Simulating 2D topological quantum phase transitions on a digital quantum computer

• URL: http://arxiv.org/abs/2312.05079v3
• Date: Sat, 28 Sep 2024 20:59:12 GMT
• Title: Simulating 2D topological quantum phase transitions on a digital quantum computer
• Authors: Yu-Jie Liu, Kirill Shtengel, Frank Pollmann,
• Abstract summary: Efficient preparation of many-body ground states is key to harnessing the power of quantum computers in studying quantum many-body systems. We propose a simple method to design exact linear-depth parameterized quantum circuits which prepare a family of ground states across topological quantum phase transitions in 2D. We show that the 2D isoTNS can also be efficiently simulated by a holographic quantum algorithm requiring only an 1D array of qubits.
• Score: 3.727382912998531
• License:
• Abstract: Efficient preparation of many-body ground states is key to harnessing the power of quantum computers in studying quantum many-body systems. In this work, we propose a simple method to design exact linear-depth parameterized quantum circuits which prepare a family of ground states across topological quantum phase transitions in 2D. We achieve this by constructing ground states represented by isometric tensor networks (isoTNS), which form a subclass of tensor network states that are efficiently preparable. By continuously tuning a parameter in the wavefunction, the many-body ground state undergoes quantum phase transitions, exhibiting distinct 2D quantum phases. We illustrate this by constructing an isoTNS path with bond dimension $D = 2$ interpolating between distinct symmetry-enriched topological (SET) phases. At the transition point, the wavefunction is related to a gapless point in the classical six-vertex model. Furthermore, the critical wavefunction supports a power-law correlation along one spatial direction while remaining long-range ordered in the other spatial direction. We provide an explicit parametrized local quantum circuit for the path and show that the 2D isoTNS can also be efficiently simulated by a holographic quantum algorithm requiring only an 1D array of qubits.

Related papers

• Unveiling quantum phase transitions from traps in variational quantum algorithms [0.0]
  We introduce a hybrid algorithm that combines quantum optimization with classical machine learning. We use LASSO for identifying conventional phase transitions and the Transformer model for topological transitions. Our protocol significantly enhances efficiency and precision, opening new avenues in the integration of quantum computing and machine learning.
  arXiv  Detail & Related papers  (2024-05-14T09:01:41Z)
• A vertical gate-defined double quantum dot in a strained germanium double quantum well [48.7576911714538]
  Gate-defined quantum dots in silicon-germanium heterostructures have become a compelling platform for quantum computation and simulation. We demonstrate the operation of a gate-defined vertical double quantum dot in a strained germanium double quantum well. We discuss challenges and opportunities and outline potential applications in quantum computing and quantum simulation.
  arXiv  Detail & Related papers  (2023-05-23T13:42:36Z)
• Efficient variational quantum circuit structure for correlated topological phases [0.0]
  We propose an efficient circuit structure of variational quantum circuit textitAnsatz used for the variational quantum eigensolver (VQE) algorithm. We investigate the symmetry-protected topological Haldane phase in a textitnon-exactly solvable alternating spin-$1/2$ Heisenberg chain by VQE calculations.
  arXiv  Detail & Related papers  (2023-03-30T06:49:28Z)
• Variational waveguide QED simulators [58.720142291102135]
  Waveguide QED simulators are made by quantum emitters interacting with one-dimensional photonic band-gap materials. Here, we demonstrate how these interactions can be a resource to develop more efficient variational quantum algorithms.
  arXiv  Detail & Related papers  (2023-02-03T18:55:08Z)
• Quantum Simulation of Quantum Phase Transitions Using the Convex Geometry of Reduced Density Matrices [0.0]
  We present a general quantum-computing approach to quantum phase transitions. The origin of phase transitions can be understood geometrically in terms of the set of two-particle reduced density matrices (2-RDMs) We compute the convex set of 2-RDMs for a Lipkin-Meshkov-Glick spin model on IBM superconducting-qubit quantum processors.
  arXiv  Detail & Related papers  (2022-07-27T00:30:33Z)
• Neural-Network Quantum States for Periodic Systems in Continuous Space [66.03977113919439]
  We introduce a family of neural quantum states for the simulation of strongly interacting systems in the presence of periodicity. For one-dimensional systems we find very precise estimations of the ground-state energies and the radial distribution functions of the particles. In two dimensions we obtain good estimations of the ground-state energies, comparable to results obtained from more conventional methods.
  arXiv  Detail & Related papers  (2021-12-22T15:27:30Z)
• Determining ground-state phase diagrams on quantum computers via a generalized application of adiabatic state preparation [61.49303789929307]
  We use a local adiabatic ramp for state preparation to allow us to directly compute ground-state phase diagrams on a quantum computer via time evolution. We are able to calculate an accurate phase diagram on both two and three site systems using IBM quantum machines.
  arXiv  Detail & Related papers  (2021-12-08T23:59:33Z)
• A quantum processor based on coherent transport of entangled atom arrays [44.62475518267084]
  We show a quantum processor with dynamic, nonlocal connectivity, in which entangled qubits are coherently transported in a highly parallel manner. We use this architecture to realize programmable generation of entangled graph states such as cluster states and a 7-qubit Steane code state.
  arXiv  Detail & Related papers  (2021-12-07T19:00:00Z)
• Efficient Tensor Network ansatz for high-dimensional quantum many-body problems [0.0]
  We introduce a novel tensor network structure augmenting the well-established Tree Network representation of a quantum many-body wave function. We benchmark this novel approach against paradigmatic two-dimensional spin models demonstrating unprecedented precision and system sizes.
  arXiv  Detail & Related papers  (2020-11-16T19:00:04Z)
• Solving Quantum Master Equations with Deep Quantum Neural Networks [0.0]
  We use deep quantum feedforward neural networks capable of universal quantum computation to represent the mixed states for open quantum many-body systems. Owning to the special structure of the quantum networks, this approach enjoys a number of notable features, including the absence of barren plateaus.
  arXiv  Detail & Related papers  (2020-08-12T18:00:08Z)
• Entanglement generation via power-of-SWAP operations between dynamic electron-spin qubits [62.997667081978825]
  Surface acoustic waves (SAWs) can create moving quantum dots in piezoelectric materials. We show how electron-spin qubits located on dynamic quantum dots can be entangled.
  arXiv  Detail & Related papers  (2020-01-15T19:00:01Z)

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.