Controlled quantum mechanical devices provide a means of simulating more complex quantum systems exponentially faster than classical computers. Such "quantum simulators" rely heavily upon being able to prepare the ground state of Hamiltonians, whose properties can be used to calculate correlation functions or even the solution to certain classical computations. While adiabatic preparation remains the primary means of producing such ground states, here we provide a different avenue of preparation: cooling to the ground state via simulated dissipation. This is in direct analogy to contemporary efforts to realize generalized forms of simulated annealing in quantum systems.
Controlled quantum mechanical devices provide a means of simulating more complex quantum systems exponentially faster than classical computers. Such "quantum simulators" rely heavily upon being able to prepare the ground state of Hamiltonians, whose properties can be used to calculate correlation functions or even the solution to certain classical computations. While adiabatic preparation remains the primary means of producing such ground states, here we provide a different avenue of preparation: cooling to the ground state via simulated dissipation. This is in direct analogy to contemporary efforts to realize generalized forms of simulated annealing in quantum systems.
In this chapter, we discuss the notion of a quantum simulator as a device that emulates a complex quantum many-body Hamiltonian, and a quantum annealer as an extension of such a paradigm that focuses on the preparation of the ground state in those Hamiltonians. Starting from the Landau–Zener processes and the adiabatic theorem, we illustrate how such ground states can be prepared by slow (adiabatic) deformations of a Hamiltonian. We discuss how this results in an adiabatic quantum computing algorithm and how, depending on the Hamiltonian we apply it to, we can solve problems of different classical and quantum complexity. The chapter closes with a thorough discussion of the D-Wave quantum annealer as a real-world superconducting quantum simulator of Ising-type models. This discussion centers both on the design of the superconducting annealers as well as on the conclusion from the literature on how this device works in practice, including how quantum operations are still possible even in the pressence of decoherence. We close the chapter with an outlook on the challenges that need to be overcome for making coherent quantum annealers and universal adiabatic quantum computers.
Ground-state preparation of quantum many-body systems is a fundamental challenge across quantum science, with implications for quantum simulation, quantum computing, and the study of complex quantum matter. The exponential growth of Hilbert space and the complexity of entangled eigenstates motivate the development of new approaches that go beyond conventional strategies based on adiabatic evolution, variational optimization, imaginary-time methods, and engineered dissipative processes. Here, we demonstrate that the recently proposed quantum Landau-Lifshitz-Gilbert (QLLG) dynamics [Phys. Rev. Lett. {\bf 133}, 266704 (2024)] provides an intrinsic nonlinear dissipative mechanism for real-time ground-state preparation. Unlike engineered dissipative schemes, QLLG encodes relaxation directly into the quantum equation of motion while preserving the underlying quantum structure of the evolution. The QLLG evolution selectively suppresses excited-state contributions, driving the system toward the lowest-energy eigenstate within the accessible symmetry sector. We show that the dynamics admits a monotonic energy functional and a stable ground-state fixed point, and that for generic initial states in an N-qubit Hilbert space the characteristic convergence time scales linearly with N and inversely with the spectral gap. Numerical simulations of an interacting spin chain confirm our analytical predictions. These results establish nonlinear dissipative QLLG dynamics as a new avenue for quantum state preparation, opening a new route for quantum simulation, computation, and state engineering.
Quantum algorithms for probing ground-state properties of quantum systems require good initial states. Projection-based methods such as eigenvalue filtering rely on inputs that have a significant overlap with the low-energy subspace, which can be challenging for large, strongly-correlated systems. This issue has motivated the study of physically-inspired dynamical approaches such as thermodynamic cooling. In this work, we introduce a ground-state preparation algorithm based on the simulation of quantum dynamics. Our main insight is to transform the Hamiltonian by a shifted sign function via quantum signal processing, effectively mapping eigenvalues into positive and negative subspaces separated by a large gap. This automatically ensures that all states within each subspace conserve energy with respect to the transformed Hamiltonian. Subsequent time-evolution with a perturbed Hamiltonian induces transitions to lower-energy states while preventing unwanted jumps to higher energy states. The approach does not rely on a priori knowledge of energy gaps and requires no additional qubits to model a bath. Furthermore, it makes O~(d3/2/ε) queries to the time-evolution operator of the system and O~(d3/2) queries to a block-encoding of the perturbation, for d cooling steps and an ε-accurate energy resolution. Our results provide a framework for combining quantum signal processing and Hamiltonian simulation to design heuristic quantum algorithms for ground-state preparation.
In his famous 1981 talk, Feynman proposed that unlike classical computers, which would presumably experience an exponential slowdown when simulating quantum phenomena, a universal quantum simulator would not. An ideal quantum simulator would be controllable, and built using existing technology. In some cases, moving away from gate-model-based implementations of quantum computing may offer a more feasible solution for particular experimental implementations. Here we consider an adiabatic quantum simulator which simulates the ground state properties of sparse Hamiltonians consisting of one- and two-local interaction terms, using sparse Hamiltonians with at most three-local interactions. Properties of such Hamiltonians can be well approximated with Hamiltonians containing only two-local terms. The register holding the simulated ground state is brought adiabatically into interaction with a probe qubit, followed by a single diabatic gate operation on the probe which then undergoes free evolution until measured. This allows one to recover e.g. the ground state energy of the Hamiltonian being simulated. Given a ground state, this scheme can be used to verify the QMA-complete problem LOCAL HAMILTONIAN, and is therefore likely more powerful than classical computing.
The last two decades feature an ever-increasing interest in quantum information processing - generalization of the classical computational models in the view of quantum mechanics (QM). In theory, quantum computational devices are capable of solving in polynomial time problems for which only algorithms with exponential time complexity are known. Such enormous advantage explains the global scale of scientific efforts for creating the quantum computer - physical realization of such computational device. While the results of those efforts are still constrained inside the large experimental laboratories, an adequate tool for studying quantum algorithms will be of great help for educating the next generation of computer scientists - the engineers that will be responsible for operating these devices. The paper describes a quantum computer simulation model that exhibits a certain attractive property - the simulation slowdown does not depend directly on the size of the input data but rather on the complexity of the quantum state, meaning that transformations upon less-entangled data are performed faster. Based on this property the simulation can be spread between the nodes of a grid cluster in a way as to keep the entanglement in each job minimal
Finding the global minimum in a rugged potential landscape is a computationally hard task, often equivalent to relevant optimization problems. Annealing strategies, either classical or quantum, explore the configuration space by evolving the system under the influence of thermal or quantum fluctuations. The thermal annealing dynamics can rapidly freeze the system into a low-energy configuration, and it can be simulated well on a classical computer, but it easily gets stuck in local minima. Quantum annealing, on the other hand, can be guaranteed to find the true ground state and can be implemented in modern quantum simulators; however, quantum adiabatic schemes become prohibitively slow in the presence of quasidegeneracies. Here, we propose a strategy which combines ideas from simulated annealing and quantum annealing. In such a hybrid algorithm, the outcome of a quantum simulator is processed on a classical device. While the quantum simulator explores the configuration space by repeatedly applying quantum fluctuations and performing projective measurements, the classical computer evaluates each configuration and enforces a lowering of the energy. We have simulated this algorithm for small instances of the random energy model, showing that it potentially outperforms both simulated thermal annealing and adiabatic quantum annealing. It becomes most efficient for problems involving many quasidegenerate ground states.