Dissipative Quantum Eigensolver for Ground State Preparation
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Solution Overview
Problem
Current methods for approaching or preparing the ground state of a Hamiltonian on a quantum computer face limitations due to noise tolerance and computational resource constraints, particularly in finding or approximating ground or Gibbs states efficiently, especially for complex quantum systems where prior knowledge of spectral gaps is required.
Innovation Solution
A method involving local generalized measurements on a quantum computer system, where data qudits are perturbed based on measurement outcomes, allowing iterative convergence to a ground or Gibbs state without relying on spectral gap knowledge, using a dissipative quantum eigensolver (DQE) or dissipative Gibbs sampler (DGS) algorithm.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If phase estimation algorithm is used to approach ground state, then ground state can be identified with high probability, but the algorithm requires prior knowledge of spectral gap and involves complex quantum computations that are beyond near-term hardware reach
Solution Approach 1:
The algorithm segments the ground state preparation process into multiple iterative steps, where in each step a local generalised measurement is performed and the outcome is used to determine whether to accept or reject a perturbation. This segmentation allows the complex task of ground state identification to be broken down into simpler, manageable operations that can be performed on near-term quantum hardware without requiring full phase estimation computations.
Solution Approach 2:
The algorithm employs feedback mechanisms where the measurement outcomes from local generalised measurements are used to dynamically determine the next step in the process. The feedback from measurement results guides whether to accept or reject perturbations and when to stop iterating, enabling the system to adaptively converge on the ground state without requiring prior spectral gap knowledge or complex pre-computed parameters.
2Reliability
If adiabatic state preparation is used, then ground state can be prepared by slowly transforming Hamiltonian, but the algorithm fails when spectral gap vanishes along the path and requires knowledge of spectral gap properties
Solution Approach 1:
The algorithm changes the approach by using parameterized local generalised measurements that can be adapted to different Hamiltonians without requiring knowledge of their spectral gap properties. The measurement parameters are adjusted based on the specific Hamiltonian structure, allowing the algorithm to work reliably across different quantum systems regardless of whether they have vanishing spectral gaps or complex energy spectra.
Solution Approach 2:
The algorithm makes the quantum system self-correcting by using local generalised measurements to identify and reject perturbations that move the system away from the ground state. The system automatically adapts to the specific Hamiltonian being studied through the measurement outcomes, eliminating the need for external guidance based on spectral gap knowledge or manual tuning of adiabatic parameters.
3Measurement precision
If variational quantum eigensolver is used, then ground state can be approached by minimizing energy, but the method requires complex variational optimization and may get stuck in local minima
Solution Approach 1:
The algorithm replaces the complex variational optimization mechanism with a simpler stochastic process based on local generalised measurements and random perturbations. Instead of using gradient-based optimization that requires careful parameter tuning and can get stuck in local minima, the system uses measurement-guided acceptance/rejection of perturbations to naturally converge on the ground state, substituting mechanical optimization with a more robust statistical approach.
4Power
If quantum computers are used to solve ground state problems, then computational power is enhanced, but noise and errors accumulate during the computation process
Solution Approach 1:
The algorithm converts the harmful effect of noise and errors into a beneficial feature by using stochastic local generalised measurements that are inherently robust to noise. The measurement-based approach naturally filters out erroneous perturbations through the acceptance/rejection mechanism, and the random nature of the measurements helps the system escape from noise-induced local minima, turning noise from a liability into an advantage for finding the true ground state.
Data Source
AI summary
The present invention provides methods and apparatuses for approximating a ground state or a Gibbs state of a k-local Hamiltonian using a quantum computer system. The procedure begins by providing a set of local generalised measurements corresponding to the terms of the k-local Hamiltonian. A set of data qudits is initialised into an initial state and a local generalised measurement is subsequently performed to perturb a subset of the data qudits from an initial state to a perturbed state. The perturbation is accepted or rejected based on a measurement outcome of the local generalised measurement. The perturbation and accept/reject steps are repeated unless or until a stopping condition is met. The result of the procedure is to provably drive the encoded Hamiltonian toward or even into a ground state or a Gibbs state, a useful starting point in many quantum algorithms, such as those relating to materials simulation.