# A Variational Quantum Algorithm for Preparing Quantum Gibbs States

@article{Chowdhury2020AVQ, title={A Variational Quantum Algorithm for Preparing Quantum Gibbs States}, author={Anirban Narayan Chowdhury and Guang Hao Low and Nathan Wiebe}, journal={arXiv: Quantum Physics}, year={2020} }

Preparation of Gibbs distributions is an important task for quantum computation. It is a necessary first step in some types of quantum simulations and further is essential for quantum algorithms such as quantum Boltzmann training. Despite this, most methods for preparing thermal states are impractical to implement on near-term quantum computers because of the memory overheads required. Here we present a variational approach to preparing Gibbs states that is based on minimizing the free energy…

## 28 Citations

Variational quantum Gibbs state preparation with a truncated Taylor series

- Physics, Computer SciencePhysical Review Applied
- 2021

This paper proposes variational hybrid quantum-classical algorithms for quantum Gibbs state preparation and finds that shallow parameterized circuits with only one additional qubit can be trained to prepare the Ising chain and spin chain Gibbs states with a fidelity higher than 95%.

Adaptive variational algorithms for quantum Gibbs state preparation

- Computer Science
- 2022

This work introduces an objective function that, unlike the free energy, is easily measured, and uses dynamically generated, problem-tailored ans¨atze, which allows for arbitrarily accurate Gibbs state preparation using low-depth circuits.

Noise-assisted variational quantum thermalization

- Computer ScienceScientific reports
- 2022

A new algorithm for thermal state preparation that tackles three challenges by exploiting the noise of quantum circuits by considering a variational architecture containing a depolarizing channel after each unitary layer, with the ability to directly control the level of noise.

Toward a quantum computing algorithm to quantify classical and quantum correlation of system states

- Computer ScienceQuantum Inf. Process.
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A variational hybrid quantum-classical (VHQC) algorithm to achieve classical and quantum correlations for system states under the Noisy-Intermediate Scale Quantum (NISQ) technology and the output of the algorithm is compatible with the exact calculation.

Engineering a Cost Function for Real-world Implementation of a Variational Quantum Algorithm

- Computer Science2020 IEEE International Conference on Quantum Computing and Engineering (QCE)
- 2020

This work applies a new approach for engineering cost functions for a certain class of quantum- classical hybrid variation algorithms to a variational algorithm that generates thermofield double states (in the transverse field Ising model), which are relevant for studying thermal phase transitions in condensed matter systems.

Variational quantum algorithms for trace distance and fidelity estimation

- Computer ScienceQuantum Science and Technology
- 2021

This work introduces the variational trace distance estimation (VTDE) algorithm, and combines Uhlmann’s theorem and the freedom in purification to translate the estimation task into an optimization problem over a unitary on an ancillary system with fixed purified inputs.

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

- Computer Science, Physics
- 2021

A new approach of PITE which requires only a single ancillary qubit, leading to a novel framework denoted by first-quantized quantum eigensolver, which is used for obtaining the Gibbs state at a finite temperature and the partition function.

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- Computer Science
- 2020

This work proposes a method to implement the Boltzmann machine learning by using Noisy Intermediate-Scale Quantum (NISQ) devices, prepares an initial pure state that contains all possible computational basis states with the same amplitude, and applies a variational imaginary time simulation.

Quantum many-body systems in thermal equilibrium

- Physics
- 2022

The thermal or equilibrium ensemble is one of the most ubiquitous states of matter. For models comprised of many locally interacting quantum particles, it describes a wide range of physical…

Quantum Generative Training Using R\'enyi Divergences

- Computer Science
- 2021

This work examines the assumptions that give rise to barren plateaus and shows that an unbounded loss function can circumvent the existing no-go results and proposes a training algorithm that minimizes the maximal Rényi divergence of order two and presents techniques for gradient computation.

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