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 errormitigation 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. Our scalable approach is a first step to using near-term quantum computers to determine low-energy properties of stronglycorrelated electronic systems that cannot be solved exactly by classical computers.

Simulating groundstate and dynamical quantum phase transitions on a superconducting quantum computer

“…Supplementary Materials: Simulating groundstate and dynamical quantum phase transitions on a superconducting quantum computer James Dborin, 1 Vinul Wimalaweera, 1 F. Barratt,2 Eric Ostby, 3 Thomas E. O'Brien, 3 and A. G. Green 1, 4 In this supplementary material we further explain the methods used to construct circuits for timeevolution. We pay particular attention to the tradeoffs between circuit approximations and fidelity in constructing cost-functions.…”

“…Strongly correlated condensed matter systems are amongst those most likely to yield a quantum advantage [1][2][3][4][5][6]. These are systems in which the underlying spins or electrons are strongly renormalised and whose quantum properties are beyond the reach of standard perturbative or density functional type approaches.…”

Gutzwiller wave function on a quantum computer using a discrete Hubbard-Stratonovich transformation

“…It should also be pointed out that, as one of the next-generation computing paradigms, quantum computing [2] has attracted growing interest for solving quantum many-body systems, which is becoming realistic, evidenced by the recent technological advances [3][4][5][6][7][8][9][10][11][12]. In this regards, the variationalquantum-eigensolver method and its variants have been proposed and demonstrated for computing ground-state [13][14][15][16][17][18][19][20][21][22][23] and low-lying excited-state [24][25][26][27][28][29] properties of quantummany-body systems by exploiting noisy intermediate-scale quantum (NISQ) [30] computers and classical computers in a hybrid manner. For recent reviews on variational quantum algorithms, see for example Refs.…”

Spatial, spin, and charge symmetry projections for a Fermi-Hubbard model on a quantum computer

“…Recent technological advances in quantum devices [1][2][3][4][5][6][7][8][9][10][11] have suggested that quantum computation of quantum physics and chemistry systems [12] is becoming a reality in the notso-distant future [13,14]. Currently available quantum computers are, however, prone to noise and hence the size of a quantum circuit to be reliably executed is limited.…”

“…It should also be noted that the Hamiltonian symmetry can also be utilized to mitigate errors due to different noise channels [54]. Remarkably, recent experiments have demonstrated a significant improvement for mitigating errors in a VQE simulation of a Fermi-Hubbard model by an error mitigation technique based on the Hamiltonian symmetry, including spin-and particle-number conservations, time-reversal symmetry, particle-hole symmetry, and spatial symmetry [14].…”