Distributed quantum algorithm for divergence estimation and beyond

• URL: http://arxiv.org/abs/2503.09431v1
• Date: Wed, 12 Mar 2025 14:28:22 GMT
• Title: Distributed quantum algorithm for divergence estimation and beyond
• Authors: Honglin Chen, Wei Xie, Yingqi Yu, Hao Fu, Xiang-Yang Li,
• Abstract summary: We propose a distributed quantum algorithm framework to compute $rm Tr(f(A)g(B))$ within an additive error $varepsilon$.<n>This framework holds broad applicability across a range of distributed quantum computing tasks.
• Score: 16.651306526783564
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: With the rapid advancement of quantum information technology, designing efficient distributed quantum algorithms to perform various information processing tasks remains challenging. In this paper, we consider a distributed scenario where two parties, Alice and Bob, given access to matrices $A$ and $B$ respectively, aim to estimate ${\rm Tr}(f(A)g(B))$, where $f$ and $g$ are known functions. In this task, only local quantum operations, classical communication and single-qubit measurements are allowed due to the high cost of quantum communication and entangled measurements. We propose a distributed quantum algorithm framework to compute ${\rm Tr}(f(A)g(B))$ within an additive error $\varepsilon$. The proposed algorithm framework requires $\widetilde{O}\left(d^2 / (\delta \varepsilon^2)\right)$ quantum queries and two-qubit gates, assuming that the minimum singular value of each matrix $A, B \in \mathbb{C}^{d \times d}$ is at least $\delta$. Additionally, our algorithm framework uses a simple Hadamard test architecture, enabling easier quantum hardware implementation. This algorithm framework allows for various applications including quantum divergence estimation, distributed solving of linear system, and distributed Hamiltonian simulation, while preserving the privacy of both parties. Furthermore, we establish a lower bound of $\Omega\left(\max\left\{1 /\varepsilon^2, \sqrt{dr}/\varepsilon\right\}\right)$ on the query complexity for the task, where $r$ denotes the rank of the input matrices. We believe this framework holds broad applicability across a range of distributed quantum computing tasks.

Related papers

• Matrix encoding method in variational quantum singular value decomposition [49.494595696663524]
  Conditional measurement is involved to avoid small success probability in ancilla measurement. The objective function for the algorithm can be obtained probabilistically via measurement of the state of a one-qubit subsystem.
  arXiv  Detail & Related papers  (2025-03-19T07:01:38Z)
• Entanglement-Assisted Coding for Arbitrary Linear Computations Over a Quantum MAC [34.32444379837011]
  We study a linear computation problem over a quantum multiple access channel (LC-QMAC)<n>We propose an achievable scheme for LC-QMAC based on the stabilizer formalism and the ideas from entanglement-assisted quantum error-correcting codes (EAQECC)
  arXiv  Detail & Related papers  (2025-01-27T18:35:33Z)
• Resource-efficient algorithm for estimating the trace of quantum state powers [1.5133368155322298]
  Estimating the trace of quantum state powers, $textTr(rhok)$, for $k$ identical quantum states is a fundamental task.<n>We introduce an algorithm that requires only $mathcalO(tilder)$ qubits and $mathcalO(tilder)$ multi-qubit gates.<n>We extend our algorithm to the estimation of $textTr(rhok)$ for arbitrary observables and $textTr(rhok)
  arXiv  Detail & Related papers  (2024-08-01T06:23:52Z)
• Quantum hashing algorithm implementation [0.0]
  We implement a quantum hashing algorithm which is based on a fingerprinting technique presented by Ambainis and Frievalds, 1988, on gate-based quantum computers. We consider 16-qubit and 27-qubit IBMQ computers with the special graphs of qubits representing nearest neighbor architecture that is not Linear Nearest Neighbor (LNN) one.
  arXiv  Detail & Related papers  (2024-07-14T09:41:16Z)
• A Novel Quantum-Classical Hybrid Algorithm for Determining Eigenstate Energies in Quantum Systems [1.9714447272714082]
  This paper presents a novel quantum algorithm, XZ24, for efficiently computing the eigen-energy spectra of arbitrary quantum systems. XZ24 has three key advantages: It removes the need for eigenstate preparation, requiring only a reference state with non-negligible overlap. It enables simultaneous computation of multiple eigen-energies, depending on the reference state.
  arXiv  Detail & Related papers  (2024-06-01T04:31:43Z)
• Calculating response functions of coupled oscillators using quantum phase estimation [40.31060267062305]
  We study the problem of estimating frequency response functions of systems of coupled, classical harmonic oscillators using a quantum computer. Our proposed quantum algorithm operates in the standard $s-sparse, oracle-based query access model. We show that a simple adaptation of our algorithm solves the random glued-trees problem in time.
  arXiv  Detail & Related papers  (2024-05-14T15:28:37Z)
• Linear gate bounds against natural functions for position-verification [0.0]
  A quantum position-verification scheme attempts to verify the spatial location of a prover.<n>We consider two well-studied position-verification schemes known as $f$-routing and $f$-BB84.
  arXiv  Detail & Related papers  (2024-02-28T19:00:10Z)
• Mind the $\tilde{\mathcal{O}}$: Asymptotically Better, but Still Impractical, Quantum Distributed Algorithms [0.0]
  We present two algorithms in the Quantum CONGEST-CLIQUE model of distributed computation that succeed with high probability. The algorithms achieve a lower round and message complexity than any known algorithms in the classical CONGEST-CLIQUE model. An existing framework for using distributed version of Grover's search algorithm to accelerate triangle finding lies at the core of the speedup.
  arXiv  Detail & Related papers  (2023-04-06T02:18:52Z)
• A Quantum Algorithm Framework for Discrete Probability Distributions with Applications to Rényi Entropy Estimation [13.810917492304565]
  We propose a unified quantum algorithm framework for estimating properties of discrete probability distributions. Our framework estimates $alpha$-R'enyi entropy $H_alpha(p)$ to within additive error $epsilon$ with probability at least $2/3$.
  arXiv  Detail & Related papers  (2022-12-03T08:01:55Z)
• Quantum Goemans-Williamson Algorithm with the Hadamard Test and Approximate Amplitude Constraints [62.72309460291971]
  We introduce a variational quantum algorithm for Goemans-Williamson algorithm that uses only $n+1$ qubits. Efficient optimization is achieved by encoding the objective matrix as a properly parameterized unitary conditioned on an auxilary qubit. We demonstrate the effectiveness of our protocol by devising an efficient quantum implementation of the Goemans-Williamson algorithm for various NP-hard problems.
  arXiv  Detail & Related papers  (2022-06-30T03:15:23Z)
• Quantum Resources Required to Block-Encode a Matrix of Classical Data [56.508135743727934]
  We provide circuit-level implementations and resource estimates for several methods of block-encoding a dense $Ntimes N$ matrix of classical data to precision $epsilon$. We examine resource tradeoffs between the different approaches and explore implementations of two separate models of quantum random access memory (QRAM) Our results go beyond simple query complexity and provide a clear picture into the resource costs when large amounts of classical data are assumed to be accessible to quantum algorithms.
  arXiv  Detail & Related papers  (2022-06-07T18:00:01Z)
• Exponential separations between learning with and without quantum memory [17.763817187554096]
  We study the power of quantum memory for learning properties of quantum systems and dynamics. Many state-of-the-art learning algorithms require access to an additional external quantum memory. We show that this trade-off is inherent in a wide range of learning problems.
  arXiv  Detail & Related papers  (2021-11-10T19:03:49Z)
• Halving the cost of quantum multiplexed rotations [0.0]
  We improve the number of $T$ gates needed for a $b$-bit approximation of a multiplexed quantum gate with $c$ controls. Our results roughly halve the cost of state-of-art electronic structure simulations based on qubitization of double-factorized or tensor-hypercontracted representations.
  arXiv  Detail & Related papers  (2021-10-26T06:49:44Z)
• Towards Tight Communication Lower Bounds for Distributed Optimisation [30.134447658488057]
  We consider a standard distributed optimisation setting where $N$ machines aim to jointly minimise the sum of the functions $sum_i = 1N f_i (x)$. Our main result provides the first fully unconditional bounds on total number of bits which need to be sent and received by the $N$ machines. We show that $Omega( Nd log d / Nvarepsilon)$ total bits need to be communicated between the machines to find an additive $epsilon$-approximation to the minimum of $sum_i = 1N
  arXiv  Detail & Related papers  (2020-10-16T08:10:02Z)
• Emulating Quantum Interference with Generalized Ising Machines [0.0]
  This paper presents an exact and general procedure for mapping any sequence of quantum gates onto a network of probabilistic p-bits. We can view this structure as a Boltzmann machine whose states each represent a Feynman path leading from an initial configuration of qubits to a final configuration. Our results for mapping an arbitrary quantum circuit to a Boltzmann machine with a complex energy function should help push the boundaries of the simulability of quantum circuits with probabilistic resources.
  arXiv  Detail & Related papers  (2020-07-14T22:10:29Z)
• 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.