Nuclear Spectra from Quantum Lanczos Algorithm with Real-Time Evolution and Multiple Reference States

• URL: http://arxiv.org/abs/2309.00759v2
• Date: Mon, 11 Sep 2023 20:11:53 GMT
• Title: Nuclear Spectra from Quantum Lanczos Algorithm with Real-Time Evolution and Multiple Reference States
• Authors: Amanda Bowman
• Abstract summary: I performed numerical simulations to find the low-lying eigenstates of $20$Ne, $22$Na, and $29$Na to compare imaginary- and real-time evolution. I present the quantum circuits for the QLanczos algorithm with real-time evolution and multiple references.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Models of quantum systems scale exponentially with the addition of single-particle states, which can present computationally intractable problems. Alternatively, quantum computers can store a many-body basis of $2^n$ dimensions on $n$ qubits. This motivated the quantum eigensolver algorithms developed in recent years, such as the quantum Lanczos algorithm based on the classical, iterative Lanczos algorithm. I performed numerical simulations to find the low-lying eigenstates of $^{20}$Ne, $^{22}$Na, and $^{29}$Na to compare imaginary- and real-time evolution. Though imaginary-time evolution leads to faster convergence, real-time evolution still converges within tens of iterations and satisfies the requirement for unitary operators on quantum computers. Additionally, using multiple reference states leads to faster convergences or higher accuracy for a fixed number of real-time iterations. I performed quantum circuit prototype numerical simulations on a classical computer of the QLanczos algorithm with real-time evolution and multiple reference states to find the low-lying eigenstates of $^{8}$Be. These simulations were run in both the spherical basis and Hartree-Fock basis, demonstrating that an M-scheme spherical basis leads to lower depth circuits than the Hartree-Fock basis. Finally, I present the quantum circuits for the QLanczos algorithm with real-time evolution and multiple references.

Related papers

• Spin coupling is all you need: Encoding strong electron correlation on quantum computers [0.0]
  We show that quantum computers can efficiently simulate strongly correlated molecular systems by directly encoding the dominant entanglement structure in the form of spin-coupled initial states. Our work paves the way towards scalable quantum simulation of electronic structure for classically challenging systems.
  arXiv  Detail & Related papers  (2024-04-29T17:14:21Z)
• Quantum Clustering with k-Means: a Hybrid Approach [117.4705494502186]
  We design, implement, and evaluate three hybrid quantum k-Means algorithms. We exploit quantum phenomena to speed up the computation of distances. We show that our hybrid quantum k-Means algorithms can be more efficient than the classical version.
  arXiv  Detail & Related papers  (2022-12-13T16:04:16Z)
• Differentiable matrix product states for simulating variational quantum computational chemistry [6.954927515599816]
  We propose a parallelizable classical simulator for variational quantum eigensolver(VQE) Our simulator seamlessly integrates the quantum circuit evolution into the classical auto-differentiation framework. As applications, we use our simulator to study commonly used small molecules such as HF, LiH and H$$O, as well as larger molecules CO$$, BeH$ and H$_4$ with up to $40$ qubits.
  arXiv  Detail & Related papers  (2022-11-15T08:36:26Z)
• Improved algorithms of quantum imaginary time evolution for ground and excited states of molecular systems [0.0]
  Quantum imaginary time evolution (QITE) is a recently proposed quantum-classical hybrid algorithm that is guaranteed to reach the lowest state of system. We analyze the derivation of the underlying QITE equation order-by-order, and suggest a modification that is theoretically well founded. We also discuss how to accurately estimate the norm of an imaginary-time-evolved state, and applied it to excited state calculations.
  arXiv  Detail & Related papers  (2022-05-04T10:32:16Z)
• 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)
• Error-resilient Monte Carlo quantum simulation of imaginary time [5.625946422295428]
  We propose an algorithm for simulating the imaginary-time evolution and solving the ground-state problem. Compared with quantum phase estimation, the Trotter step number can be thousands of times smaller. Results show that Monte Carlo quantum simulation is promising even without a fully fault-tolerant quantum computer.
  arXiv  Detail & Related papers  (2021-09-16T08:51:24Z)
• Fault-Tolerant Quantum Simulations of Chemistry in First Quantization [0.18374319565577155]
  We analyze and optimize the resources required to implement two first quantized quantum algorithms for chemistry. We demonstrate that our qubitized algorithm often requires much less surface code spacetime volume for simulating millions of plane waves than the best second quantized algorithms.
  arXiv  Detail & Related papers  (2021-05-26T18:06:33Z)
• Imaginary Time Propagation on a Quantum Chip [50.591267188664666]
  Evolution in imaginary time is a prominent technique for finding the ground state of quantum many-body systems. We propose an algorithm to implement imaginary time propagation on a quantum computer.
  arXiv  Detail & Related papers  (2021-02-24T12:48:00Z)
• Quantum simulation with hybrid tensor networks [20.177464200362337]
  We introduce the framework of hybrid tensor networks with building blocks consisting of measurable quantum states and classically contractable tensors. We numerically benchmark our method for finding the ground state of 1D and 2D spin systems of up to $8times 8$ and $9times 8$ qubits with operations only acting on $8+1$ and $9+1$ qubits. Our approach sheds light on simulation of large practical problems with intermediate-scale quantum computers, with potential applications in chemistry, quantum many-body physics, quantum field theory, and quantum gravity thought experiments.
  arXiv  Detail & Related papers  (2020-07-02T08:29:32Z)
• Quadratic Sieve Factorization Quantum Algorithm and its Simulation [16.296638292223843]
  We have designed a quantum variant of the second fastest classical factorization algorithm named "Quadratic Sieve" We have constructed the simulation framework of quantized quadratic sieve algorithm using high-level programming language Mathematica.
  arXiv  Detail & Related papers  (2020-05-24T07:14:19Z)
• 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.