Inverse Depolarizing Approximation), a simple universal method that harnesses randomly generated circuits to estimate a given circuit's global depolarization probability and corresponding error-free expectation value.<n> Numerical tests indicate RIDA outperforms key benchmarks, suggestive of significant accuracy improvements for applications of quantum computing across fields including physics and chemistry.
  arXiv  Detail & Related papers  (2025-08-24T20:30:08Z)
• Efficient Learning for Linear Properties of Bounded-Gate Quantum Circuits [63.733312560668274]
  Given a quantum circuit containing d tunable RZ gates and G-d Clifford gates, can a learner perform purely classical inference to efficiently predict its linear properties? We prove that the sample complexity scaling linearly in d is necessary and sufficient to achieve a small prediction error, while the corresponding computational complexity may scale exponentially in d. We devise a kernel-based learning model capable of trading off prediction error and computational complexity, transitioning from exponential to scaling in many practical settings.
  arXiv  Detail & Related papers  (2024-08-22T08:21:28Z)
• 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)
• Measurement-Based Quantum Approximate Optimization [0.24861619769660645]
  We focus on measurement-based quantum computing protocols for approximate optimization. We derive measurement patterns for applying QAOA to the broad and important class of QUBO problems. We discuss the resource requirements and tradeoffs of our approach to that of more traditional quantum circuits.
  arXiv  Detail & Related papers  (2024-03-18T06:59:23Z)
• Hybrid algorithm simulating non-equilibrium steady states of an open quantum system [10.752869788647802]
  Non-equilibrium steady states are a focal point of research in the study of open quantum systems. Previous variational algorithms for searching these steady states have suffered from resource-intensive implementations. We present a novel variational quantum algorithm that efficiently searches for non-equilibrium steady states by simulating the operator-sum form of the Lindblad equation.
  arXiv  Detail & Related papers  (2023-09-13T01:57:27Z)
• Randomized semi-quantum matrix processing [0.0]
  We present a hybrid quantum-classical framework for simulating generic matrix functions. The method is based on randomization over the Chebyshev approximation of the target function. We prove advantages on average depths, including quadratic speed-ups on costly parameters.
  arXiv  Detail & Related papers  (2023-07-21T18:00:28Z)
• End-to-end resource analysis for quantum interior point methods and portfolio optimization [63.4863637315163]
  We provide a complete quantum circuit-level description of the algorithm from problem input to problem output. We report the number of logical qubits and the quantity/depth of non-Clifford T-gates needed to run the algorithm.
  arXiv  Detail & Related papers  (2022-11-22T18:54:48Z)
• Automatic and effective discovery of quantum kernels [41.61572387137452]
  Quantum computing can empower machine learning models by enabling kernel machines to leverage quantum kernels for representing similarity measures between data.<n>We present an approach to this problem, which employs optimization techniques, similar to those used in neural architecture search and AutoML.<n>The results obtained by testing our approach on a high-energy physics problem demonstrate that, in the best-case scenario, we can either match or improve testing accuracy with respect to the manual design approach.
  arXiv  Detail & Related papers  (2022-09-22T16:42:14Z)
• Generalization Metrics for Practical Quantum Advantage in Generative Models [68.8204255655161]
  Generative modeling is a widely accepted natural use case for quantum computers. We construct a simple and unambiguous approach to probe practical quantum advantage for generative modeling by measuring the algorithm's generalization performance. Our simulation results show that our quantum-inspired models have up to a $68 times$ enhancement in generating unseen unique and valid samples.
  arXiv  Detail & Related papers  (2022-01-21T16:35:35Z)
• Quantum machine learning with adaptive linear optics [0.0]
  We study supervised learning algorithms in which a quantum device is used to perform a computational subroutine. We design implementations of these quantum subroutines using Boson Sampling architectures in linear optics, supplemented by adaptive measurements.
  arXiv  Detail & Related papers  (2021-02-08T23:56:49Z)
• Efficient classical simulation and benchmarking of quantum processes in the Weyl basis [0.0]
  We develop a randomized benchmarking algorithm which uses Weyl unitaries to efficiently identify and learn a mixture of error models. We apply our methods to ansatz circuits that appear in the Variational Quantum Eigensolver.
  arXiv  Detail & Related papers  (2020-08-27T16:46:12Z)

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.