Exponential quantum space advantage for Shannon entropy estimation in data streams

• URL: http://arxiv.org/abs/2604.18014v1
• Date: Mon, 20 Apr 2026 09:37:19 GMT
• Title: Exponential quantum space advantage for Shannon entropy estimation in data streams
• Abstract summary: Near-term quantum devices with limited qubits motivate the study of space-bounded quantum computation in the data stream model.<n>We show that Shannon entropy estimation exhibits an exponential separation between quantum and classical space complexity in this setting.
• Score: 4.740331063526406
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Near-term quantum devices with limited qubits motivate the study of space-bounded quantum computation in the data stream model. We show that Shannon entropy estimation exhibits an exponential separation between quantum and classical space complexity in this setting. Technically, we develop a two-stage quantum streaming algorithm based on a quantum procedure with an explicitly constructed oracle derived from the streaming input. This algorithm achieves logarithmic space complexity in the accuracy parameter, whereas any classical streaming algorithm requires polynomial space. In sharp contrast, existing results for Shannon entropy estimation in the quantum query model achieve only a quadratic speedup. Our work establishes a natural problem with practical applications in computer networking that admits an exponential quantum space advantage, revealing a fundamental gap between quantum query complexity and streaming space complexity.

Related papers

• Realization of a Quantum Streaming Algorithm on Long-lived Trapped-ion Qubits [2.886955168147019]
  In this work, we realize a data-streaming model using a trapped-ion quantum computer with long-lived qubits that communicate with an external server.<n>We show that the quantum space advantage persists even with the overheads of fault-tolerance.
  arXiv  Detail & Related papers  (2025-11-05T18:16:21Z)
• Quantum smoothed particle hydrodynamics algorithm inspired by quantum walks [0.0]
  We propose a quantum algorithm for the time-dependent smoothed particle hydrodynamics (SPH) method.<n>Our algorithm uses concepts from discrete-time quantum walks to solve the one-dimensional advection partial differential equation.<n>We construct a quantum circuit to carry out the calculations for a two-particle system over one, two and three timesteps.
  arXiv  Detail & Related papers  (2025-03-07T13:09:33Z)
• Efficient Learning for Linear Properties of Bounded-Gate Quantum Circuits [62.46800898243033]
  Recent progress in quantum learning theory prompts a question: can linear properties of a large-qubit circuit be efficiently learned from measurement data generated by varying classical inputs?<n>We prove that the sample complexity scaling linearly in $d$ is required to achieve a small prediction error, while the corresponding computational complexity may scale exponentially in d.<n>We propose a kernel-based method leveraging classical shadows and truncated trigonometric expansions, enabling a controllable trade-off between prediction accuracy and computational overhead.
  arXiv  Detail & Related papers  (2024-08-22T08:21:28Z)
• 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)
• Digital quantum simulator for the time-dependent Dirac equation using discrete-time quantum walks [0.7036032466145112]
  We introduce a quantum algorithm for simulating the time-dependent Dirac equation in 3+1 dimensions using discrete-time quantum walks. Our findings indicate that relativistic dynamics is achievable with quantum computers.
  arXiv  Detail & Related papers  (2023-05-31T05:36:57Z)
• Hybrid quantum gap estimation algorithm using a filtered time series [0.0]
  We prove that classical post-processing, i.e., long-time filtering of an offline time series, exponentially improves the circuit depth needed for quantum time evolution. We apply the filtering method to the construction of a hybrid quantum-classical algorithm to estimate energy gap. Our findings set the stage for unbiased quantum simulation to offer memory advantage in the near term.
  arXiv  Detail & Related papers  (2022-12-28T18:59:59Z)
• Saturation and recurrence of quantum complexity in random local quantum dynamics [5.803309695504831]
  Quantum complexity is a measure of the minimal number of elementary operations required to prepare a given state or unitary channel. Brown and Susskind conjectured that the complexity of a chaotic quantum system grows linearly in time up to times exponential in the system size, saturating at a maximal value, and remaining maximally complex until undergoing recurrences at doubly-exponential times.
  arXiv  Detail & Related papers  (2022-05-19T17:42:31Z)
• Preparing random states and benchmarking with many-body quantum chaos [48.044162981804526]
  We show how to predict and experimentally observe the emergence of random state ensembles naturally under time-independent Hamiltonian dynamics. The observed random ensembles emerge from projective measurements and are intimately linked to universal correlations built up between subsystems of a larger quantum system. Our work has implications for understanding randomness in quantum dynamics, and enables applications of this concept in a wider context.
  arXiv  Detail & Related papers  (2021-03-05T08:32:43Z)
• Imaginary Time Propagation on a Quantum Chip [50.591267188664666]
  Evolution in imaginary time is a prominent technique for finding the ground state of quantum many-body systems. We propose an algorithm to implement imaginary time propagation on a quantum computer.
  arXiv  Detail & Related papers  (2021-02-24T12:48:00Z)
• Continuous-time dynamics and error scaling of noisy highly-entangling quantum circuits [58.720142291102135]
  We simulate a noisy quantum Fourier transform processor with up to 21 qubits. We take into account microscopic dissipative processes rather than relying on digital error models. We show that depending on the dissipative mechanisms at play, the choice of input state has a strong impact on the performance of the quantum algorithm.
  arXiv  Detail & Related papers  (2021-02-08T14:55:44Z)
• Information Scrambling in Computationally Complex Quantum Circuits [56.22772134614514]
  We experimentally investigate the dynamics of quantum scrambling on a 53-qubit quantum processor. We show that while operator spreading is captured by an efficient classical model, operator entanglement requires exponentially scaled computational resources to simulate.
  arXiv  Detail & Related papers  (2021-01-21T22:18:49Z)
• 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.