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arXiv:1706.08644 · Scientific Reports

Quantum algorithm for preparing the ground state of a system via resonance transition

Hefeng Wang

Published Nov 21, 2017• 13 citations
arXivHTMLPDF

Abstract

Preparing the ground state of a system is an important task in physics. We propose a quantum algorithm for preparing the ground state of a physical system that can be simulated on a quantum computer. The system is coupled to an ancillary qubit, by introducing a resonance mechanism between the ancilla qubit and the system, and combined with measurements performed on the ancilla qubit, the system can be evolved to monotonically converge to its ground state through an iterative procedure. We have simulated the application of this algorithm for the Afflect-Kennedy-Lieb-Tasaki model, whose ground state can be used as resource state in one-way quantum computation.

DOI
10.1038/s41598-017-16396-0

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Preparing the ground state of a system is an important task in physics. We propose a quantum algorithm for preparing the ground state of a physical system that can be simulated on a quantum computer. The system is coupled to an ancillary qubit, by introducing a resonance mechanism between the ancilla qubit and the system, and combined with measurements performed on the ancilla qubit, the system can be evolved to monotonically converge to its ground state through an iterative procedure. We have simulated the application of this algorithm for the Afflect-Kennedy-Lieb-Tasaki model, whose ground state can be used as resource state in one-way quantum computation.
We design a quantum algorithm for ground state preparation in the early fault tolerant regime. As a Monte Carlo style quantum algorithm, our method features a Lindbladian where the target state is stationary. The construction of this Lindbladian is algorithmic and should not be seen as a specific approximation to some weakly coupled system-bath dynamics in nature. Our algorithm can be implemented using just one ancilla qubit and efficiently simulated on a quantum computer. It can prepare the ground state even when the initial state has zero overlap with the ground state, bypassing the most significant limitation of methods like quantum phase estimation. As a variant, we also propose a discrete-time algorithm, demonstrating even better efficiency and providing a near-optimal simulation cost depending on the desired evolution time and precision. Numerical simulations using Ising and Hubbard models demonstrate the efficacy and applicability of our method. Published by the American Physical Society 2024
Abstract The simulation of the dynamics of a system coupled to a low-temperature environment is a promising application of quantum computers to determine ground-state properties of physical systems. However, this approach requires not only the existence of an environment that allows the system to dissipate energy and evolve to its ground state, but also the detailed knowledge of the properties of the bath. In this paper, we propose a polynomial-time algorithm for ground state preparation which only relies on the existence of a physical bath which achieves the same task, while a detailed description of the environment may remain unknown . In particular, we show that this ''super-bath quantum eigensolver algorithm'' prepares the ground state of the system by combining a Gaussian stabilization dephasing procedure with the simulation of the interaction between the system and a super-bath which only requires minimal knowledge of the physical environment. Based on our algorithmic framework, we establish a partial order relation among environments. Supported by experimental lifetime data of nuclear metastable states, we suggest that our algorithm is applicable to determine nuclear ground states in polynomial time. These results highlight the potential advantage of quantum computing in addressing ground state problems in real-world physical systems.
Ground-state preparation for a given Hamiltonian is a common quantum-computing task of great importance and has relevant applications in quantum chemistry, computational material modeling, and combinatorial optimization. We consider an approach to simulate dissipative non-Hermitian Hamiltonian quantum dynamics using Hamiltonian simulation techniques to efficiently recover the ground state of a target Hamiltonian. The proposed method facilitates the energy transfer by repeatedly projecting ancilla qubits to the desired state, rendering the effective non-Hermitian Hamiltonian evolution on the system qubits. To make the method more resource friendly in the noisy intermediate-scale quantum (NISQ) and early fault-tolerant era, we combine the non-Hermitian projection algorithm with multiple variational gadgets, including variational module enhancement and variational state recording, to reduce the required circuit depth and avoid the exponentially vanishing success probability for post-selections. We compare our method, the non-Hermitian-variational algorithm, with a pure variational method -- QAOA for solving the 3-SAT problem and preparing the ground state for the transverse-field Ising model. As demonstrated by numerical evidence, the non-Hermitian-variational algorithm outperforms QAOA in convergence speed with improved quantum resource efficiency.
We present a quantum algorithm that provides a general approach for obtaining the energy spectrum of a physical system without making a guess on its eigenstates. In this algorithm, a probe qubit is coupled to a quantum register R which consists of one ancilla qubit and an n-qubit register that represents the system. R is prepared in a general reference state, and a general excitation operator that acts on R is constructed. The probe exhibits a dynamical response only when it is resonant with a transition from the reference state to an excited state of R which contains the eigenstates of the system. By varying the probe's frequency, the energy spectrum and the eigenstates of the system can be obtained.
Abstract We propose a procedure to extract a true ground state from an approximate ground state by using quantum entanglement. We use plural ancilla qubits with hierarchical structure, intending to gradually improve the precision of the approximation. We demonstrate the procedure for quantum systems with a few qubits that derive from the (1+1)-dimensional Schwinger model by classically emulated digital quantum simulation. Although we use for simplicity an approximate ground state prepared by adiabatic quantum computation, our procedure is applicable to any approximate ground state that is a superposition of a true ground state and excited states. Our procedure is applicable for an NNN-qubits Hamiltonian with a nondegenerate ground state.
Ground-state preparation for a given Hamiltonian is a common quantum-computing task of great importance and has relevant applications in quantum chemistry, computational material modeling, and combinatorial optimization. We consider an approach to simulate dissipative non-Hermitian Hamiltonian quantum dynamics using Hamiltonian simulation techniques to efficiently recover the ground state of a target Hamiltonian. The proposed method facilitates the energy transfer by repeatedly projecting ancilla qubits to the desired state, rendering the effective non-Hermitian Hamiltonian evolution on the system qubits. To make the method more resource friendly in the noisy intermediate-scale quantum (NISQ) and early fault-tolerant era, we combine the non-Hermitian projection algorithm with multiple variational gadgets, including variational module enhancement and variational state recording, to reduce the required circuit depth and avoid the exponentially vanishing success probability for postselections. We compare our method, the non-Hermitian-variational algorithm, with a pure variational method, the quantum approximate optimization algorithm (QAOA), for solving the 3-SAT problem and preparing the ground state for the transverse field Ising model. As demonstrated by numerical evidence, the non-Hermitian-variational algorithm outperforms QAOA in convergence speed with improved quantum resource efficiency.