Recent publications have introduced the concept of quantum-like (QL) bits, along with their associated QL-states and QL-gate operations, emerging from the dynamics of complex synchronized networks. The present work builds on this framework to present a simulation of quantum dynamics in spin systems. We focus on the transverse field Ising model, a widely studied Hamiltonian for interacting spin systems. We show how circuits, built using the QL analog of quantum gates, can be used to prepare an arbitrary initial wavepacket and simulate the time evolution of the resulting state for extracting physical observables such as magnetization. Beyond the statevector dynamics, we introduce a set of metrics that characterize how QL-circuit operations transform the underlying graph connections. These metrics quantify the microscopic coupling, phase coherence, and effective inter-block coupling generated by the circuit. These graph-level quantities provide constraints and design targets for potential physical implementations, indicating where interconnection resources, phase control, and effective coupling strength must be engineered in a hardware realization. Overall, this study demonstrates how classical resources can be harnessed to simulate quantum systems and we discuss the advantages and limitations.
Recent publications have introduced the concept of quantum-like (QL) bits, along with their associated QL-states and QL-gate operations, emerging from the dynamics of complex synchronized networks. The present work builds on this framework to present a simulation of quantum dynamics in spin systems. We focus on the transverse field Ising model, a widely studied Hamiltonian for interacting spin systems. We show how circuits, built using the QL analog of quantum gates, can be used to prepare an arbitrary initial wavepacket and simulate the time evolution of the resulting state for extracting physical observables such as magnetization. Beyond the statevector dynamics, we introduce a set of metrics that characterize how QL-circuit operations transform the underlying graph connections. These metrics quantify the microscopic coupling, phase coherence, and effective inter-block coupling generated by the circuit. These graph-level quantities provide constraints and design targets for potential physical implementations, indicating where interconnection resources, phase control, and effective coupling strength must be engineered in a hardware realization. Overall, this study demonstrates how classical resources can be harnessed to simulate quantum systems and we discuss the advantages and limitations.
Quantum simulation is a promising near term application for quantum information processors with the potential to solve computationally intractable problems using just a few dozen interacting qubits. A range of experimental platforms have recently demonstrated the basic functionality of quantum simulation applied to quantum magnetism, quantum phase transitions and relativistic quantum mechanics. However, in all cases, the physics of the underlying hardware restricts the achievable inter-particle interactions and forms a serious constraint on the versatility of the simulators. To broaden the scope of these analog devices, we develop a suite of pulse sequences that permit a user to efficiently realize average Hamiltonians that are beyond the native interactions of the system. Specifically, this approach permits the generation of all symmetrically coupled translation-invariant two-body Hamiltonians with homogeneous on-site terms, a class which includes all spin- XYZ chains, but generalized to include long-range couplings. Our work builds on previous work proving that universal simulation is possible using both entangling gates and single-qubit unitaries. We show that determining the appropriate 'program' of unitary pulse sequences which implements an arbitrary Hamiltonian transformation can be formulated as a linear program over functions defined by those pulse sequences, running in polynomial time and scaling efficiently in hardware resources. Our analysis extends from circuit model quantum information to adiabatic quantum evolutions, representing an important and broad-based success in applying functional analysis to the field of quantum information.
Abstract. Quantum simulation is a promising near term application for quantum information processors with the potential to solve computationally intractable problems using just a few dozen interacting qubits [1, 2, 3]. A range of experimental platforms have recently demonstrated the basic functionality of quantum simulation applied to quantum magnetism, quantum phase transitions, and relativistic quantum mechanics [4, 5, 6, 7, 8, 9, 10, 11]. However, in all cases, the physics of the underlying hardware restricts the achievable inter-particle interactions and forms a serious constraint on the versatility of the simulators. To broaden the scope of these analog devices, we develop a suite of pulse sequences that permit a user to efficiently realize average Hamiltonians that are beyond the native interactions of the system [12, 13]. Specifically, this approach permits the generation of all symmetrically coupled translation-invariant two-body Hamiltonians with homogeneous on-site terms, a class which includes all spin-1/2 XYZ chains, but generalized to include long-range couplings. Our work builds on previous work proving that universal simulation is possible using both entangling gates and single-qubit unitaries [14, 15, 16]. We show that determining the appropriate “program ” of unitary pulse sequences which implements an arbitrary Hamiltonian transformation can be formulated as a linear program over functions defined by those pulse sequences, running in polynomial time and scaling efficiently in hardware resources. Our analysis extends from circuit model quantum information to adiabatic quantum evolutions, representing an important and broad-based success in applying functional analysis to the field of quantum information. ar X iv
Quantum computers offer a powerful platform for simulating real-time molecular and materials dynamics, where coherence, entanglement, and many-body correlations govern processes such as charge transport, tunneling, and spin exchange. Building on the foundations introduced in Part I, this tutorial presents practical algorithms for quantum dynamical simulation on qubit-based hardware using the open-source QFlux framework. We formulate molecular and spin Hamiltonians in the Pauli basis and map their propagators to quantum circuits using parity-based phase constructions and local basis rotations. Expectation values and state overlaps are obtained with the Hadamard test, or by direct measurement of Pauli strings, providing a unified protocol for extracting complex observables and variational quantities. We introduce the Quantum Split-Operator Fourier Transform ( Q-SOFT ), the quantum analog of the classical SOFT method for quantum dynamics simulations, which applies kinetic and potential phase operators in conjugate bases connected by the Quantum Fourier Transform to implement second-order Trotterized evolution. A simulation of proton transfer in an asymmetric double-well potential modeling a DNA base pair reproduces benchmark simulations. We also present a variational time-evolution scheme based on the McLachlan principle, implemented in QFlux’s VarQRTE driver. Applied to a two-spin Heisenberg model, it captures coherent spin exchange with shallow, noise-resilient circuits. Together, these methods establish a reproducible workflow—from Hamiltonian encoding to circuit execution and measurement—bridging classical and quantum simulation and providing a practical toolkit for real-time quantum dynamics on near-term hardware.
Quantum computers offer a powerful platform for simulating real-time molecular and materials dynamics, where coherence, entanglement, and many-body correlations govern processes such as charge transport, tunneling, and spin exchange. Building on the foundations introduced in Part I, this tutorial presents practical algorithms for quantum dynamical simulation on qubit-based hardware using the open-source QFlux framework. We formulate molecular and spin Hamiltonians in the Pauli basis and map their propagators to quantum circuits using parity-based phase constructions and local basis rotations. Expectation values and state overlaps are obtained with the Hadamard test, or by direct measurement of Pauli strings, providing a unified protocol for extracting complex observables and variational quantities. We introduce the Quantum Split-Operator Fourier Transform ( Q-SOFT ), the quantum analog of the classical SOFT method for quantum dynamics simulations, which applies kinetic and potential phase operators in conjugate bases connected by the Quantum Fourier Transform to implement second-order Trotterized evolution. A simulation of proton transfer in an asymmetric double-well potential modeling a DNA base pair reproduces benchmark simulations. We also present a variational time-evolution scheme based on the McLachlan principle, implemented in QFlux’s VarQRTE driver. Applied to a two-spin Heisenberg model, it captures coherent spin exchange with shallow, noise-resilient circuits. Together, these methods establish a reproducible workflow—from Hamiltonian encoding to circuit execution and measurement—bridging classical and quantum simulation and providing a practical toolkit for real-time quantum dynamics on near-term hardware.
We propose a detailed analysis of datasets generated from simulations of two-dimensional quantum spin systems using the quantum Ising model at absolute zero temperature. Our focus is on examining how fundamental physical properties, energy, magnetization, and entanglement entropy, evolve under varying external transverse magnetic fields and system sizes. From the Quantum Toolbox in Python (QuTiP), we simulate systems with 4, 8, and 16 spins arranged in square lattices, generating extensive datasets with 5000 samples per magnetic field value. The Hamiltonian operator incorporates quantum mechanical effects such as superposition and tunneling, challenging classical interpretations of spin states. We compute extended Pauli operators and construct the Hamiltonian to include spin-spin interactions and transverse field terms. Our analysis reveals that as the system size increases, fluctuations in energy and entanglement entropy become more evident, indicating lifted sensitivity to external perturbations and suggesting the onset of quantum phase transitions. Spin-spin correlation functions demonstrate that interactions are predominantly local, but larger systems exhibit more complex and fluctuating correlations. These findings provide valuable insights into the behavior of quantum spin systems and lay the groundwork for future machine learning applications aimed at predicting physical quantities and identifying phase transitions from a quantum perspective.
Simulating quantum many-body systems is essential for understanding complex phenomena in condensed matter, chemistry, and materials science. Quantum computing offers a way to overcome the limitations of classical methods by operating directly in exponentially large Hilbert spaces. In particular, classical methods often fail to capture the dynamics of strongly correlated systems, which makes quantum algorithms a promising alternative for exploring these challenging regimes. This thesis uses quantum dynamics simulations to probe the behaviour of many-body systems. We first introduce a spectroscopy-based protocol to extract excitation spectra from the time evolution of observables and analyse its performance on near-term quantum devices. We show that the protocol requires only short evolution times and is resilient to errors, facilitating its implementation on real hardware. Building on this, we simulate fermionic excitation spectra using current quantum devices, introducing resource optimisations - including an approximate free-fermion initial state, a unitary quench without ancillae, and reduced Trotter steps - that significantly lower circuit depth. These improvements enable simulations at system sizes competitive with the state of the art, yielding results that match classical benchmarks. While most studies focus on unitary dynamics of isolated systems, open quantum dynamics is increasingly relevant for describing non-equilibrium processes across biology, materials science, and quantum control. We extend our scope to systems coupled to an environment and governed by Lindbladian evolution. By studying simulation complexity through physically meaningful quantities - such as correlation length and mixing time - we explore whether open-system dynamics can be as tractable as their unitary counterparts. These findings provide insights into the computational complexity landscape of open-system simulation and highlight regimes where quantum methods offer a clear advantage.