Simulating Static and Dynamic Properties of Magnetic Molecules with Prototype Quantum Computers
Luca Crippa, Francesco Tacchino, Mario Chizzini, Antonello Aita, Michele Grossi, Alessandro Chiesa, Paolo Maria Santini, Ivano Tavernelli, Stefano Carretta
Magnetic molecules are prototypical systems to investigate peculiar quantum mechanical phenomena. As such, simulating their static and dynamical behavior is intrinsically difficult for a classical computer, due to the exponential increase of required resources with the system size. Quantum computers solve this issue by providing an inherently quantum platform, suited to describe these magnetic systems. Here, we show that both the ground state properties and the spin dynamics of magnetic molecules can be simulated on prototype quantum computers, based on superconducting qubits. In particular, we study small-size anti-ferromagnetic spin chains and rings, which are ideal test-beds for these pioneering devices. We use the variational quantum eigensolver algorithm to determine the ground state wave-function with targeted ansatzes fulfilling the spin symmetries of the investigated models. The coherent spin dynamics are simulated by computing dynamical correlation functions, an essential ingredient to extract many experimentally accessible properties, such as the inelastic neutron cross-section.
Magnetic molecules are prototypical systems to investigate peculiar quantum mechanical phenomena. As such, simulating their static and dynamical behavior is intrinsically difficult for a classical computer, due to the exponential increase of required resources with the system size. Quantum computers solve this issue by providing an inherently quantum platform, suited to describe these magnetic systems. Here, we show that both the ground state properties and the spin dynamics of magnetic molecules can be simulated on prototype quantum computers, based on superconducting qubits. In particular, we study small-size anti-ferromagnetic spin chains and rings, which are ideal test-beds for these pioneering devices. We use the variational quantum eigensolver algorithm to determine the ground state wave-function with targeted ansatzes fulfilling the spin symmetries of the investigated models. The coherent spin dynamics are simulated by computing dynamical correlation functions, an essential ingredient to extract many experimentally accessible properties, such as the inelastic neutron cross-section.
Computer simulation is central to understanding the behaviour of matter. Yet, more than a century after the development of quantum theory, first-principles simulation of chemistry remains a daunting challenge, owing to the exponential growth in memory required to represent interacting quantum particles such as electrons in molecules. Quantum computing offers, in principle, a fundamentally more efficient paradigm for simulating quantum systems, with quantum chemistry often cited as a flagship application. However, many quantum algorithms face intrinsic limitations, and any genuine quantum advantage must surpass the strong baseline set by decades of progress in classical algorithms and hardware. While classical methods often suffice for simulating weakly correlated systems, systems with many strongly correlated electrons remain a challenge for both classical and quantum approaches. In this thesis, we develop quantum algorithms for solving the time-independent Schrödinger equation, with a focus on molecular systems with strongly correlated electrons. We introduce a framework for identifying a compact set of states that parametrise the many-body wavefunction by capturing the correlation due to spin coupling between localised electrons. This representation requires very few variational parameters but incurs a very high memory cost on classical computers. To overcome this, we design quantum circuits that efficiently prepare such states by exploiting their symmetry, encoding the dominant entanglement structure of electronic wavefunctions into the initial qubit states. Through theoretical analysis and classical simulations of quantum computers, we show that this substantially reduces the quantum resources required to accurately compute ground- and excitedstate properties. Finally, we develop an approach for approximating the optimal ansatz within the variational quantum eigensolver, an algorithm designed for near-term quantum devices. Our method constructs wavefunctions from products of symmetrypreserving unitary operators and couples discrete and continuous optimisation to yield highly compact representations of strongly correlated electrons using shallow quantum circuits. Together, these results establish complementary directions for embedding problemspecific structure into quantum simulation algorithms, advancing the practical simulation of strongly correlated electrons.
The performance of quantum algorithms for eigenvalue problems, such as computing Hamiltonian spectra, depends strongly on the overlap of the initial wave function and the target eigenvector. In a basis of Slater determinants, the representation of energy eigenstates of systems with N strongly correlated electrons requires a number of determinants that scales exponentially with N . On classical processors, this restricts simulations to systems where N is small. Here, we show that quantum computers can efficiently simulate strongly correlated molecular systems by directly encoding the dominant entanglement structure in the form of spin-coupled initial states. This avoids resorting to expensive classical or quantum state preparation heuristics and instead exploits symmetries in the wave function. We provide quantum circuits for deterministic preparation of a family of spin eigenfunctions with ( N N / 2 ) Slater determinants with depth O ( N ) and O ( N 2 ) local gates. Their use as highly entangled initial states in quantum algorithms reduces the total runtime of quantum phase estimation and related fault-tolerant methods by orders of magnitude. Furthermore, we assess the application of spin-coupled wave functions as initial states for a range of heuristic quantum algorithms, namely, the variational quantum eigensolver, adiabatic state preparation, and different versions of quantum subspace diagonalization (QSD) including QSD based on real-time-evolved states. We also propose a QSD algorithm that exploits states obtained through adaptive quantum eigensolvers. For all algorithms, we demonstrate that using spin-coupled initial states drastically reduces the quantum resources required to simulate strongly correlated ground and excited states. Our work provides a crucial component for enabling scalable quantum simulation of classically challenging electronic systems.
The elementary excitation spectrum of a many-body quantum system encodes many key properties, including phenomena as diverse as transport, thermalisation and ground state structure. Excitation spectra of strongly correlated systems are typically encoded in dynamical structure factors, which are demanding to measure experimentally and challenging to compute classically. Here we use quench spectroscopy on a superconducting quantum processor to extract excitation spectra of spin chains of L=101 spins. By tailoring the combination of quench protocol and observable, we selectively access distinct excitation sectors across several phases of the spin-1/2 XXZ chain, resolving free magnons, multi-magnon bound states, and two-spinon continua. Notably, we demonstrate that the protocol does not rely on ground state preparation: in the classically challenging gapless regime, we extract spectra directly from the quench dynamics of easily prepared product states, a procedure that is natural and straightforward on quantum hardware. Our work establishes quench spectroscopy as a fast and flexible probe of many-body excitation spectra on digital quantum hardware, introduces a novel quench protocol that does not require costly state preparation routines, and provides a scalable route towards regimes where classical simulation may become intractable.
Particle physics describes the interplay of matter and forces through gauge theories. Yet, the intrinsic quantum nature of gauge theories makes important problems notoriously difficult for classical computational techniques. Quantum computers offer a promising way to overcome these roadblocks. We demonstrate two essential requirements on this path: first, we perform a quantum computation of the properties of the basic building block of two-dimensional lattice quantum electrodynamics, involving both gauge fields and matter. Second, we show how to refine the gauge-field discretization beyond its minimal representation, using a trapped-ion qudit quantum processor, where quantum information is encoded in several states per ion. Such qudits are ideally suited for describing gauge fields, which are naturally high dimensional, leading to reduced register size and circuit complexity. We prepare the ground state of the model using a variational quantum eigensolver and observe the effect of dynamical matter on quantized magnetic fields. By controlling the qudit dimension, we also show how to seamlessly observe the effect of different gauge-field truncations. Finally, we experimentally study the dynamics of pair creation and magnetic energy. Our results open the door for hardware-efficient quantum simulations of gauge theories with qudits in near-term quantum devices.
Fermions are basic building blocks in the standard model. Interactions among these elementary particles determine how they assemble and consequently form various states of matter in our nature. Simulating fermionic degrees of freedom is also a central problem in condensed matter physics and quantum chemistry, which is crucial to understanding high-temperature superconductivity, quantum magnetism and molecular structure and functionality. However, simulating interacting fermions by classical computing generically face the minus sign problem, encountering the exponential computation complexity. Ultracold atoms provide an ideal experimental platform for quantum simulation of interacting fermions. This highly-controllable system enables the realizing of nontrivial fermionic models, by which the physical properties of the models can be obtained by measurements in experiment. This deepens our understanding of related physical mechanisms and helps determine the key parameters. In recent years, there have been versatile experimental studies on quantum ground state physics, finite temperature thermal equilibrium, and quantum many-body dynamics, in fermionic quantum simulation systems. Quantum simulation offers an access to the physical problems that are intractable on the classical computer, including studying macroscopic quantum phenomena and microscopic physical mechanisms, which demonstrates the quantum advantages of controllable quantum systems. This paper briefly introduces the model of interacting fermions describing the quantum states of matter in such a system. Then we discuss various states of matter, which can arise in interacting fermionic quantum systems, including Cooper pair superfluids and density-wave orders. These exotic quantum states play important roles in describing high-temperature superconductivity and quantum magnetism, but their simulations on the classical computers have exponentially computational cost. Related researches on quantum simulation of interacting fermions in determining the phase diagrams and equation of states reflect the quantum advantage of such systems.