Quantum resources in Harrow-Hassidim-Lloyd algorithm

• URL: http://arxiv.org/abs/2308.04021v2
• Date: Wed, 24 Jul 2024 08:06:04 GMT
• Title: Quantum resources in Harrow-Hassidim-Lloyd algorithm
• Authors: Pradeep Kumar, Tanoy Kanti Konar, Leela Ganesh Chandra Lakkaraju, Aditi Sen De,
• Abstract summary: We prove that nonvanishing quantum correlations, both bipartite and genuine multipartite entanglement, are required for solving nontrivial linear systems of equations. We find a nonvanishing l1-norm quantum coherence of the entire system and the register qubit which turns out to be related to the success probability of the algorithm.
• Score: 1.4605137432098108
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum algorithms have the ability to reduce runtime for executing tasks beyond the capabilities of classical algorithms. Therefore, identifying the resources responsible for quantum advantages is an interesting endeavour. We prove that nonvanishing quantum correlations, both bipartite and genuine multipartite entanglement, are required for solving nontrivial linear systems of equations in the Harrow-Hassidim-Lloyd (HHL) algorithm. Moreover, we find a nonvanishing l1-norm quantum coherence of the entire system and the register qubit which turns out to be related to the success probability of the algorithm. Quantitative analysis of the quantum resources reveals that while a significant amount of bipartite entanglement is generated in each step and required for this algorithm, multipartite entanglement content is inversely proportional to the performance indicator. In addition, we report that when imperfections chosen from Gaussian distribution are incorporated in controlled rotations, multipartite entanglement increases with the strength of the disorder, albeit error also increases while bipartite entanglement and coherence decreases, confirming the beneficial role of bipartite entanglement and coherence in this algorithm.

Related papers

• The Algorithm for Solving Quantum Linear Systems of Equations With Coherent Superposition and Its Extended Applications [8.8400072344375]
  We propose two quantum algorithms for solving quantum linear systems of equations with coherent superposition. The two quantum algorithms can both compute the rank and general solution by one measurement. Our analysis indicates that the proposed algorithms are mainly suitable for conducting attacks against lightweight symmetric ciphers.
  arXiv  Detail & Related papers  (2024-05-11T03:03:14Z)
• Quantum Subroutine for Variance Estimation: Algorithmic Design and Applications [80.04533958880862]
  Quantum computing sets the foundation for new ways of designing algorithms. New challenges arise concerning which field quantum speedup can be achieved. Looking for the design of quantum subroutines that are more efficient than their classical counterpart poses solid pillars to new powerful quantum algorithms.
  arXiv  Detail & Related papers  (2024-02-26T09:32:07Z)
• Calibrating the role of entanglement in variational quantum circuits [0.6435156676256051]
  Entanglement is a key property of quantum computing that separates it from its classical counterpart. We systematically probe the role of entanglement in the working of two variational quantum algorithms. We find that for the MAX-CUT problem solved using QAOA, the fidelity as a function of entanglement is highly dependent on the number of layers. In the case of QNNs, trained circuits with high test accuracies are underpinned by higher entanglement, with any enforced limitation in entanglement resulting in a sharp decline in test accuracy.
  arXiv  Detail & Related papers  (2023-10-16T23:36:40Z)
• Error Analysis of the Variational Quantum Eigensolver Algorithm [0.18188255328029254]
  We study variational quantum eigensolver (VQE) and its individual quantum subroutines. We show through explicit simulation that the VQE algorithm effectively collapses already when single errors occur during a quantum processing call.
  arXiv  Detail & Related papers  (2023-01-18T02:02:30Z)
• Quantum Worst-Case to Average-Case Reductions for All Linear Problems [66.65497337069792]
  We study the problem of designing worst-case to average-case reductions for quantum algorithms. We provide an explicit and efficient transformation of quantum algorithms that are only correct on a small fraction of their inputs into ones that are correct on all inputs.
  arXiv  Detail & Related papers  (2022-12-06T22:01:49Z)
• Entanglement and coherence in Bernstein-Vazirani algorithm [58.720142291102135]
  Bernstein-Vazirani algorithm allows one to determine a bit string encoded into an oracle. We analyze in detail the quantum resources in the Bernstein-Vazirani algorithm. We show that in the absence of entanglement, the performance of the algorithm is directly related to the amount of quantum coherence in the initial state.
  arXiv  Detail & Related papers  (2022-05-26T20:32:36Z)
• Improved Quantum Algorithms for Fidelity Estimation [77.34726150561087]
  We develop new and efficient quantum algorithms for fidelity estimation with provable performance guarantees. Our algorithms use advanced quantum linear algebra techniques, such as the quantum singular value transformation. We prove that fidelity estimation to any non-trivial constant additive accuracy is hard in general.
  arXiv  Detail & Related papers  (2022-03-30T02:02:16Z)
• Efficient Bipartite Entanglement Detection Scheme with a Quantum Adversarial Solver [89.80359585967642]
  Proposal reformulates the bipartite entanglement detection as a two-player zero-sum game completed by parameterized quantum circuits. We experimentally implement our protocol on a linear optical network and exhibit its effectiveness to accomplish the bipartite entanglement detection for 5-qubit quantum pure states and 2-qubit quantum mixed states.
  arXiv  Detail & Related papers  (2022-03-15T09:46:45Z)
• Quantum amplitude damping for solving homogeneous linear differential equations: A noninterferometric algorithm [0.0]
  This work proposes a novel approach by using the Quantum Amplitude Damping operation as a resource, in order to construct an efficient quantum algorithm for solving homogeneous LDEs. We show that such an open quantum system-inspired circuitry allows for constructing the real exponential terms in the solution in a non-interferometric.
  arXiv  Detail & Related papers  (2021-11-10T11:25:32Z)
• Detailed Account of Complexity for Implementation of Some Gate-Based Quantum Algorithms [55.41644538483948]
  In particular, some steps of the implementation, as state preparation and readout processes, can surpass the complexity aspects of the algorithm itself. We present the complexity involved in the full implementation of quantum algorithms for solving linear systems of equations and linear system of differential equations.
  arXiv  Detail & Related papers  (2021-06-23T16:33:33Z)
• Resource-efficient encoding algorithm for variational bosonic quantum simulations [0.0]
  In the Noisy Intermediate Scale Quantum (NISQ) era of quantum computing, quantum resources are limited. We present a resource-efficient quantum algorithm for bosonic ground and excited state computations.
  arXiv  Detail & Related papers  (2021-02-23T19:00:05Z)

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.