Partial oracles quantum algorithm framework -- Part I: Analysis of in-place operations

• URL: http://arxiv.org/abs/2604.21788v1
• Date: Thu, 23 Apr 2026 15:44:59 GMT
• Title: Partial oracles quantum algorithm framework -- Part I: Analysis of in-place operations
• Abstract summary: We introduce a new type of transform, the reciprocal transform, which is applied to the oracle function.<n>We show that the reciprocal transform obeys a chain rule, which makes it possible to break down complex transforms into simple steps.<n>We also introduce the QFrame python library, which is used to automate the construction of quantum circuits that represent reciprocal transforms.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The partial oracles framework is a quantum search algorithm that has the potential to exceed the quadratic speedup of Grover's algorithm, up to a theoretical maximum of an exponential speedup. Until now, however, the framework has lacked an explicit method for constructing the operator that represents the search iteration. In this paper, we provide the missing construction, for the special case of an oracle function definable using only in-place operations (that is, where the calculated result of the oracle function can be read just from the qubits in the search index). The restriction to in-place operations means that the current work does not yet exhibit quantum advantage: oracle functions constructed using only in-place operations are always classically reversible. To demonstrate quantum advantage, it will be necessary to extend this construction method to include out-of-place operations (part II). As part of the construction of the search iteration operator, we define a new type of transform, the reciprocal transform, which is applied to the oracle function. We show that the reciprocal transform obeys a chain rule, which makes it possible to break down complex transforms into simple steps. To illustrate the practical application of this search method, we apply the reciprocal transform to elementary operations from the SHA-256 hash algorithm: addition modulo $2^n$, the $Maj(a, b, c)$ function, the $Ch(a, b, c)$ function, and the bit shift functions. We also introduce the QFrame python library, which is used to automate the construction of quantum circuits that represent reciprocal transforms.

Related papers

• Operator Learning for efficient Quantum Computation [0.0]
  An efficient implementation of quantum algorithms is often hindered by the lack of efficient primitives for operators and state preparation.<n>We propose a full-stack variational framework that transforms arbitrary operators to compact quantum circuits.<n>The framework is validated for both quantum mechanical and engineering applications.
  arXiv  Detail & Related papers  (2026-06-18T12:58:25Z)
• Efficient Complex-Valued State Preparation on Bucket Brigade QRAM [47.72095699729477]
  Efficient quantum state preparation is a critical component in quantum algorithms that process large classical data.<n>We present two improvements within the same architecture-aware framework.
  arXiv  Detail & Related papers  (2026-04-28T13:43:29Z)
• Improved quantum circuits for division [42.76841620787673]
  We develop new fault-tolerant quantum circuits for various integer division algorithms.<n> circuits achieve an up to 76.08% and 68.35% reduction in T-count and CNOT-count.
  arXiv  Detail & Related papers  (2026-03-18T13:41:43Z)
• Block encoding of sparse matrices with a periodic diagonal structure [67.45502291821956]
  We provide an explicit quantum circuit for block encoding a sparse matrix with a periodic diagonal structure.<n>Various applications for the presented methodology are discussed in the context of solving differential problems.
  arXiv  Detail & Related papers  (2026-02-11T07:24:33Z)
• A discrete Fourier transform based quantum circuit for modular multiplication in Shor's algorithm [0.0]
  We propose a quantum circuit for modular exponentiation.<n>The gate-complexity of our proposal is $O(L3)$ where L is the number of bits required to store the number being factorized.
  arXiv  Detail & Related papers  (2025-03-13T03:39:13Z)
• Simple Quantum Gradient Descent Without Coherent Oracle Access [0.0]
  We develop an alternative quantum framework for the gradient descent problem, based on the seminal quantum singular value transformation framework.<n>We show that given only classical information of function of interest, it is possible to construct a quantum gradient descent algorithm with a running time logarithmical in the number of variables.
  arXiv  Detail & Related papers  (2024-12-24T09:48:38Z)
• Geometric structure and transversal logic of quantum Reed-Muller codes [51.11215560140181]
  In this paper, we aim to characterize the gates of quantum Reed-Muller (RM) codes by exploiting the well-studied properties of their classical counterparts. A set of stabilizer generators for a RM code can be described via $X$ and $Z$ operators acting on subcubes of particular dimensions.
  arXiv  Detail & Related papers  (2024-10-10T04:07:24Z)
• Quantum One-Wayness of the Single-Round Sponge with Invertible Permutations [49.1574468325115]
  Sponge hashing is a widely used class of cryptographic hash algorithms.<n>Intrepid permutations have so far remained a fundamental open problem.<n>We show that finding zero-pairs in a random $2n$-bit permutation requires at least $Omega (2n/2)$ many queries.
  arXiv  Detail & Related papers  (2024-03-07T18:46:58Z)
• Quantum state preparation without coherent arithmetic [3.5707423185282665]
  We introduce a versatile method for preparing a quantum state whose amplitudes are given by some known function.magnitude existing approaches.<n>We use a template quantum eigenvalue transformation circuit to convert a low cost block encoding of the sine function into the desired function.
  arXiv  Detail & Related papers  (2022-10-26T17:48:31Z)
• Fourier-based quantum signal processing [0.0]
  Implementing general functions of operators is a powerful tool in quantum computation. Quantum signal processing is the state of the art for this aim. We present an algorithm for Hermitian-operator function design from an oracle given by the unitary evolution.
  arXiv  Detail & Related papers  (2022-06-06T18:02:30Z)
• Alternatives to a nonhomogeneous partial differential equation quantum algorithm [52.77024349608834]
  We propose a quantum algorithm for solving nonhomogeneous linear partial differential equations of the form $Apsi(textbfr)=f(textbfr)$. These achievements enable easier experimental implementation of the quantum algorithm based on nowadays technology.
  arXiv  Detail & Related papers  (2022-05-11T14:29:39Z)
• Interactive Protocols for Classically-Verifiable Quantum Advantage [46.093185827838035]
  "Interactions" between a prover and a verifier can bridge the gap between verifiability and implementation. We demonstrate the first implementation of an interactive quantum advantage protocol, using an ion trap quantum computer.
  arXiv  Detail & Related papers  (2021-12-09T19:00:00Z)

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.