Noise-induced shallow circuits and absence of barren plateaus

• URL: http://arxiv.org/abs/2403.13927v2
• Date: Thu, 10 Oct 2024 17:00:14 GMT
• Title: Noise-induced shallow circuits and absence of barren plateaus
• Authors: Antonio Anna Mele, Armando Angrisani, Soumik Ghosh, Sumeet Khatri, Jens Eisert, Daniel Stilck França, Yihui Quek,
• Abstract summary: We show that any noise truncates' most quantum circuits to effectively logarithmic depth. We then prove that quantum circuits under any non-unital noise exhibit lack of barren plateaus for cost functions composed of local observables.
• Score: 2.5295633594332334
• License:
• Abstract: Motivated by realistic hardware considerations of the pre-fault-tolerant era, we comprehensively study the impact of uncorrected noise on quantum circuits. We first show that any noise `truncates' most quantum circuits to effectively logarithmic depth, in the task of estimating observable expectation values. We then prove that quantum circuits under any non-unital noise exhibit lack of barren plateaus for cost functions composed of local observables. But, by leveraging the effective shallowness, we also design an efficient classical algorithm to estimate observable expectation values within any constant additive accuracy, with high probability over the choice of the circuit, in any circuit architecture. The runtime of the algorithm is independent of circuit depth, and for any inverse-polynomial target accuracy, it operates in polynomial time in the number of qubits for one-dimensional architectures and quasi-polynomial time for higher-dimensional ones. Taken together, our results showcase that, unless we carefully engineer the circuits to take advantage of the noise, it is unlikely that noisy quantum circuits are preferable over shallow quantum circuits for algorithms that output observable expectation value estimates, like many variational quantum machine learning proposals. Moreover, we anticipate that our work could provide valuable insights into the fundamental open question about the complexity of sampling from (possibly non-unital) noisy random circuits.

Related papers

• A polynomial-time classical algorithm for noisy quantum circuits [1.2708457954150887]
  We provide a-time classical algorithm for noisy quantum circuits. Our approach is based upon the intuition that noise exponentially damps non-local correlations. For constant noise rates, any quantum circuit for which error mitigation is efficient on most input states, is also classically simulable on most input states.
  arXiv  Detail & Related papers  (2024-07-17T17:48:39Z)
• Noise-tolerant learnability of shallow quantum circuits from statistics and the cost of quantum pseudorandomness [0.0]
  We prove the natural robustness of quantum statistical queries for learning quantum processes. We adapt a learning algorithm for constant-depth quantum circuits to the quantum statistical query setting. We show the hardness of the quantum threshold search problem from quantum statistical queries.
  arXiv  Detail & Related papers  (2024-05-20T14:55:20Z)
• Power Characterization of Noisy Quantum Kernels [52.47151453259434]
  We show that noise may make quantum kernel methods to only have poor prediction capability, even when the generalization error is small. We provide a crucial warning to employ noisy quantum kernel methods for quantum computation.
  arXiv  Detail & Related papers  (2024-01-31T01:02:16Z)
• QuantumSEA: In-Time Sparse Exploration for Noise Adaptive Quantum Circuits [82.50620782471485]
  QuantumSEA is an in-time sparse exploration for noise-adaptive quantum circuits. It aims to achieve two key objectives: (1) implicit circuits capacity during training and (2) noise robustness. Our method establishes state-of-the-art results with only half the number of quantum gates and 2x time saving of circuit executions.
  arXiv  Detail & Related papers  (2024-01-10T22:33:00Z)
• Robust Quantum Gates against Correlated Noise in Integrated Quantum Chips [11.364693110852738]
  We report the experimental realization of robust quantum gates in superconducting quantum circuits. Our work provides a versatile toolbox for achieving noise-resilient complex quantum circuits.
  arXiv  Detail & Related papers  (2024-01-03T16:12:35Z)
• Quantum circuit debugging and sensitivity analysis via local inversions [62.997667081978825]
  We present a technique that pinpoints the sections of a quantum circuit that affect the circuit output the most. We demonstrate the practicality and efficacy of the proposed technique by applying it to example algorithmic circuits implemented on IBM quantum machines.
  arXiv  Detail & Related papers  (2022-04-12T19:39:31Z)
• Limitations of variational quantum algorithms: a quantum optimal transport approach [11.202435939275675]
  We obtain extremely tight bounds for standard NISQ proposals in both the noisy and noiseless regimes. The bounds limit the performance of both circuit model algorithms, such as QAOA, and also continuous-time algorithms, such as quantum annealing.
  arXiv  Detail & Related papers  (2022-04-07T13:58:44Z)
• Gaussian initializations help deep variational quantum circuits escape from the barren plateau [87.04438831673063]
  Variational quantum circuits have been widely employed in quantum simulation and quantum machine learning in recent years. However, quantum circuits with random structures have poor trainability due to the exponentially vanishing gradient with respect to the circuit depth and the qubit number. This result leads to a general belief that deep quantum circuits will not be feasible for practical tasks.
  arXiv  Detail & Related papers  (2022-03-17T15:06:40Z)
• Probabilistic error cancellation with sparse Pauli-Lindblad models on noisy quantum processors [0.7299729677753102]
  We present a protocol for learning and inverting a sparse noise model that is able to capture correlated noise and scales to large quantum devices. These advances allow us to demonstrate PEC on a superconducting quantum processor with crosstalk errors.
  arXiv  Detail & Related papers  (2022-01-24T18:40:43Z)
• Quantum circuit architecture search for variational quantum algorithms [88.71725630554758]
  We propose a resource and runtime efficient scheme termed quantum architecture search (QAS) QAS automatically seeks a near-optimal ansatz to balance benefits and side-effects brought by adding more noisy quantum gates. We implement QAS on both the numerical simulator and real quantum hardware, via the IBM cloud, to accomplish data classification and quantum chemistry tasks.
  arXiv  Detail & Related papers  (2020-10-20T12:06:27Z)
• Boundaries of quantum supremacy via random circuit sampling [69.16452769334367]
  Google's recent quantum supremacy experiment heralded a transition point where quantum computing performed a computational task, random circuit sampling. We examine the constraints of the observed quantum runtime advantage in a larger number of qubits and gates.
  arXiv  Detail & Related papers  (2020-05-05T20:11:53Z)

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.