Observing ground-state properties of the Fermi-Hubbard model using a scalable algorithm on a quantum computer

Abstract

The famous, yet unsolved, Fermi-Hubbard model for strongly-correlated electronic systems is a prominent target for quantum computers. However, accurately representing the Fermi-Hubbard ground state for large instances may be beyond the reach of near-term quantum hardware. Here we show experimentally that 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 1 × 8 and 2 × 4 instances on 16 qubits on a superconducting quantum processor, substantially larger than previous work based on less scalable compression techniques, and going beyond the family of 1D Fermi-Hubbard instances, which are solvable classically. Consistent with predictions for the ground state, we observe the onset of the metal-insulator transition and Friedel oscillations in 1D, and antiferromagnetic order in both 1D and 2D. We use a variety of error-mitigation techniques, including symmetries of the Fermi-Hubbard model and a recently developed technique tailored to simulating fermionic systems. We also introduce a new variational optimisation algorithm based on iterative Bayesian updates of a local surrogate model.

Quantum information processing with superconducting circuits: a perspective

“…The question of the feasibility of powerful quantum computers beating classical super-HPC hinges on that it will be ultimately possible to perform quantum error correction (QEC). When John Martinis' group was able to demonstrate that their superconducting quantum circuits were at the surface code threshold for fault tolerance [24], then the field opened up and went from quantum physics toward quantum computing, scaling up HW and SW [12,[25][26][27][28][29][30][31][32], and implementing significant quantum algorithms and quantum physics experiments [25][26][27][29][30][31][32][33][34][35][36][37][38], including demonstrations of significant steps toward QEC [39][40][41][42][43].…”

Quantum simulation costs for Suzuki-Trotter decomposition of quantum many-body lattice models

“…Numerous approaches, have been pursued, including experimental analog simulations using using atoms confined in optical lattices [20][21][22][23][24][25] as well as quantum dots [26] and NMR systems [27]. The Hubbard model has also received focus as test-bed model for simulation on nearterm quantum computers [28][29][30][31]. With this in mind, it is important to identify whether or not the Hubbard model is truly the most efficient model, in terms of simulation resources, that captures the physics of interest.…”

Purification-based quantum error mitigation of pair-correlated electron simulations

“…With fault-tolerant quantum computing in its infancy [19] and many years from promised applications [20][21][22][23][24] attention has focused on algorithms requiring only short-depth quantum circuits, such as the variational quantum eigensolver (VQE) [1,25]. Theoretical developments in ansatz design [16,[25][26][27][28][29] and measurement optimization [30][31][32][33][34] have enabled small to midscale VQE experiments [2,3,28,[35][36][37][38][39][40]. A key target of variational quantum algorithms has been the electronic structure problem in chemistry [2,3,25,28,[35][36][37]41].…”

“…Recent quantum experiments have relied on error mitigation techniques [11], which are not scalable like error correction [19,44], but promise to substantially shrink experimental errors. Popular methods are based on postselection [6,7], rescaling [4,5,38], purification [3,[8][9][10] and probabilistic cancellation [4,45]. Various schemes and combinations of error mitigation techniques have been implemented in practice [3,35,[37][38][39][40]46].…”

“…Popular methods are based on postselection [6,7], rescaling [4,5,38], purification [3,[8][9][10] and probabilistic cancellation [4,45]. Various schemes and combinations of error mitigation techniques have been implemented in practice [3,35,[37][38][39][40]46]. However, many of these methods do not promise to remove bias to the level of accuracy needed for useful simulation of chemistry, or remain untested beyond few-qubit experiments.…”