Partitioned Quantum Subspace Expansion

• URL: http://arxiv.org/abs/2403.08868v2
• Date: Mon, 18 Mar 2024 04:58:15 GMT
• Title: Partitioned Quantum Subspace Expansion
• Authors: Tom O'Leary, Lewis W. Anderson, Dieter Jaksch, Martin Kiffner,
• Abstract summary: We present an iterative generalisation of the quantum subspace expansion algorithm used with a Krylov basis. By exchanging quantum circuit depth for additional measurements the quantum subspace expansion algorithm appears to be an approach suited to near term or early error-corrected quantum hardware.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We present an iterative generalisation of the quantum subspace expansion algorithm used with a Krylov basis. The iterative construction connects a sequence of subspaces via their lowest energy states. Diagonalising a Hamiltonian in a given Krylov subspace requires the same quantum resources in both the single step and sequential cases. We propose a variance-based criterion for determining a good iterative sequence and provide numerical evidence that these good sequences display improved numerical stability over a single step in the presence of finite sampling noise. Implementing the generalisation requires additional classical processing with a polynomial overhead in the subspace dimension. By exchanging quantum circuit depth for additional measurements the quantum subspace expansion algorithm appears to be an approach suited to near term or early error-corrected quantum hardware. Our work suggests that the numerical instability limiting the accuracy of this approach can be substantially alleviated beyond the current state of the art.

Related papers

• Estimating quantum amplitudes can be exponentially improved [11.282486674587236]
  Estimating quantum amplitudes is a fundamental task in quantum computing. We present a novel framework for estimating quantum amplitudes by transforming pure states into their matrix forms. Our framework achieves the standard quantum limit $epsilon-2$ and the Heisenberg limit $epsilon-1$, respectively.
  arXiv  Detail & Related papers  (2024-08-25T04:35:53Z)
• Bias-field digitized counterdiabatic quantum optimization [39.58317527488534]
  We call this protocol bias-field digitizeddiabatic quantum optimization (BF-DCQO) Our purely quantum approach eliminates the dependency on classical variational quantum algorithms. It achieves scaling improvements in ground state success probabilities, increasing by up to two orders of magnitude.
  arXiv  Detail & Related papers  (2024-05-22T18:11:42Z)
• Characterizing randomness in parameterized quantum circuits through expressibility and average entanglement [39.58317527488534]
  Quantum Circuits (PQCs) are still not fully understood outside the scope of their principal application. We analyse the generation of random states in PQCs under restrictions on the qubits connectivities. We place a connection between how steep is the increase on the uniformity of the distribution of the generated states and the generation of entanglement.
  arXiv  Detail & Related papers  (2024-05-03T17:32:55Z)
• A circuit-generated quantum subspace algorithm for the variational quantum eigensolver [0.0]
  We propose combining quantum subspace techniques with the variational quantum eigensolver (VQE) In our approach, the parameterized quantum circuit is divided into a series of smaller subcircuits. The sequential application of these subcircuits to an initial state generates a set of wavefunctions that we use as a quantum subspace to obtain high-accuracy groundstate energies.
  arXiv  Detail & Related papers  (2024-04-09T18:00:01Z)
• Quantum Computing and Tensor Networks for Laminate Design: A Novel Approach to Stacking Sequence Retrieval [1.6421520075844793]
  A prime example is the weight optimization of laminated composite materials, which to this day remains a formidable problem. The rapidly developing field of quantum computation may offer novel approaches for addressing these intricate problems.
  arXiv  Detail & Related papers  (2024-02-09T15:01:56Z)
• 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)
• Analyzing Prospects for Quantum Advantage in Topological Data Analysis [35.423446067065576]
  We analyze and optimize an improved quantum algorithm for topological data analysis. We show that super-quadratic quantum speedups are only possible when targeting a multiplicative error approximation. We argue that quantum circuits with tens of billions of Toffoli can solve seemingly classically intractable instances.
  arXiv  Detail & Related papers  (2022-09-27T17:56:15Z)
• Quantum Davidson Algorithm for Excited States [42.666709382892265]
  We introduce the quantum Krylov subspace (QKS) method to address both ground and excited states. By using the residues of eigenstates to expand the Krylov subspace, we formulate a compact subspace that aligns closely with the exact solutions. Using quantum simulators, we employ the novel QDavidson algorithm to delve into the excited state properties of various systems.
  arXiv  Detail & Related papers  (2022-04-22T15:03:03Z)
• Quantum algorithms for grid-based variational time evolution [36.136619420474766]
  We propose a variational quantum algorithm for performing quantum dynamics in first quantization. Our simulations exhibit the previously observed numerical instabilities of variational time propagation approaches.
  arXiv  Detail & Related papers  (2022-03-04T19:00:45Z)
• Quantum Krylov subspace algorithms for ground and excited state energy estimation [0.0]
  Quantum Krylov subspace diagonalization (QKSD) algorithms provide a low-cost alternative to the conventional quantum phase estimation algorithm. We show that a wide class of Hamiltonians relevant to condensed matter physics and quantum chemistry contain symmetries that can be exploited to avoid the use of the Hadamard test. We develop a unified theory of quantum Krylov subspace algorithms and present three new quantum-classical algorithms for the ground and excited-state energy estimation problems.
  arXiv  Detail & Related papers  (2021-09-14T17:56:53Z)
• Quantum computing critical exponents [0.0]
  We show that the Variational Quantum-Classical Simulation algorithm admits a finite circuit depth scaling collapse when targeting the critical point of the transverse field Ising chain. The order parameter only collapses on one side of the transition due to a slowdown of the quantum algorithm when crossing the phase transition.
  arXiv  Detail & Related papers  (2021-04-02T17:38:20Z)

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.