We present an exact simulation of a one-dimensional transverse Ising spin chain with a quantum computer. We construct an efficient quantum circuit that diagonalizes the Ising Hamiltonian and allows to obtain all eigenstates of the model by just preparing the computational basis states. With an explicit example of that circuit for n = 4 spins, we compute the expected value of the ground state transverse magnetization, the time evolution simulation and provide a method to also simulate thermal evolution. All circuits are run in IBM and Rigetti quantum devices to test and compare them qualitatively.
Abstract In the noisy intermediate-scale quantum (NISQ) era, quantum computers have become important tools to simulate the real-time evolution of strong correlated many-body systems. The general scheme of designing quantum circuits to simulate the quantum dynamics is based on the Trotter-Suzuki decomposition technique, which has its limitation because the accuracy of evolution process depends on the size of trotter steps when the evolution operator is decomposed as quantum gates. Going beyond the limitation of the Trotter-Suzuki scheme, we design a parameterized quantum circuit named α -circuit with simple determined size and the only one control parameter θ to simulate the real-time evolution of the specific XXX Heisenberg model with the specific initial state . The α -circuit can accurately generate the time-evolution results by tuning parameter θ , which means the circuit can also be regarded as a good state preparation machine (SPM).
The field of quantum computing has grown fast in recent years, both in theoretical advancements and the practical construction of quantum computers. These computers were initially proposed, among other reasons, to efficiently simulate and comprehend the complexities of quantum physics. In this paper, we present a comprehensive scheme for the exact simulation of the 1-D XY model on a quantum computer. We successfully diagonalize the proposed Hamiltonian, enabling access to the complete energy spectrum. Furthermore, we propose a novel approach to design a quantum circuit to perform exact time evolution. Among all the possibilities this opens, we compute the ground and excited state energies for the symmetric XY model with spin chains of n=4 n = 4 and n=8 n = 8 spins. Further, we calculate the expected value of transverse magnetization for the ground state in the transverse Ising model. Both studies allow the observation of a quantum phase transition from an antiferromagnetic to a paramagnetic state. Additionally, we have simulated the time evolution of the state all spins up in the transverse Ising model. The scalability and high performance of our algorithm make it an ideal candidate for benchmarking purposes, while also laying the foundation for simulating other integrable models on quantum computers.
The dynamical generation of complex correlations in quantum many-body systems is of renewed interest in the context of quantum chaos, where the out-of-time-ordered (OTO) correlation function appears as a convenient measure of scrambling. To detect the the transition from scrambling to many-body localization, the latter of which has limited dynamical complexity and is often classically simulatable, we develop both exact and approximate methods to compute OTO correlators for arbitrary universal quantum circuits. We take advantage of the mapping of quantum circuits to the dynamics of interacting fermions in one dimension, as Gaussian time evolution supplemented by quartic interaction gates. In this framework, the OTO correlator can be calculated exactly as a superposition of exponentially many Gaussian-fermionic trajectories in the number of interaction gates. We develop a variationally-optimized, Gaussian approximation to the spatial propagation of an initially-local operator by restriction to the fastest-traveling fermionic modes, in a similar spirit as light-front computational methods in quantum field theory. We demonstrate that our method can detect the many-body localization transitions of generally time-dependent dynamics without the need for perturbatively weak interactions.
We introduce an efficient classical algorithm for designing quantum circuits to simulate local manybody quantum dynamics efficiently without requiring commutativity of the the local terms summed to construct the Hamiltonian, a Hamiltonian oracle, or ancillary qubits. Our efficient algorithm with its resultant low-cost quantum circuit will be valuable for near-future quantum-simulation experiments, and we apply our circuit-design algorithm to two examples: Kitaev’s toric-code and honeycomb models.
Abstract Hamiltonian simulation is one of the main proposed applications of near-term quantum computers, but its practical value depends on whether real hardware can preserve intended Hamiltonian dynamics once sampling limits, gate noise, decoherence, and circuit depth are taken into account. This study investigates whether the IBM quantum backend \texttt{ibm\_marrakesh} can reproduce the many-body dynamics shown by ideal simulation, using a 15-qubit one-dimensional tilted-field Ising chain as the benchmark system. The system was initialized with all qubits spin-up except for a localized spin-down excitation at the central qubit,
q8, and evolved using a second-order Trotterized circuit with timestep
Δt=0.1. The reference case,
hz=0, was compared with the tilted-field case,
hz=hx=0.35625, across three interaction regimes:
J=0.90hx,
J=hx, and
J=1.40hx. Local magnetization, total magnetization, and connected spin correlations were used to track magnetization memory and finite-speed correlation spreading from the central excitation. The ideal simulation shows clear local and total magnetization evolution, as well as connected-correlation spreading outward from
q8, giving a baseline for the intended Hamiltonian dynamics. The IBM hardware results reproduce the broad early-time magnetization trend but show compressed local-magnetization values, reduced separation between qubits, and weaker long-range connected-correlation structure. These differences indicate that the open-access quantum hardware preserves some early-time features of the intended dynamics, while longer-time correlation spreading is increasingly obscured by finite sampling, two-qubit gate errors, readout error, decoherence, and circuit depth. Overall, the study uses this spin-chain system as a direct benchmark for testing how much physically meaningful many-body behavior can still be extracted from noisy open-access quantum hardware.