Adiabatic quantum imaginary time evolution

• URL: http://arxiv.org/abs/2308.03292v2
• Date: Mon, 22 Apr 2024 05:49:52 GMT
• Title: Adiabatic quantum imaginary time evolution
• Authors: Kasra Hejazi, Mario Motta, Garnet Kin-Lic Chan,
• Abstract summary: We introduce an adiabatic state preparation protocol which implements quantum imaginary time evolution under the Hamiltonian of the system. Unlike the original quantum imaginary time evolution algorithm, adiabatic quantum imaginary time evolution does not require quantum state tomography during its runtime.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We introduce an adiabatic state preparation protocol which implements quantum imaginary time evolution under the Hamiltonian of the system. Unlike the original quantum imaginary time evolution algorithm, adiabatic quantum imaginary time evolution does not require quantum state tomography during its runtime, and unlike standard adiabatic state preparation, the final Hamiltonian is not the system Hamiltonian. Instead, the algorithm obtains the adiabatic Hamiltonian by integrating a classical differential equation that ensures that one follows the imaginary time evolution state trajectory. We introduce some heuristics that allow this protocol to be implemented on quantum architectures with limited resources. We explore the performance of this algorithm via classical simulations in a one-dimensional spin model and highlight essential features that determine its cost, performance, and implementability for longer times, and compare to the original quantum imaginary time evolution for ground-state preparation. More generally, our algorithm expands the range of states accessible to adiabatic state preparation methods beyond those that are expressed as ground-states of simple explicit Hamiltonians.

Related papers

• Sparse random Hamiltonians are quantumly easy [105.6788971265845]
  A candidate application for quantum computers is to simulate the low-temperature properties of quantum systems. This paper shows that, for most random Hamiltonians, the maximally mixed state is a sufficiently good trial state. Phase estimation efficiently prepares states with energy arbitrarily close to the ground energy.
  arXiv  Detail & Related papers  (2023-02-07T10:57:36Z)
• Improved iterative quantum algorithm for ground-state preparation [4.921552273745794]
  We propose an improved iterative quantum algorithm to prepare the ground state of a Hamiltonian system. Our approach has advantages including the higher success probability at each iteration, the measurement precision-independent sampling complexity, the lower gate complexity, and only quantum resources are required when the ancillary state is well prepared.
  arXiv  Detail & Related papers  (2022-10-16T05:57:43Z)
• Improved algorithms of quantum imaginary time evolution for ground and excited states of molecular systems [0.0]
  Quantum imaginary time evolution (QITE) is a recently proposed quantum-classical hybrid algorithm that is guaranteed to reach the lowest state of system. We analyze the derivation of the underlying QITE equation order-by-order, and suggest a modification that is theoretically well founded. We also discuss how to accurately estimate the norm of an imaginary-time-evolved state, and applied it to excited state calculations.
  arXiv  Detail & Related papers  (2022-05-04T10:32:16Z)
• Time Dependent Hamiltonian Simulation Using Discrete Clock Constructions [42.3779227963298]
  We provide a framework for encoding time dependent dynamics as time independent systems. First, we create a time dependent simulation algorithm based on performing qubitization on the augmented clock system. Second, we define a natural generalization of multiproduct formulas for time-ordered exponentials.
  arXiv  Detail & Related papers  (2022-03-21T21:29:22Z)
• Variational quantum simulation of the imaginary-time Lyapunov control for accelerating the ground-state preparation [17.802280143175235]
  We first propose a Lyapunov control-inspired strategy to accelerate the well-established imaginary-time method for ground-state preparation. To make the method accessible in the noisy intermediate-scale quantum era, we propose a variational form of the algorithm that could work with shallow quantum circuits.
  arXiv  Detail & Related papers  (2021-12-22T10:40:33Z)
• Probabilistic imaginary-time evolution by using forward and backward real-time evolution with a single ancilla: first-quantized eigensolver of quantum chemistry for ground states [0.0]
  Imaginary-time evolution (ITE) on a quantum computer is a promising formalism for obtaining the ground state of a quantum system. We propose a new approach of PITE which requires only a single ancillary qubit. We discuss the application of our approach to quantum chemistry by focusing on the scaling of computational cost.
  arXiv  Detail & Related papers  (2021-11-24T12:54:27Z)
• Quantum algorithms for quantum dynamics: A performance study on the spin-boson model [68.8204255655161]
  Quantum algorithms for quantum dynamics simulations are traditionally based on implementing a Trotter-approximation of the time-evolution operator. variational quantum algorithms have become an indispensable alternative, enabling small-scale simulations on present-day hardware. We show that, despite providing a clear reduction of quantum gate cost, the variational method in its current implementation is unlikely to lead to a quantum advantage.
  arXiv  Detail & Related papers  (2021-08-09T18:00:05Z)
• Algebraic Compression of Quantum Circuits for Hamiltonian Evolution [52.77024349608834]
  Unitary evolution under a time dependent Hamiltonian is a key component of simulation on quantum hardware. We present an algorithm that compresses the Trotter steps into a single block of quantum gates. This results in a fixed depth time evolution for certain classes of Hamiltonians.
  arXiv  Detail & Related papers  (2021-08-06T19:38:01Z)
• Non-equilibrium stationary states of quantum non-Hermitian lattice models [68.8204255655161]
  We show how generic non-Hermitian tight-binding lattice models can be realized in an unconditional, quantum-mechanically consistent manner. We focus on the quantum steady states of such models for both fermionic and bosonic systems.
  arXiv  Detail & Related papers  (2021-03-02T18:56:44Z)
• Imaginary Time Propagation on a Quantum Chip [50.591267188664666]
  Evolution in imaginary time is a prominent technique for finding the ground state of quantum many-body systems. We propose an algorithm to implement imaginary time propagation on a quantum computer.
  arXiv  Detail & Related papers  (2021-02-24T12:48:00Z)
• Sufficient conditions for adiabaticity in open quantum systems [0.0]
  We introduce sufficient conditions for the adiabatic approximation in open quantum systems. We first illustrate our results by showing that the adiabatic approximation for open systems is compatible with the description of quantum thermodynamics at thermal equilibrium. We also apply our sufficient conditions as a tool in quantum control, evaluating the adiabatic behavior for the Hamiltonians of both the Deutsch algorithm and the Landau-Zener model under decoherence.
  arXiv  Detail & Related papers  (2020-07-29T22:19:42Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.