Abstract We demonstrate quantum circuit simulations of the transverse field Ising model with longitudinal fields, displaying salient features of glassy dynamics. The energy landscape and spin configurations of toy models are considered, using the Variational Quantum Eigensolver to obtain the ground-state energies and corresponding eigenstates for a 6 $$\times$$ × 6 Ising lattice using 36 qubits and a 1-D Ising chain of length 25 using 25 qubits. The former showed disordered spin configurations for a specific mixture of values of the two fields. These insights mirror catalytic processes, where disorder within a catalyst can lead to inefficient reaction mechanisms. Results obtained from our proof-of-principle implementation make the case for kick-starting more concentrated efforts in harnessing existing quantum computational tools for computationally probing complex dynamical behavior arising in quantum matter. Our aim is to leverage tools from quantum information processing to bring about a more nuanced understanding of the dynamics and structure of glassy systems, ultimately informing the development of novel materials and technology.
Abstract We demonstrate quantum circuit simulations of the transverse field Ising model with longitudinal fields, displaying salient features of glassy dynamics. The energy landscape and spin configurations of toy models are considered, using the Variational Quantum Eigensolver to obtain the ground-state energies and corresponding eigenstates for a 6 × × 6 Ising lattice using 36 qubits and a 1-D Ising chain of length 25 using 25 qubits. The former showed disordered spin configurations for a specific mixture of values of the two fields. These insights mirror catalytic processes, where disorder within a catalyst can lead to inefficient reaction mechanisms. Results obtained from our proof-of-principle implementation make the case for kick-starting more concentrated efforts in harnessing existing quantum computational tools for computationally probing complex dynamical behavior arising in quantum matter. Our aim is to leverage tools from quantum information processing to bring about a more nuanced understanding of the dynamics and structure of glassy systems, ultimately informing the development of novel materials and technology.
In this paper, quantum algorithms are to be used to simulate glassy systems in toy models. To look for glassy behavior, the energy landscape and spin configurations of the transverse field Ising model in a longitudinal field are studied. The Variational Quantum Eigensolver (VQE) is used to obtain the ground-state energies and corresponding eigenstates for a 6×6 Ising lattice using 36 qubits and a 1-dimensional Ising chain of length 25. For the 8×8 Cellular Potts model, the original Hamiltonian is converted to an Ising formulation for the VQE to reduce to its ground state. The energy change during minimization is carefully analyzed to find whether the effects of interfacial tension among cells could probably induce glassiness in the cell system.
In this Ph.D. thesis we examine the Adiabatic Quantum Algorithm from the point of view of statistical and condensed matter physics. We do this by studying the transverse-field Ising spin glass model defined on the Bethe lattice, which is of independent interest to both the physics community and the quantum computation community. Using quantum Monte Carlo methods, we perform an extensive study of the the ground-state properties of the model, including the R\'enyi entanglement entropy, quantum Fisher information, Edwards--Anderson parameter, correlation functions. Through the finite-size scaling of these quantities we find multiple independent and coinciding estimates for the critical point of the glassy phase transition at zero temperature, which completes the phase diagram of the model as was previously known in the literature. We find volumetric bipartite and finite multipartite entanglement for all values of the transverse field considered, both in the paramagnetic and in the glassy phase, and at criticality. We discuss their implication with respect to quantum computing. By writing a perturbative expansion in the large transverse field regime we develop a mean-field quasiparticle theory that explains the numerical data. The emerging picture is that of degenerate bands of localized quasiparticle excitations on top of a vacuum. The perturbative energy corrections to these bands are given by pair creation/annihilation and hopping processes of the quasiparticles on the Bethe lattice. The transition to the glassy phase is explained as a crossing of the energy level of the vacuum with one of the bands, so that creation of quasiparticles becomes energetically favoured. We also study the localization properties of the model by employing the forward scattering approximation of the locator expansion, which we compute using a numerical transfer matrix technique. We obtain a lower bound for the mobility edge of the system. We find a localized region inside of the glassy phase and we discuss the consequences of its presence for the Adiabatic Quantum Algorithm.
The Variational Quantum Eigensolver (VQE) is a leading hybrid quantum-classical algorithm for simulating many-body systems in the NISQ era. Its effectiveness, however, depends on the faithful preparation of eigenstates, which becomes challenging in degenerate and strongly entangled regimes. We study this problem using the transverse-field Ising model (TFIM) with periodic boundary conditions in one, two, and three dimensions, considering systems of up to 27 qubits. We employ different ansatzes: the hardware-efficient EfficientSU2 from Qiskit, the physics-inspired Hamiltonian Variational Ansatz (HVA) and HVA with symmetry breaking, and benchmark their performance using energy variance, entanglement entropy, spin correlations, and magnetization.
The quantum phase transitions provide a paradigm for studying collective quantum phenomena that are a result of competing non-commuting interactions. This paper will study the ground state properties and quantum critical dynamics of the one-dimensional transverse field Ising model through a combined perspective that includes exact diagonalisation, variational quantum eigensolver (VQE) simulations, and simulations on realistic physical quantum devices. We focus on a lattice of four spins, where we calculate the ground-state energies, magnetic order parameters and correlation functions at uniformly applied conditions, which is repeated by all systems. Precise diagonalisation provides both a benchmark, which is symmetry-conserving, and a depth-two, physics inspired variational approximation, which provides simulations accessible to hardware. The circuits that have been optimised identically are then placed on the IQM Garnet quantum processor, using a resource-efficient batched protocol. We find that the ground-state energies of shallow variational circuits are reliably captured by the circuit over the entire parameter space; the magnetic arrangement parameters and observables sensitive to correlation signal significantly more noise. The error analysis of quantitative analysis reveals a strong broadening of critical crossover on hardware, which is consistent with the noise attenuation of long-range correlations. These findings highlight the current capabilities as well as the fundamental limitations of noisy intermediate-scale quantum systems in modelling quantum critical phenomena as a benchmark to future enhancements in obtaining quantum hardware and quantum algorithms development.
The Variational Quantum Eigensolver (VQE) is a leading hybrid quantum-classical algorithm for simulating many-body systems in the NISQ era. Its effectiveness, however, depends on the faithful preparation of eigenstates, which becomes challenging in degenerate and strongly entangled regimes. We study this problem using the transverse-field Ising model (TFIM) with periodic boundary conditions in one, two, and three dimensions, considering systems of up to 27 qubits. We employ different ansatzes: the hardware-efficient EfficientSU2 from Qiskit, the physics-inspired Hamiltonian Variational Ansatz (HVA) and HVA with symmetry breaking, and benchmark their performance using energy variance, entanglement entropy, spin correlations, and magnetization.
Quantum computers are an ideal platform to study the ground state properties of strongly correlated systems due to the limitation of classical computing techniques particularly for systems exhibiting quantum phase transitions. While the error rates of Noisy Intermediate-Scale Quantum (NISQ) computers are still high, simulating strongly correlated systems on such devices and extracting information of possible phases may be within reach. The frustrated transverse-field Ising model (TFIM) is such a system with multiple ordered magnetic phases. In this study, we simulate a two-dimensional frustrated TFIM with next-nearest-neighbor spin-exchange interactions at zero temperature. The competition between the nearest-neighbor ferromagnetic and next-nearest-neighbor antiferromagnetic coupling gives rise to frustration in the system. Moreover, the presence of quantum fluctuations makes the ground-state phase profile even richer. We use the Variational Quantum Eigensolver (VQE) to compute the phases on a square lattice with periodic boundary conditions for a system of 16 sites (qubits). The trained VQE circuits are compared to exact diagonalization, allowing us to extract error measures of VQE. We focus on the ground-state phase transitions of this model, where VQE succeeds in finding the dominant magnetic phases. The optimized VQE circuits are then executed on the Quantinuum H1-1 trapped-ion quantum computer without using any error mitigation techniques. Our experiments show near perfect recovery of the magnetic phases of the frustrated model through ground-state energy, the energy derivative, and the spin correlation functions. Thus, we show that the trapped-ion quantum processor is able to achieve reliable simulations of a strongly correlated system within the limitations of the VQE approach.