# Towards a variational Jordan-Lee-Preskill quantum algorithm

arXiv: https://arxiv.org/abs/2109.05547 · HTML: https://mlsanity.com/paper/2109.05547/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 102 references that are in the map.
- First posted on arXiv 12 Sep 2021.

## Builds on (most cited first, 6 of 6)

- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [Predicting Many Properties of a Quantum System from Very Few Measurements](https://mlsanity.com/paper/2002.08953/) (2020)
- [Quantum Natural Gradient](https://mlsanity.com/paper/1909.02108/) (2019)
- [Efficient estimation of Pauli observables by derandomization](https://mlsanity.com/paper/2103.07510/) (2021)
- [A Theory of Trotter Error](https://mlsanity.com/paper/1912.08854/) (2019)
- [Decision Diagrams for Quantum Measurements with Shallow Circuits](https://mlsanity.com/paper/2105.06932/) (2021)

## Built on by (most cited first, 1 of 1)

- [Numerical and geometrical aspects of flow-based variational quantum Monte Carlo](https://mlsanity.com/paper/2203.14824/) (2022)

## Abstract (arXiv)

Rapid developments of quantum information technology show promising opportunities for simulating quantum field theory in near-term quantum devices. In this work, we formulate the theory of (time-dependent) variational quantum simulation of the 1+1 dimensional λ φ4 quantum field theory including encoding, state preparation, and time evolution, with several numerical simulation results. These algorithms could be understood as near-term variational quantum circuit (quantum neural network) analogs of the Jordan-Lee-Preskill algorithm, the basic algorithm for simulating quantum field theory using universal quantum devices. Besides, we highlight the advantages of encoding with harmonic oscillator basis based on the LSZ reduction formula and several computational efficiency such as when implementing a bosonic version of the unitary coupled cluster ansatz to prepare initial states. We also discuss how to circumvent the "spectral crowding" problem in the quantum field theory simulation and appraise our algorithm by both state and subspace fidelities.