Amplitude amplification and estimation require inverses

• URL: http://arxiv.org/abs/2507.23787v1
• Date: Thu, 31 Jul 2025 17:59:59 GMT
• Title: Amplitude amplification and estimation require inverses
• Authors: Ewin Tang, John Wright,
• Abstract summary: generic quantum speedups for brute-force search and counting only hold when the process we apply them to can be efficiently inverted.<n>We give problem instances based on trace estimation where no algorithm which uses only $U$ beats the naive, quadratically slower approach.<n>Our result suggests a dichotomy: without inverse access, quantum speedups are scarce; with it, quantum speedups abound.
• Score: 3.084918555654188
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We prove that the generic quantum speedups for brute-force search and counting only hold when the process we apply them to can be efficiently inverted. The algorithms speeding up these problems, amplitude amplification and amplitude estimation, assume the ability to apply a state preparation unitary $U$ and its inverse $U^\dagger$; we give problem instances based on trace estimation where no algorithm which uses only $U$ beats the naive, quadratically slower approach. Our proof of this is simple and goes through the compressed oracle method introduced by Zhandry. Since these two subroutines are responsible for the ubiquity of the quadratic "Grover" speedup in quantum algorithms, our result explains why such speedups are far harder to come by in the settings of quantum learning, metrology, and sensing. In these settings, $U$ models the evolution of an experimental system, so implementing $U^\dagger$ can be much harder -- tantamount to reversing time within the system. Our result suggests a dichotomy: without inverse access, quantum speedups are scarce; with it, quantum speedups abound.

Related papers

• Augmenting Simulated Noisy Quantum Data Collection by Orders of Magnitude Using Pre-Trajectory Sampling with Batched Execution [47.60253809426628]
  We present the Pre-Trajectory Sampling technique, increasing efficiency and utility of trajectory simulations by tailoring error types.<n>We generate massive datasets of one trillion and one million shots, respectively.
  arXiv  Detail & Related papers  (2025-04-22T22:36:18Z)
• Space-Efficient Quantum Error Reduction without log Factors [50.10645865330582]
  We present a new highly simplified construction of a purifier, that can be understood as a weighted walk on a line similar to a random walk interpretation of majority voting.<n>Our purifier has exponentially better space complexity than the previous one, and quadratically better dependence on the soundness-completeness gap of the algorithm being purified.
  arXiv  Detail & Related papers  (2025-02-13T12:04:39Z)
• Towards Entropic Constraints on Quantum Speedups [0.0]
  Some quantum algorithms have "quantum speedups": improved time complexity as compared with the best-known classical algorithms for solving the same tasks. Can we understand what fuels these speedups from an entropic perspective? Information theory gives us a multitude of metrics we might choose from to measure how fundamentally 'quantum' is the behavior of a quantum computer running an algorithm.
  arXiv  Detail & Related papers  (2024-11-05T19:00:04Z)
• Demonstrating real-time and low-latency quantum error correction with superconducting qubits [52.08698178354922]
  We demonstrate low-latency feedback with a scalable FPGA decoder integrated into a superconducting quantum processor. We observe logical error suppression as the number of decoding rounds is increased. The decoder throughput and latency developed in this work, combined with continued device improvements, unlock the next generation of experiments.
  arXiv  Detail & Related papers  (2024-10-07T17:07:18Z)
• Global Phase Helps in Quantum Search: Yet Another Look at the Welded Tree Problem [55.80819771134007]
  In this paper, we give a short proof of the optimal linear hitting time for a welded tree problem by a discrete-time quantum walk. The same technique can be applied to other 1-dimensional hierarchical graphs.
  arXiv  Detail & Related papers  (2024-04-30T11:45:49Z)
• Demonstration of Algorithmic Quantum Speedup for an Abelian Hidden Subgroup Problem [0.0]
  Simon's problem is to find a hidden period encoded into an unknown 2-to-1 function.<n>We demonstrate an algorithmic quantum speedup for a variant of Simon's problem where the hidden period has a restricted Hamming weight $w$.
  arXiv  Detail & Related papers  (2024-01-15T19:52:31Z)
• Non-Linear Transformations of Quantum Amplitudes: Exponential Improvement, Generalization, and Applications [0.0]
  Quantum algorithms manipulate the amplitudes of quantum states to find solutions to computational problems. We present a framework for applying a general class of non-linear functions to the amplitudes of quantum states. Our work provides an important and efficient building block with potentially numerous applications in areas such as optimization, state preparation, quantum chemistry, and machine learning.
  arXiv  Detail & Related papers  (2023-09-18T14:57:21Z)
• Grover Speedup from Many Forms of the Zeno Effect [0.0]
  We show that other manifestations of the Zeno effect can support an optimal speedup in a physically realistic model. We group these algorithms into three families to facilitate a structured understanding of how speedups can be obtained.
  arXiv  Detail & Related papers  (2023-05-18T17:40:32Z)
• Quantum Computing Provides Exponential Regret Improvement in Episodic Reinforcement Learning [35.11103784048256]
  We propose an textitUpper Confidence Bound (UCB) based quantum algorithmic framework to facilitate learning of a finite-horizon MDP. Our quantum algorithm achieves an exponential improvement in regret as compared to the classical counterparts.
  arXiv  Detail & Related papers  (2023-02-16T23:01:27Z)
• One-Way Ticket to Las Vegas and the Quantum Adversary [78.33558762484924]
  We show that quantum Las Vegas query complexity is exactly equal to the quantum adversary bound. This is achieved by transforming a feasible solution to the adversary inversion problem into a quantum query algorithm.
  arXiv  Detail & Related papers  (2023-01-05T11:05:22Z)
• Quantum State Preparation with Optimal Circuit Depth: Implementations and Applications [10.436969366019015]
  We show that any $Theta(n)$-depth circuit can be prepared with a $Theta(log(nd)) with $O(ndlog d)$ ancillary qubits. We discuss applications of the results in different quantum computing tasks, such as Hamiltonian simulation, solving linear systems of equations, and realizing quantum random access memories.
  arXiv  Detail & Related papers  (2022-01-27T13:16:30Z)
• Quantum speedup for track reconstruction in particle accelerators [51.00143435208596]
  We identify four fundamental routines present in every local tracking method and analyse how they scale in the context of a standard tracking algorithm. Although the found quantum speedups are mild, this constitutes to the best of our knowledge, the first rigorous evidence of a quantum advantage for a high-energy physics data processing task.
  arXiv  Detail & Related papers  (2021-04-23T13:32:14Z)
• Quantum Gram-Schmidt Processes and Their Application to Efficient State Read-out for Quantum Algorithms [87.04438831673063]
  We present an efficient read-out protocol that yields the classical vector form of the generated state. Our protocol suits the case that the output state lies in the row space of the input matrix. One of our technical tools is an efficient quantum algorithm for performing the Gram-Schmidt orthonormal procedure.
  arXiv  Detail & Related papers  (2020-04-14T11:05:26Z)

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.