Exponential optimization of adiabatic quantum-state preparation

• URL: http://arxiv.org/abs/2405.03656v2
• Date: Sat, 11 Jan 2025 22:40:21 GMT
• Title: Exponential optimization of adiabatic quantum-state preparation
• Authors: Davide Cugini, Davide Nigro, Mattia Bruno, Dario Gerace,
• Abstract summary: We use the adiabatic theorem for state preparation, whose error decreases exponentially as a function of the preparation time.<n>We then design a preconditioning term that modifies the adiabatic preparation, thus reducing its characteristic time.<n>We prove the efficiency of our method with extensive numerical experiments on prototypical spin-models.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The preparation of a given quantum state on a quantum computing register is a typically demanding operation, requiring a number of elementary gates that scales exponentially with the size of the problem. Using the adiabatic theorem for state preparation, whose error decreases exponentially as a function of the preparation time, we derive an explicit analytic expression for the dependence of the characteristic time on the Hamiltonian used in the adiabatic evolution. Exploiting this knowledge, we then design a preconditioning term that modifies the adiabatic preparation, thus reducing its characteristic time and hence giving an exponential advantage in state preparation. We prove the efficiency of our method with extensive numerical experiments on prototypical spin-models, which gives a promising strategy to perform quantum simulations of manybody models via Trotter evolution on near-term quantum processors.

Related papers

• Reducing the sampling complexity of energy estimation in quantum many-body systems using empirical variance information [45.18582668677648]
  We consider the problem of estimating the energy of a quantum state preparation for a given Hamiltonian in Pauli decomposition. We construct an adaptive estimator using the state's actual variance.
  arXiv  Detail & Related papers  (2025-02-03T19:00:01Z)
• Adiabatic quantum imaginary time evolution [0.0]
  We introduce an adiabatic state preparation protocol which implements quantum imaginary time evolution under the Hamiltonian of the system. Unlike the original quantum imaginary time evolution algorithm, adiabatic quantum imaginary time evolution does not require quantum state tomography during its runtime.
  arXiv  Detail & Related papers  (2023-08-07T04:27:30Z)
• Optimal scheduling in probabilistic imaginary-time evolution on a quantum computer [0.6615826432503729]
  probabilistic imaginary-time evolution (PITE) is a promising candidate for preparing the ground state of the Hamiltonian. We analyze the computational costs of the PITE method for both linear and exponential scheduling of the imaginary-time step size. The findings of this study can make a significant contribute to the field of ground-state preparation of many-body Hamiltonians on quantum computers.
  arXiv  Detail & Related papers  (2023-05-08T10:20:57Z)
• Critical behavior of Ising model by preparing thermal state on quantum computer [3.570760625392093]
  We simulate the critical behavior of the Ising model utilizing a thermal state prepared using quantum computing techniques. We calculate the specific heat and susceptibility of the long-range interacting Ising model and observe indications of the Ising criticality on a small lattice size.
  arXiv  Detail & Related papers  (2023-02-28T03:29:19Z)
• Universality of critical dynamics with finite entanglement [68.8204255655161]
  We study how low-energy dynamics of quantum systems near criticality are modified by finite entanglement. Our result establishes the precise role played by entanglement in time-dependent critical phenomena.
  arXiv  Detail & Related papers  (2023-01-23T19:23:54Z)
• Stochastic Representation of the Quantum Quartic Oscillator [0.0]
  We show how to parameterize the time evolution of this model via the dynamics of a set of classical variables. We propose a novel way to numerically simulate the time evolution of the system.
  arXiv  Detail & Related papers  (2022-11-03T16:04:26Z)
• Real-Time Krylov Theory for Quantum Computing Algorithms [0.0]
  New approaches using subspaces generated by real-time evolution have shown efficiency in extracting eigenstate information. We develop the variational quantum phase estimation (VQPE) method, a compact and efficient real-time algorithm to extract eigenvalues on quantum hardware. We discuss its application to fundamental problems in quantum computation such as electronic structure predictions for strongly correlated systems.
  arXiv  Detail & Related papers  (2022-08-01T18:00:48Z)
• Thermalization of the Quantum Planar Rotor with external potential [0.0]
  We study decoherence, diffusion, friction, and how they thermalize a planar rotor in the presence of an external potential. We analytically and numerically verify the existence of a steady state that, in the high-temperature regime, closely approximates a Gibbs state.
  arXiv  Detail & Related papers  (2022-07-11T12:15:50Z)
• Probing finite-temperature observables in quantum simulators of spin systems with short-time dynamics [62.997667081978825]
  We show how finite-temperature observables can be obtained with an algorithm motivated from the Jarzynski equality. We show that a finite temperature phase transition in the long-range transverse field Ising model can be characterized in trapped ion quantum simulators.
  arXiv  Detail & Related papers  (2022-06-03T18:00:02Z)
• Fermionic approach to variational quantum simulation of Kitaev spin models [50.92854230325576]
  Kitaev spin models are well known for being exactly solvable in a certain parameter regime via a mapping to free fermions. We use classical simulations to explore a novel variational ansatz that takes advantage of this fermionic representation. We also comment on the implications of our results for simulating non-Abelian anyons on quantum computers.
  arXiv  Detail & Related papers  (2022-04-11T18:00:01Z)
• Numerical Simulations of Noisy Quantum Circuits for Computational Chemistry [51.827942608832025]
  Near-term quantum computers can calculate the ground-state properties of small molecules. We show how the structure of the computational ansatz as well as the errors induced by device noise affect the calculation.
  arXiv  Detail & Related papers  (2021-12-31T16:33:10Z)
• Sampling, rates, and reaction currents through reverse stochastic quantization on quantum computers [0.0]
  We show how to tackle the problem using a suitably quantum computer. We propose a hybrid quantum-classical sampling scheme to escape local minima.
  arXiv  Detail & Related papers  (2021-08-25T18:04:52Z)
• Quantum algorithms for quantum dynamics: A performance study on the spin-boson model [68.8204255655161]
  Quantum algorithms for quantum dynamics simulations are traditionally based on implementing a Trotter-approximation of the time-evolution operator. variational quantum algorithms have become an indispensable alternative, enabling small-scale simulations on present-day hardware. We show that, despite providing a clear reduction of quantum gate cost, the variational method in its current implementation is unlikely to lead to a quantum advantage.
  arXiv  Detail & Related papers  (2021-08-09T18:00:05Z)
• Continuous-time dynamics and error scaling of noisy highly-entangling quantum circuits [58.720142291102135]
  We simulate a noisy quantum Fourier transform processor with up to 21 qubits. We take into account microscopic dissipative processes rather than relying on digital error models. We show that depending on the dissipative mechanisms at play, the choice of input state has a strong impact on the performance of the quantum algorithm.
  arXiv  Detail & Related papers  (2021-02-08T14:55:44Z)
• Benchmarking adaptive variational quantum eigensolvers [63.277656713454284]
  We benchmark the accuracy of VQE and ADAPT-VQE to calculate the electronic ground states and potential energy curves. We find both methods provide good estimates of the energy and ground state. gradient-based optimization is more economical and delivers superior performance than analogous simulations carried out with gradient-frees.
  arXiv  Detail & Related papers  (2020-11-02T19:52:04Z)

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.