Separations in query complexity for total search problems

• URL: http://arxiv.org/abs/2410.16245v1
• Date: Mon, 21 Oct 2024 17:51:24 GMT
• Title: Separations in query complexity for total search problems
• Authors: Shalev Ben-David, Srijita Kundu,
• Abstract summary: We study the query complexity analogue of the class TFNP of total search problems. We give a way to convert partial functions to total search problems under certain settings. We also give a way to convert search problems back into partial functions.
• Score: 0.0
• License:
• Abstract: We study the query complexity analogue of the class TFNP of total search problems. We give a way to convert partial functions to total search problems under certain settings; we also give a way to convert search problems back into partial functions. As an application, we give new separations for degree-like measures. We give an exponential separation between quantum query complexity and approximate degree for a total search problem. We also give an exponential separation between approximate degree and the positive quantum adversary for a total search problem. We then strengthen the former separation to upper bound a larger measure: the two-sided approximate non-negative degree, also called the conical junta degree. This measure is often larger than quantum query complexity and even a separation from randomized query complexity was not known. We extend our results to communication complexity, and obtain an exponential separation between quantum information complexity and the relaxed partition bound for a total search problem. Even a weaker separation between randomized communication complexity and the relaxed partition bound was not known for total search problems (or even for partial functions). Most of our separations for total search problems can be converted to separations for partial functions. Using this, we reprove the recent exponential separation between quantum query complexity and approximate degree for a partial function by Ambainis and Belovs (2023), among other new results.

Related papers

• Taming Quantum Time Complexity [45.867051459785976]
  We show how to achieve both exactness and thriftiness in the setting of time complexity. We employ a novel approach to the design of quantum algorithms based on what we call transducers.
  arXiv  Detail & Related papers  (2023-11-27T14:45:19Z)
• The Complexity of Being Entangled [0.0]
  Nielsen's approach to quantum state complexity relates the minimal number of quantum gates required to prepare a state to the length of geodesics computed with a certain norm on the manifold of unitary transformations. For a bipartite system, we investigate binding complexity, which corresponds to norms in which gates acting on a single subsystem are free of cost.
  arXiv  Detail & Related papers  (2023-11-07T19:00:02Z)
• Information-Computation Tradeoffs for Learning Margin Halfspaces with Random Classification Noise [50.64137465792738]
  We study the problem of PAC $gamma$-margin halfspaces with Random Classification Noise. We establish an information-computation tradeoff suggesting an inherent gap between the sample complexity of the problem and the sample complexity of computationally efficient algorithms.
  arXiv  Detail & Related papers  (2023-06-28T16:33:39Z)
• An Exponential Separation Between Quantum Query Complexity and the Polynomial Degree [79.43134049617873]
  In this paper, we demonstrate an exponential separation between exact degree and approximate quantum query for a partial function. For an alphabet size, we have a constant versus separation complexity.
  arXiv  Detail & Related papers  (2023-01-22T22:08:28Z)
• Circuit Complexity through phase transitions: consequences in quantum state preparation [0.0]
  We analyze the circuit complexity for preparing ground states of quantum many-body systems. In particular, how this complexity grows as the ground state approaches a quantum phase transition.
  arXiv  Detail & Related papers  (2023-01-11T19:00:10Z)
• A Closer Look at Branch Classifiers of Multi-exit Architectures [103.27533521196817]
  Constant-complexity branching keeps all branches the same, while complexity-increasing and complexity-decreasing branching place more complex branches later or earlier in the backbone respectively. We investigate a cause by using knowledge consistency to probe the effect of adding branches onto a backbone. Our findings show that complexity-decreasing branching yields the least disruption to the feature abstraction hierarchy of the backbone.
  arXiv  Detail & Related papers  (2022-04-28T08:37:25Z)
• On query complexity measures and their relations for symmetric functions [0.0]
  We show how to give lower bounds on quantum query complexity using Boolean and adversary methods. We also look at the quantum query complexity of Gap Majority, a partial symmetric function. We show how large certificate complexity and block sensitivity can be as compared to sensitivity for symmetric functions.
  arXiv  Detail & Related papers  (2021-10-25T02:55:39Z)
• Forster Decomposition and Learning Halfspaces with Noise [60.691817861402676]
  A Forster transform is an operation that turns a distribution into one with good anti-concentration properties. We show that any distribution can be decomposed efficiently as a disjoint mixture of few distributions for which a Forster transform exists and can be computed efficiently.
  arXiv  Detail & Related papers  (2021-07-12T17:00:59Z)
• Sample-Efficient Reinforcement Learning of Undercomplete POMDPs [91.40308354344505]
  This work shows that these hardness barriers do not preclude efficient reinforcement learning for rich and interesting subclasses of Partially Observable Decision Processes (POMDPs) We present a sample-efficient algorithm, OOM-UCB, for episodic finite undercomplete POMDPs, where the number of observations is larger than the number of latent states and where exploration is essential for learning, thus distinguishing our results from prior works.
  arXiv  Detail & Related papers  (2020-06-22T17:58:54Z)
• Aspects of The First Law of Complexity [0.0]
  We investigate the first law of complexity proposed in arXiv:1903.04511, i.e., the variation of complexity when the target state is perturbed. Based on Nielsen's geometric approach to quantum circuit complexity, we find the variation only depends on the end of the optimal circuit.
  arXiv  Detail & Related papers  (2020-02-13T21:15:57Z)

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.