Compressed variational quantum eigensolver for the Fermi-Hubbard model

• URL: http://arxiv.org/abs/2006.01179v2
• Date: Thu, 18 Jun 2020 21:20:06 GMT
• Title: Compressed variational quantum eigensolver for the Fermi-Hubbard model
• Authors: Ashley Montanaro and Stasja Stanisic
• Abstract summary: The Fermi-Hubbard model is a plausible target to be solved by a quantum computer. Here we use a simple method which compresses the first nontrivial subcase of the Hubbard model. We implement this method on a superconducting quantum hardware platform.
• Score: 0.05076419064097732
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The Fermi-Hubbard model is a plausible target to be solved by a quantum computer using the variational quantum eigensolver algorithm. However, problem sizes beyond the reach of classical exact diagonalisation are also beyond the reach of current quantum computing hardware. Here we use a simple method which compresses the first nontrivial subcase of the Hubbard model -- with one spin-up and one spin-down fermion -- enabling larger instances to be addressed using current quantum computing hardware. We implement this method on a superconducting quantum hardware platform for the case of the $2 \times 1$ Hubbard model, including error-mitigation techniques, and show that the ground state is found with relatively high accuracy.

Related papers

• Optimizing random local Hamiltonians by dissipation [44.99833362998488]
  We prove that a simplified quantum Gibbs sampling algorithm achieves a $Omega(frac1k)$-fraction approximation of the optimum. Our results suggest that finding low-energy states for sparsified (quasi)local spin and fermionic models is quantumly easy but classically nontrivial.
  arXiv  Detail & Related papers  (2024-11-04T20:21:16Z)
• Realizing fracton order from long-range quantum entanglement in programmable Rydberg atom arrays [45.19832622389592]
  Storing quantum information requires battling quantum decoherence, which results in a loss of information over time. To achieve error-resistant quantum memory, one would like to store the information in a quantum superposition of degenerate states engineered in such a way that local sources of noise cannot change one state into another. We show that this platform also allows to detect and correct certain types of errors en route to the goal of true error-resistant quantum memory.
  arXiv  Detail & Related papers  (2024-07-08T12:46:08Z)
• Parallel Quantum Computing Simulations via Quantum Accelerator Platform Virtualization [44.99833362998488]
  We present a model for parallelizing simulation of quantum circuit executions. The model can take advantage of its backend-agnostic features, enabling parallel quantum circuit execution over any target backend.
  arXiv  Detail & Related papers  (2024-06-05T17:16:07Z)
• Utilizing Quantum Processor for the Analysis of Strongly Correlated Materials [34.63047229430798]
  This study introduces a systematic approach for analyzing strongly correlated systems by adapting the conventional quantum cluster method to a quantum circuit model. We have developed a more concise formula for calculating the cluster's Green's function, requiring only real-number computations on the quantum circuit instead of complex ones.
  arXiv  Detail & Related papers  (2024-04-03T06:53:48Z)
• Schr\"odinger-Heisenberg Variational Quantum Algorithms [1.9887498823918806]
  Recent breakthroughs have opened the possibility to intermediate-scale quantum computing with tens to hundreds of qubits. The extremely high accuracy needed to surpass classical computers poses a critical demand to the circuit depth. Here, we propose a paradigm of Schr"odinger-Heisenberg variational quantum algorithms to resolve this problem.
  arXiv  Detail & Related papers  (2021-12-15T04:53:01Z)
• Observing ground-state properties of the Fermi-Hubbard model using a scalable algorithm on a quantum computer [0.029316801942271296]
  We show an efficient, low-depth variational quantum algorithm with few parameters can reproduce important qualitative features of medium-size instances of the Fermi-Hubbard model. We address 1x8 and 2x4 instances on 16 qubits on a superconducting quantum processor. We observe the onset of the metal-insulator transition and Friedel oscillations in 1D, and antiferromagnetic order in both 1D and 2D.
  arXiv  Detail & Related papers  (2021-12-03T17:14:20Z)
• Model-Independent Error Mitigation in Parametric Quantum Circuits and Depolarizing Projection of Quantum Noise [1.5162649964542718]
  Finding ground states and low-lying excitations of a given Hamiltonian is one of the most important problems in many fields of physics. quantum computing on Noisy Intermediate-Scale Quantum (NISQ) devices offers the prospect to efficiently perform such computations. Current quantum devices still suffer from inherent quantum noise.
  arXiv  Detail & Related papers  (2021-11-30T16:08:01Z)
• Variational Quantum Eigensolver for SU($N$) Fermions [0.0]
  Variational quantum algorithms aim at harnessing the power of noisy intermediate-scale quantum computers. We apply the variational quantum eigensolver to study the ground-state properties of $N$-component fermions. Our approach lays out the basis for a current-based quantum simulator of many-body systems.
  arXiv  Detail & Related papers  (2021-06-29T16:39:30Z)
• Hardware-Efficient, Fault-Tolerant Quantum Computation with Rydberg Atoms [55.41644538483948]
  We provide the first complete characterization of sources of error in a neutral-atom quantum computer. We develop a novel and distinctly efficient method to address the most important errors associated with the decay of atomic qubits to states outside of the computational subspace. Our protocols can be implemented in the near-term using state-of-the-art neutral atom platforms with qubits encoded in both alkali and alkaline-earth atoms.
  arXiv  Detail & Related papers  (2021-05-27T23:29:53Z)
• Simulating a ring-like Hubbard system with a quantum computer [0.0]
  We develop a workflow to use current quantum computing hardware for solving quantum many-body problems. We study a four-site Hubbard ring that exhibits a transition from a product state to an intrinsically interacting ground state as hopping amplitudes are changed. We locate this transition and solve for the ground state energy with high quantitative accuracy using a variational quantum algorithm executed on an IBM quantum computer.
  arXiv  Detail & Related papers  (2021-04-13T18:08:09Z)
• Electronic structure with direct diagonalization on a D-Wave quantum annealer [62.997667081978825]
  This work implements the general Quantum Annealer Eigensolver (QAE) algorithm to solve the molecular electronic Hamiltonian eigenvalue-eigenvector problem on a D-Wave 2000Q quantum annealer. We demonstrate the use of D-Wave hardware for obtaining ground and electronically excited states across a variety of small molecular systems.
  arXiv  Detail & Related papers  (2020-09-02T22:46:47Z)

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.