We propose a hybrid quantum-classical method to investigate the equilibrium physics and the dynamics of strongly correlated fermionic models with spin-based quantum processors. Our proposal avoids the usual pitfalls of fermion-to-spin mappings thanks to a slave-spin method which allows to approximate the original Hamiltonian into a sum of self-correlated free fermions and spin Hamiltonians. Taking as an example a Rydberg-based analog quantum processor to solve the interacting spin model, we avoid the challenges of variational algorithms or Trotterization methods. We explore the robustness of the method to experimental imperfections by applying it to the half-filled, single-orbital Hubbard model on the square lattice in and out of equilibrium. We show, through realistic numerical simulations of current Rydberg processors, that the method yields quantitatively viable results even in the presence of imperfections: it allows to gain insights into equilibrium Mott physics as well as the dynamics under interaction quenches. This method thus paves the way to the investigation of physical regimes, whether out of equilibrium, doped, or multiorbital, that are difficult to explore with classical processors.
We propose a hybrid quantum-classical method to investigate the equilibrium physics and the dynamics of strongly correlated fermionic models with spin-based quantum processors. Our proposal avoids the usual pitfalls of fermion-to-spin mappings thanks to a slave-spin method which allows to approximate the original Hamiltonian into a sum of self-correlated free fermions and spin Hamiltonians. Taking as an example a Rydberg-based analog quantum processor to solve the interacting spin model, we avoid the challenges of variational algorithms or Trotterization methods. We explore the robustness of the method to experimental imperfections by applying it to the half-filled, single-orbital Hubbard model on the square lattice in and out of equilibrium. We show, through realistic numerical simulations of current Rydberg processors, that the method yields quantitatively viable results even in the presence of imperfections: it allows to gain insights into equilibrium Mott physics as well as the dynamics under interaction quenches. This method thus paves the way to the investigation of physical regimes, whether out of equilibrium, doped, or multiorbital, that are difficult to explore with classical processors.
We experimentally study the two-dimensional Fermi-Hubbard model using a Rydberg-based quantum processing unit in the analog mode. Our approach avoids encoding directly the original fermions into qubits and instead relies on reformulating the original model onto a system of fermions coupled to spins and then decoupling them in a self-consistent manner. We then introduce the auxiliary spin solver: this hybrid quantum-classical algorithm handles a free-fermion problem, which can be solved efficiently with a few classical resources, and an interacting spin problem, which can be naturally encoded in the analog quantum computer. This algorithm can be used to study both the equilibrium Mott transition as well as non-equilibrium properties of the original Fermi-Hubbard model, highlighting the potential of quantum-classical hybrid approaches to study strongly correlated matter.
This work is a theoretical study of fermionic models. We focus on problems where highly controllable quantum simulators of these models have an important role, and we utilise both the analogue and the digital paradigm of quantum simulation. In the part on analogue quantum simulation, we focus on the proposed 'spin-asymmetric' Josephson effect where Cooper-paired spins display frequency synchronized Josephson oscillations with spin-dependent amplitudes. We consider different scenarios where the phenomenon could manifest in ultracold atomic Fermi gases. We study a Fermi gas Josephson junction in the recently realized Josephson plasma oscillation regime with an additional spin-dependent potential and show that the asymmetry in the resulting spin-dependent plasma oscillation amplitudes is on the order of a couple of per cent. We also demonstrate numerically that spin-asymmetric Josephson-like currents occur in a one-dimensional spin-dependent optical superlattice, with amplitude asymmetries up to 39%. Finally, we show that at zero temperature the tunable critical current in ferromagnetic Josephson junctions can be explained by the spin-asymmetric Josephson effect. In the part where digital quantum simulation is used, we propose a hybrid quantum-classical approach to studying strongly correlated fermion models. In this approach, a digital quantum simulator works in conjunction with a classical feedback loop to solve the infinite-dimensional Hubbard model directly in the thermodynamic limit. The scheme implements the well-established dynamical mean-field theory (DMFT) method, such that the digital quantum simulator solves the classically hard DMFT impurity problem and self-consistency is taken care of in a classical computer. We first present a few-qubit proof-of-principle setup for equilibrium systems that implements the simplified 'two-site' DMFT. This few-qubit setup is used for a qualitative description of the Mott transition in the half-filled infinite-dimensional Hubbard model. We then describe a scalable setup for simulating non-equilibrium many-body quantum dynamics by proposing the implementation of the non-equilibrium extension of DMFT with the hybrid device.
The study of quantum dynamics is an increasingly important aspect of atomic, molecular and optical physics, as well as condensed-matter physics and other disciplines. It is essential in order to understand non-equilibrium phenomena which do not fit within the framework of equilibrium thermodynamics, such as many-body localization, dynamical quantum phase transitions, and non-equilibrium steady states in driven-dissipative systems. However, the exact calculation of dynamical observables is extremely difficult in general for several reasons, which makes it challenging for theoretical predictions and analyses to keep pace with rapidly advancing experiments. In this thesis I use and develop several computational methods to investigate the dynamics of quantum many-body systems, with the two goals of better understanding the evolution of local observables and correlation functions in spin and Fermion systems as well as creating and testing more effective numerical methods for solving quantum dynamics problems. I explore quantum dynamics by using Hamiltonian parameter quenches in several commonly-used models in AMO physics and elsewhere: the Fermi-Hubbard model, the XXZ model, and the transverse-Ising model. The first represents a system of short-range interacting Fermions, while the latter two represent spin systems with different spin-spin couplings and magnetic field terms. All of these models can be realized in current experiments. First, I derive an exact solution for an extreme interaction quench in the Fermi-Hubbard model, from a strongly-interacting initial state to a noninteracting final Hamiltonian. From this result I show that there are nontrivial transient connected correlations, despite the fact that the system has very high temperature and a noninteracting Hamiltonian. Those features would suppress such correlations in equilibrium, but the dynamical correlations are still significant. Then, I develop and examine two numerical methods for solving dynamics of the spin expectation values and correlation functions in the transverse-Ising and XXZ models. Both methods rely on approximating a thermodynamically large system with a much smaller and more computationally tractable cluster of lattice sites, or a series of clusters. The first method is a dynamical numerical linked cluster expansion (NLCE). NLCEs have already been used successfully on systems in thermodynamic equilibrium, and I extended the technique to directly compute the dynamics of an observable after a quantum quench. I review the general NLCE method, describe my dynamical variant of it, and compute the quench dynamics of spin and correlation observables in the transverse-Ising and XXZ models. The second method, which I term the adaptive-boundary cluster method, relies on recently refined bounds on information propagation in quantum systems to choose a cluster of lattice sites that minimizes the finite size error bound of a dynamical computation. I briefly review these bounds, and describe a new algorithm which uses them to construct a cluster whose boundary is chosen according to a related error estimate. Such an adaptive-boundary cluster has the property that there exists a computable upper bound on the finite size error of observables measured at the cluster center, and this error bound is nearly minimal when compared to that of other clusters of the same size. I then compute the quench dynamics of spin and correlation observables in the transverse-Ising model using the adaptive boundary clusters. I apply this method to both uniform and strongly disordered systems. To evaluate the effectiveness of both dynamical NLCE and adaptive-boundary clusters, I compare the results obtained using them to results from a standard and general purpose numerical method: exact solvers applied a rectangular cluster with periodic boundary conditions. Both of the new methods usually converge faster and are more accurate than the standard method for comparable cluster sizes. This thesis illustrates that choosing numerical methods which take advantage of the geometric and entanglement structure of the initial state and Hamiltonian can substantially enhance our ability to study quantum dynamics, by reducing the computational cost of numerically exact solutions. I conclude with a discussion of various avenues for future research to build on this work.
Ultracold fermionic atoms in optical lattices offer pristine realizations of Hubbard models1, which are fundamental to modern condensed-matter physics2,3. Despite notable advancements4–6, the accessible temperatures in these optical lattice material analogues are still too high to address many open problems7–10. Here we demonstrate a several-fold reduction in temperature6,11–13, bringing large-scale quantum simulations of the Hubbard model into an entirely new regime. This is accomplished by transforming a low-entropy product state into strongly correlated states of interest via dynamic control of the model parameters14,15, which is extremely challenging to simulate classically10. At half-filling, the long-range antiferromagnetic order is close to saturation, leading to a temperature of T/t=0.05−0.05+0.06 based on comparisons with numerically exact simulations. Doped away from half-filling, it is exceedingly challenging to realize systematically accurate and predictive numerical simulations9. Importantly, we are able to use quantum simulation to identify a new pathway for achieving similarly low temperatures with doping. This is confirmed by comparing short-range spin correlations to state-of-the-art, but approximate, constrained-path auxiliary-field quantum Monte Carlo simulations16–18. Compared with the cuprates2,19,20, the reported temperatures correspond to a reduction from far above to below room temperature, at which physics such as the pseudogap and stripe phases may be expected3,19,21–24. Our work opens the door to quantum simulations that solve open questions in material science, develop synergies with numerical methods and theoretical studies, and lead to discoveries of new physics8,10. A several-fold reduction in temperature is accomplished using a neutral-atom Hubbard quantum simulator by transforming a low-entropy product state into strongly correlated states of interest via dynamic control of the model parameters.
Among the most compelling targets for quantum simulation are strongly correlated phases and electronic-structure problems, where interactions organize electrons into collective states and produce intricate low-temperature phase diagrams. Cuprate superconductors are a canonical example: at low doping, superconductivity emerges from a metallic regime that exhibits a pseudogap above the critical temperature. Ultracold atoms in optical lattices provide a well-controlled, tunable setting to probe the microscopic mechanisms behind this behavior and, in fermion-native architectures, to implement electronic structure dynamics directly. This thesis demonstrates both large scale systematic analog quantum simulations in the most interesting regime of doped antiferromagnets and elementary high-fidelity gates as the basis for a digital or hybrid fermionic quantum processors in an optical lattice. Working with ultracold Lithium-6 in a two–dimensional optical superlattice, we first map the parameter space of the Fermi–Hubbard model over a wide range of temperatures and dopings. More than 40000 single-site spin- and density-resolved snapshots, spanning over a dense grid of doping levels and temperatures in a numerically challenging parameter space, reveal antiferromagnetic correlations extending across the system size and into the pseudogap regime. Temperatures down to T/t=0.2 are realized, determined by benchmarking the data to state-of-the-art numerical methods. By evaluating spin–charge correlators up to fifth order, we experimentally uncover a universal scaling behavior across the pseudogap crossover, governed by a single, doping-dependent temperature scale. These findings provide the first microscopic evidence of universal scaling in multi-point correlators and establish stringent benchmarks for future theoretical developments. On the same apparatus, we demonstrate that the controlled motion of fermions in double wells enables high-fidelity entanglement. Double-well potentials are used to engineer coherent pair-tunnelling and spin-exchange interactions that act as native SWAP^α operations. We demonstrate the collisional gate fidelities up to 99.8% and Bell-state lifetimes exceeding ten seconds, limited mainly by residual inhomogeneities in the optical potential. A composite pulse sequence isolates the pair-exchange channel, realizing the elementary building block required for fermionic quantum-chemistry algorithms. With the addition of site-selective addressing, our results mark a key step towards a fully digital, scalable fermionic quantum computer based on the controlled motion and entanglement of fermionic neutral atoms. The work establishes a hybrid analog-digital architecture: analog evolution under the Hubbard Hamiltonian yields thermodynamic states whose magnetic properties match and extend theoretical benchmarks, while digital collisional gates provide building blocks for error-corrected quantum computation and complex state preparation.
The widespread use of the noninteracting ground state as the initial state for the digital quantum simulation of the Fermi-Hubbard model is largely due to the scarcity of alternative easy-to-prepare approximations to the exact ground state in the literature. Exploiting the fact that the spin-21 Heisenberg model is the effective low-energy theory of the Fermi-Hubbard model at half-filling in the strongly interacting limit, here we propose a three-step deterministic quantum routine to prepare an educated guess of the ground state of the Fermi-Hubbard model through a shallow circuit suitable for near-term quantum hardware. First, the ground state of the Heisenberg model is initialized via a hybrid variational method using an ansatz that explores only the correct symmetry subspace. Second, a general method is devised to convert a multi-spin-21 wave function into its fermionic version. Third, taking inspiration from the Baeriswyl ansatz, a constant-depth single-parameter layer that adds doublon-holon pairs is applied to this fermionic state. Numerical simulations on chains and ladders with up to 12 sites confirm the improvement over the noninteracting ground state of the overlap with the exact ground state for the intermediate values of the interaction strength at which quantum simulation is found to be most relevant. More broadly, the general scheme to convert a multi-spin-21 state into a half-filled fermionic state may bridge the gap between quantum spin models and lattice models of correlated fermions in the realm of digital quantum simulation.