Quantum Parallelized Variational Quantum Eigensolvers for Excited States

• URL: http://arxiv.org/abs/2306.11844v1
• Date: Tue, 20 Jun 2023 18:53:09 GMT
• Title: Quantum Parallelized Variational Quantum Eigensolvers for Excited States
• Authors: Cheng-Lin Hong, Luis Colmenarez, Lexin Ding, Carlos L. Benavides-Riveros, Christian Schilling
• Abstract summary: Calculating excited-state properties of molecules and solids is one of the main computational challenges of modern electronic structure theory. By combining and advancing recent ideas from the field of quantum computing we propose a more effective variational quantum eigensolver.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Calculating excited-state properties of molecules and solids is one of the main computational challenges of modern electronic structure theory. By combining and advancing recent ideas from the field of quantum computing we propose a more effective variational quantum eigensolver based on quantum parallelism: Initial ans\"atze for various excited states are prepared into a single pure state through a minimal number of ancilla qubits. Then a global rotation in the targeted subspace is optimized. Our approach thus avoids the progressive accumulation of errors prone to schemes that calculate excited states successively. Energy gaps and transition amplitudes between eigenstates can immediately be extracted. Moreover, the use of variable auxiliary weights makes the algorithm more resilient to noise and greatly simplifies the optimization procedure. We showcase our algorithm and illustrate its effectiveness for different molecular systems. The interaction effects are treated through generalized unitary coupled cluster ans\"atze and, accordingly, the common unfavorable and artificial extension to the entire Fock space is circumvented.

Related papers

• A Unified Variational Framework for Quantum Excited States [2.935517095941649]
  We introduce a novel variational principle that overcomes limitations, enabling the textitsimultaneous determination of multiple low-energy excited states. We demonstrate the power and generality of this method across diverse physical systems and variational ansatzes. In all applications, the method accurately and simultaneously obtains multiple lowest-lying energy levels and their corresponding states.
  arXiv  Detail & Related papers  (2025-04-30T09:28:04Z)
• Universal Hamming Weight Preserving Variational Quantum Ansatz [48.982717105024385]
  Understanding variational quantum ans"atze is crucial for determining quantum advantage in Variational Quantum Eigensolvers (VQEs) This work highlights the critical role of symmetry-preserving ans"atze in VQE research, offering insights that extend beyond supremacy debates.
  arXiv  Detail & Related papers  (2024-12-06T07:42:20Z)
• Quantum Error Suppression with Subgroup Stabilisation [3.4719087457636792]
  Quantum state purification is the functionality that, given multiple copies of an unknown state, outputs a state with increased purity. We propose an effective state purification gadget with a moderate quantum overhead by projecting $M$ noisy quantum inputs to their subspace. Our method, applied in every short evolution over $M$ redundant copies of noisy states, can suppress both coherent and errors by a factor of $1/M$, respectively.
  arXiv  Detail & Related papers  (2024-04-15T17:51:47Z)
• Ground and Excited States from Ensemble Variational Principles [1.2289361708127877]
  We prove the validity of the underlying critical hypothesis: Whenever the ensemble energy is well-converged, the same holds true for the ensemble state. We derive linear bounds $d_-DeltaE_mathbfw leq Delta Q leq d_+ DeltaE_mathbfw$ on the errors $Delta Q $ of these sought-after quantities.
  arXiv  Detail & Related papers  (2024-01-22T16:39:52Z)
• Towards large-scale quantum optimization solvers with few qubits [59.63282173947468]
  We introduce a variational quantum solver for optimizations over $m=mathcalO(nk)$ binary variables using only $n$ qubits, with tunable $k>1$. We analytically prove that the specific qubit-efficient encoding brings in a super-polynomial mitigation of barren plateaus as a built-in feature.
  arXiv  Detail & Related papers  (2024-01-17T18:59:38Z)
• Quantum tomography of helicity states for general scattering processes [55.2480439325792]
  Quantum tomography has become an indispensable tool in order to compute the density matrix $rho$ of quantum systems in Physics. We present the theoretical framework for reconstructing the helicity quantum initial state of a general scattering process.
  arXiv  Detail & Related papers  (2023-10-16T21:23:42Z)
• Spectral Analysis of Product Formulas for Quantum Simulation [0.0]
  We show that the Trotter step size needed to estimate an energy eigenvalue within precision can be improved in scaling from $epsilon$ to $epsilon1/2$ for a large class of systems. Results partially generalize to diabatic processes, which remain in a narrow energy band separated from the rest of the spectrum by a gap.
  arXiv  Detail & Related papers  (2021-02-25T03:17:25Z)
• Bernstein-Greene-Kruskal approach for the quantum Vlasov equation [91.3755431537592]
  The one-dimensional stationary quantum Vlasov equation is analyzed using the energy as one of the dynamical variables. In the semiclassical case where quantum tunneling effects are small, an infinite series solution is developed.
  arXiv  Detail & Related papers  (2021-02-18T20:55:04Z)
• Tightening the Dependence on Horizon in the Sample Complexity of Q-Learning [59.71676469100807]
  This work sharpens the sample complexity of synchronous Q-learning to an order of $frac|mathcalS|| (1-gamma)4varepsilon2$ for any $0varepsilon 1$. Our finding unveils the effectiveness of vanilla Q-learning, which matches that of speedy Q-learning without requiring extra computation and storage.
  arXiv  Detail & Related papers  (2021-02-12T14:22:05Z)
• Analytic Characterization of the Hessian in Shallow ReLU Models: A Tale of Symmetry [9.695960412426672]
  We analytically characterize the Hessian at various families of spurious minima. In particular, we prove that for $dge k$ standard Gaussian inputs: (a) of the $dk$ eigenvalues of the Hessian, $dk - O(d)$ concentrate near zero, (b) $Omega(d)$ of the eigenvalues grow linearly with $k$.
  arXiv  Detail & Related papers  (2020-08-04T20:08:35Z)
• Quantum-optimal-control-inspired ansatz for variational quantum algorithms [105.54048699217668]
  A central component of variational quantum algorithms (VQA) is the state-preparation circuit, also known as ansatz or variational form. Here, we show that this approach is not always advantageous by introducing ans"atze that incorporate symmetry-breaking unitaries. This work constitutes a first step towards the development of a more general class of symmetry-breaking ans"atze with applications to physics and chemistry problems.
  arXiv  Detail & Related papers  (2020-08-03T18:00:05Z)
• Variational quantum eigensolvers by variance minimization [0.3093890460224435]
  Variational quantum eigensolver(VQE) typically minimizes energy with hybrid quantum-classical optimization. We propose a VQE by minimizing energy variance, which is called as variance-VQE(VVQE)
  arXiv  Detail & Related papers  (2020-06-29T02:44:37Z)
• Sample Complexity of Asynchronous Q-Learning: Sharper Analysis and Variance Reduction [63.41789556777387]
  Asynchronous Q-learning aims to learn the optimal action-value function (or Q-function) of a Markov decision process (MDP) We show that the number of samples needed to yield an entrywise $varepsilon$-accurate estimate of the Q-function is at most on the order of $frac1mu_min (1-gamma)5varepsilon2+ fract_mixmu_min (1-gamma)$ up to some logarithmic factor.
  arXiv  Detail & Related papers  (2020-06-04T17:51:00Z)

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.