arXiv subjects

Raul A. Santos

Publications and source records attributed to Raul A. Santos.

At least 19 recordsLinked to original sources

arXiv2026

Programmable digital quantum simulation of 2D Fermi-Hubbard dynamics using 72 superconducting qubits

Simulating the time-dynamics of quantum many-body systems was the original use of quantum computers proposed by Feynman, motivated by the critical role of quantum interactions between electrons in the properties of materials and molecules. Accurately simulating such systems remains one of the most promising applications of general-purpose digital quantum computers, in which all the parameters of the model can be programmed and any desired physical quantity output. However, performing such simulations on today's quantum computers at a scale beyond the reach of classical methods requires advances in the efficiency of simulation algorithms and error mitigation techniques. Here we demonstrate programmable digital quantum simulation of the dynamics of the 2D Fermi-Hubbard model -- one of the best-known simplified models of electrons in crystalline solids -- at a scale beyond exact classical state-vector simulation. We implement simulations of this model on lattice sizes up to ${6\times 6}$ using 72 qubits on Google's Willow quantum processor, across a range of physical parameters, including different on-site electron-electron interaction strengths and magnetic flux values, and study phenomena including formation of magnetic polarons (charge carriers surrounded by local magnetic polarisation), dynamical symmetry-breaking in stripe-ordered states, attraction of charge carriers on an entangled background state known as a valence bond solid, and the approach to equilibrium through thermalisation. We validate our results against exact calculations in parameter regimes where these are feasible, and compare them to approximate classical simulations performed using tensor network and operator propagation methods. Our results demonstrate that meaningful programmable digital quantum simulation of many-body interacting electron models is now feasible on state-of-the-art quantum hardware.

quant-ph↗

arXiv2026

Quantum algorithm for dephasing of coupled systems: decoupling and IQP duality

Noise and decoherence are ubiquitous in the dynamics of quantum systems coupled to an external environment. In the regime where environmental correlations decay rapidly, the evolution of a subsytem is well described by a Lindblad quantum master equation. In this work, we introduce a quantum algorithm for simulating unital Lindbladian dynamics by sampling unitary quantum channels without extra ancillas. Using ancillary qubits we show that this algorithm allows approximating general Lindbladians as well. For interacting dephasing Lindbladians coupling two subsystems, we develop a decoupling scheme that reduces the circuit complexity of the simulation. This is achieved by sampling from a time-correlated probability distribution - determined by the evolution of one subsystem, which specifies the stochastic circuit implemented on the complementary subsystem. We demonstrate our approach by studying a model of bosons coupled to fermions via dephasing, which naturally arises from anharmonic effects in an electron-phonon system coupled to a bath. Our method enables tracing out the bosonic degrees of freedom, reducing part of the dynamics to sampling an IQP circuit. The sampled bitstrings then define a corresponding fermionic problem, which in the non-interacting case can be solved efficiently classically. We comment on the computational complexity of this class of dissipative problems, using the known fact that sampling from IQP circuits is believed to be difficult classically.

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arXiv2026

Time evolution of impurity models and their universality for quantum computation

Impurity Hamiltonians are systems of $N$ fermionic modes where $O(1)$ of them interact among themselves via quartic (or higher order) fermion terms, while coupling quadratically with $O(N)$ bath modes. Without the quartic interactions, these systems are classically simulable with $O(N^3)$ resources. It was proved that the time-dependent evolution of these systems can perform universal quantum computation. The question of whether or not this remains true for time-independent evolution remains open. Here, we prove that the time evolution of generic time-independent impurity Hamiltonians on $O(N)$ qubits is universal on $N$ qubits if the input state is a product state of fermions in any single particle basis. In our proof we find that for a computation of depth $S$, the size of the impurity scales as $O(S\log S)$.

quant-ph↗

arXiv2026

On the stability to noise of fermion-to-qubit mappings

Quantum simulations before fault tolerance suffer from the intrinsic noise present in quantum computers. In this regime, extracting meaningful results greatly benefits from stability against that noise. This stability, defined as an error in observables that is independent of the system's size, is expected in local systems under local noise. In fermionic systems, the encoding of the fermionic degrees of freedom into qubits can introduce non-locality, making stability more delicate. Here, we investigate the stability to noise of fermion-to-qubit mappings. We consider noisy quantum circuits in $D$ dimensions modeled by alternating layers of local unitaries and general, single-qubit Pauli noise. We show that, when using local fermionic encodings, expectation values of quadratic fermionic observables are stable to noise in states with spatially decaying correlations: a power-law decay with exponent $μ>D$ is sufficient for stability. By contrast, we show that this stability cannot be achieved by non-local encodings such as Jordan-Wigner in $2D$, or quasi-local ones such as the Bravyi-Kitaev transform. Our findings formalize the intuition that decaying correlations of the physical systems under study provide protection against noise for local fermionic encodings, and help inform design principles in near-term quantum simulations.

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arXiv2026

Onset of Ergodicity Across Scales on a Digital Quantum Processor

Understanding how isolated quantum many-body systems thermalize remains a central question in modern physics. We study the onset of ergodicity in a two-dimensional disordered Heisenberg Floquet model using digital quantum simulation on IBM's Nighthawk superconducting processor, reaching system sizes of up to $10\times10$ qubits. We probe ergodicity across different length scales by coarse-graining the system into spatial patches of varying sizes and introducing a measure based on the collision entropy of each patch, enabling a detailed study of when ergodic behavior emerges across scales. The high sampling rate of superconducting quantum processing units, together with an optimal sample estimator, allow us to access patches of sizes up to $3\times3$. We observe that as the Heisenberg coupling $J$ increases, the noiseless system undergoes a smooth crossover from subergodic to ergodic behavior, with smaller patches approaching their random-matrix-theory values first, thereby revealing a hierarchy across scales. In the region of parameter space where classical tensor-network simulations are reliable, small patches or small values of $J$, we find excellent agreement with the error-mitigated quantum simulation. Beyond this regime, volume-law entanglement and contraction complexity growth causes the cost of classical methods to rise sharply. Our results open new directions for the use of quantum computers in the study of quantum thermalization.

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arXiv2026

Efficient classical simulation of time dynamics in Fermi-Hubbard models with imaginary interactions

Using a map between the Lindbladian evolution of dephasing in free fermions and the time evolution of imaginary-interaction Fermi-Hubbard models in bipartite lattices, we present an efficient classical algorithm to solve the Schrödinger equation in these interacting systems. This algorithm leverages the recently discovered algorithm for simulating Lindbladian evolution by sampling mixed unitary channels (Wang et al arXiv:2601.06298). We comment on the expected classical complexity of the problem for general complex values of the parameters and discuss some applications.

quant-ph↗

arXiv2025

Fermionic dynamics on a trapped-ion quantum computer beyond exact classical simulation

Simulation of the time-dynamics of fermionic many-body systems has long been predicted to be one of the key applications of quantum computers. Such simulations -- for which classical methods are often inaccurate -- are critical to advancing our knowledge and understanding of quantum chemistry and materials, underpinning a wide range of fields, from biochemistry to clean-energy technologies and chemical synthesis. However, the performance of all previous digital quantum simulations of fermions has been matched by classical methods, and it has thus far remained unclear whether near-term, intermediate-scale quantum hardware could offer any computational advantage in this area. Here, we implement an efficient quantum simulation algorithm on Quantinuum's System Model H2 trapped-ion quantum computer for the time dynamics of a 56-qubit system that is too complex for exact classical simulation. We focus on the periodic spinful 2D Fermi-Hubbard model and present evidence of spin-charge separation, where the elementary electron's charge and spin decouple. In the limited cases where ground truth is available through exact classical simulation, we find that it agrees with the results we obtain from the quantum device. Employing long-range Wilson operators to study deconfinement of the effective gauge field between spinons and the effective potential between charge carriers, we find behaviour that differs from predictions made by classical tensor network methods. Our results herald the use of quantum computing for simulating strongly correlated electronic systems beyond the capacity of classical computing.

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arXiv2025

Extracting the spin excitation spectrum of a fermionic system using a quantum processor

Understanding low-energy excitations in fermionic systems is crucial for their characterization. They determine the response of the system to external weak perturbations, its dynamical correlation functions, and provide mechanisms for the emergence of exotic phases of matter. In this work, we study the spin excitation spectra of the 1D Fermi-Hubbard model using a digital quantum processor. Introducing a protocol that is naturally suited for simulation on quantum computers, we recover the retarded spin Green's function from the time evolution of simple observables after a specific quantum quench. We exploit the robustness of the protocol to perturbations of the initial state to minimize the quantum resources required for the initial state preparation, and to allocate the majority of them to a Trotterized time-dynamics simulation. This, combined with the intrinsic resilience to noise of the protocol, allows us to accurately reconstruct the spin excitation spectrum for large instances of the 1D Fermi-Hubbard model without making use of expensive error mitigation techniques, using up to 30 qubits of an IBM Heron r2 device.

quant-ph↗

arXiv2025

Improving time dynamics simulation by sampling the error unitary

We introduce an algorithm to improve the error scaling of product formulas by randomly sampling the generator of their exact error unitary. Our approach takes an arbitrary product formula of time $t$, $S_k(t)$ with error $O(t^{k+1})$ and produces a stochastic formula with expected error scaling as $O(t^{2k+2})$ with respect to the exact dynamics. For a given fixed error $ε$ and total evolution time $T$ this leads to an improved gate complexity of $N=O(T(T/ε)^{\frac{1}{2k+1}})$ compared to the $O(T(T/ε)^{\frac{1}{k}})$ gate complexity of a $k$-th order product formula. This is achieved by appending an additional circuit with depth at-most logarithmic in the number of qubits, and without needing extra ancillas. We prove that each instance of these stochastic formulas quickly concentrates to the expected value. These results are based on an exact characterization of the error unitaries for product formulas. Through extensive numerical simulations we assess the performance of this approach in several spin and fermionic systems. We show that the expansion of these error unitaries naturally leads to generalized Zassenhaus formulas, a result which could be of independent mathematical interest.

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arXiv2025

Unveiling quantum phase transitions from traps in variational quantum algorithms

Understanding quantum phase transitions in physical systems is fundamental to characterize their behavior at low temperatures. Achieving this requires both accessing good approximations to the ground state and identifying order parameters to distinguish different phases. Addressing these challenges, our work introduces a hybrid algorithm that combines quantum optimization with classical machine learning. This approach leverages the capability of near-term quantum computers to prepare locally trapped states through finite optimization. Specifically, we apply LASSO for identifying conventional phase transitions and the Transformer model for topological transitions, utilizing these with a sliding window scan of Hamiltonian parameters to learn appropriate order parameters and locate critical points. We validated the method with numerical simulations and real-hardware experiments on Rigetti's Ankaa 9Q-1 quantum computer. This protocol provides a framework for investigating quantum phase transitions with shallow circuits, offering enhanced efficiency and, in some settings, higher precision-thus contributing to the broader effort to integrate near-term quantum computing and machine learning.

quant-ph↗

arXiv2025

Approximating dynamical correlation functions with constant depth quantum circuits

One of the most important quantities characterizing the microscopic properties of quantum systems are dynamical correlation functions. These correlations are obtained by time-evolving a perturbation of an eigenstate of the system, typically the ground state. In this work, we study approximations of these correlation functions that do not require time dynamics. We show that having access to a circuit that prepares an eigenstate of the Hamiltonian, it is possible to approximate the dynamical correlation functions up to exponential accuracy in the complex frequency domain $ω=\Re(ω)+i\Im(ω)$, on a strip above the real line $\Im(ω)=0$. We achieve this by exploiting the continued fraction representation of the dynamical correlation functions as functions of frequency $ω$, where the level $k$ approximant can be obtained by measuring a weight $O(k)$ operator on the eigenstate of interest. In the complex $ω$ plane, we show how this approach allows to determine approximations to correlation functions with accuracy that increases exponentially with $k$. We analyse two algorithms to generate the continuous fraction representation in scalar or matrix form, starting from either one or many initial operators. We prove that these algorithms generate an exponentially accurate approximation of the dynamical correlation functions on a region sufficiently far away from the real frequency axis. We present numerical evidence of these theoretical results through simulations of small lattice systems. We comment on the stability of these algorithms with respect to sampling noise in the context of quantum simulation using quantum computers.

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arXiv2024

How pure can we go with adiabatic state manipulation?

Dissipative systems with decoherence free subspaces, a.k.a. dark spaces (DSs), can be used to protect quantum information. At the same time, dissipation is expected to give rise to coherent information degradation outside the DS. Employed to support quantum information platforms, DSs can be adiabatically modified in a way that resembles adiabatic control of coherent systems. Here we study the slow evolution of a purely dissipative system with a spectral gap $γ$, characterized by a strong symmetry, under a cyclic protocol with period $T$. Non-adiabatic corrections to the state evolution give rise to decoherence: the evolution within the instantaneous DS is described by a time-local effective Liouvillian operator that leads to purity degradation over a period, of order $1/γT$. We obtain a closed form of the latter to order $1/(γT)^2$. Our analysis underlines speed limitations in quantum information processing in the absence of corrective measures.

quant-ph↗

arXiv2024

Efficient and practical Hamiltonian simulation from time-dependent product formulas

In this work we propose an approach for implementing time-evolution of a quantum system using product formulas. The quantum algorithms we develop have provably better scaling (in terms of gate complexity and circuit depth) than a naive application of well-known Trotter formulas, for systems where the evolution is determined by a Hamiltonian with different energy scales (i.e., one part is "large" and another part is "small"). Our algorithms generate a decomposition of the evolution operator into a product of simple unitaries that are directly implementable on a quantum computer. Although the theoretical scaling is suboptimal compared with state-of-the-art algorithms (e.g., quantum signal processing), the performance of the algorithms we propose is highly competitive in practice. We illustrate this via extensive numerical simulations for several models. For instance, in the strong-field regime of the 1D transverse-field Ising model, our algorithms achieve an improvement of one order of magnitude in both the system size and evolution time that can be simulated with a fixed budget of 1000 arbitrary 2-qubit gates, compared with standard Trotter formulas.

quant-ph↗

arXiv2024

Enhancing density functional theory using the variational quantum eigensolver

Quantum computers open up new avenues for modelling the physical properties of materials and molecules. Density Functional Theory (DFT) is the gold standard classical algorithm for predicting these properties, but relies on approximations of the unknown universal functional, limiting its general applicability for many fundamental and technologically relevant systems. In this work we develop a hybrid quantum/classical algorithm called quantum enhanced DFT (QEDFT) that systematically constructs quantum approximations of the universal functional using data obtained from a quantum computer. We benchmark the QEDFT algorithm on the Fermi-Hubbard model, both numerically and on data from experiments on real quantum hardware. We find that QEDFT surpasses the quality of groundstate results obtained from Hartree-Fock DFT, as well as from direct application of conventional quantum algorithms such as VQE. Furthermore, we demonstrate that QEDFT works even when only noisy, low-depth quantum computation is available, by benchmarking the algorithm on data obtained from Google's quantum computer. We further show how QEDFT also captures quintessential properties of strongly correlated Mott physics for large Fermi-Hubbard systems using functionals generated on much smaller system sizes. Our results indicate that QEDFT can be applied to realistic materials and molecular systems, and has the potential to outperform the direct application of either DFT or VQE alone, without the requirement of large scale or fully fault-tolerant quantum computers.

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arXiv2022

Towards near-term quantum simulation of materials

Simulation of materials is one of the most promising applications of quantum computers. On near-term hardware the crucial constraint on these simulations is circuit depth. Many quantum simulation algorithms rely on a layer of unitary evolutions generated by each term in a Hamiltonian. This appears in time-dynamics as a single Trotter step, and in variational quantum eigensolvers under the Hamiltonian variational ansatz as a single ansatz layer. We present a new quantum algorithm design for materials modelling where the depth of a layer is independent of the system size. This design takes advantage of the locality of materials in the Wannier basis and employs a tailored fermionic encoding that preserves locality. We analyse the circuit costs of this approach and present a compiler that transforms density functional theory data into quantum circuit instructions -- connecting the physics of the material to the simulation circuit. The compiler automatically optimises circuits at multiple levels, from the base gate level to optimisations derived from the physics of the specific target material. We present numerical results for materials spanning a wide structural and technological range. Our results demonstrate a reduction of many orders of magnitude in circuit depth over standard prior methods that do not consider the structure of the Hamiltonian. For example our results improve resource requirements for Strontium Vanadate (SrVO$_3$) from 864 to 180 qubits for a $3\times3\times3$ lattice, and the circuit depth of a single Trotter or variational layer from $7.5\times 10^8$ to depth $884$. Although this is still beyond current hardware, our results show that materials simulation may be feasible on quantum computers without necessarily requiring scalable, fault-tolerant quantum computers, provided quantum algorithm design incorporates understanding of the materials and applications.

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arXiv2021

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

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 1x8 and 2x4 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. Our scalable approach is a first step to using near-term quantum computers to determine low-energy properties of strongly-correlated electronic systems that cannot be solved exactly by classical computers.

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arXiv2020

Strong zero modes from geometric chirality in quasi-one-dimensional Mott insulators

Strong zero modes provide a paradigm for quantum many-body systems to encode local degrees of freedom that remain coherent far from the ground state. Example systems include $\mathbb{Z}_n$ chiral quantum clock models with strong zero modes related to $\mathbb{Z}_n$ parafermions. Here we show how these models and their zero modes arise from geometric chirality in fermionic Mott insulators, focusing on $n=3$ where the Mott insulators are three-leg ladders. We link such ladders to $\mathbb{Z}_3$ chiral clock models by combining bosonization with general symmetry considerations. We also introduce a concrete lattice model which we show to map to the $\mathbb{Z}_3$ chiral clock model, perturbed by the Uimin-Lai-Sutherland Hamiltonian arising via superexchange. We demonstrate the presence of strong zero modes in this perturbed model by showing that correlators of clock operators at the edge remain close to their initial value for times exponentially long in the system size, even at infinite temperature.

cond-mat.str-el↗

arXiv2020

Multidimensional dark space and its underlying symmetries: towards dissipation-protected qubits

Quantum systems are always subject to interactions with an environment, typically resulting in decoherence and distortion of quantum correlations. It has been recently shown that a controlled interaction with the environment may actually help to create a state, dubbed as {\em ``dark''}, which is immune to decoherence. To encode quantum information in the dark states, they need to span a space with a dimensionality larger than one, so different orthogonal states act as a computational basis. We devise a symmetry-based conceptual framework to engineer such degenerate dark spaces (DDS), protected from decoherence by the environment. We illustrate this construction with a model protocol, inspired by the fractional quantum Hall effect, where the DDS basis is isomorphic to a set of degenerate Laughlin states. The long-time steady state of our driven-dissipative model exhibits thus all the characteristics of degenerate vacua of a unitary topological system. This approach offers new possibilities for storing, protecting and manipulating quantum information in open systems.

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