Probabilistic Simulation of Quantum Circuits with the Transformer

Abstract

The fundamental question of how to best simulate quantum systems using conventional computational resources lies at the forefront of condensed matter and quantum computation. It impacts both our understanding of quantum materials and our ability to emulate quantum circuits. Here we present an exact formulation of quantum dynamics via factorized generalized measurements which maps quantum states to probability distributions with the advantage that local unitary dynamics and quantum channels map to local quasi-stochastic matrices. This representation provides a general framework for using state-of-the-art probabilistic models in machine learning for the simulation of quantum many-body dynamics. Using this framework, we have developed a practical algorithm to simulate quantum circuits with the Transformer, a powerful ansatz responsible for the most recent breakthroughs in natural language processing. We demonstrate our approach by simulating circuits which build GHZ and linear graph states of up to 60 qubits, as well as a variational quantum eigensolver circuit for preparing the ground state of the transverse field Ising model on six qubits. Our methodology constitutes a modern machine learning approach to the simulation of quantum physics with applicability both to quantum circuits as well as other quantum many-body systems.

12 pages, 11 figures including supplementary materials

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Cited by in corpus (27)

• Beyond-classical computation in quantum simulation
• Efficient quantum state tomography with convolutional neural networks
• Autoregressive Transformer Neural Network for Simulating Open Quantum Systems via a Probabilistic Formulation
• Neural Error Mitigation of Near-Term Quantum Simulations
• Transformer Quantum State: A Multi-Purpose Model for Quantum Many-Body Problems
• Gauge Invariant and Anyonic Symmetric Transformer and RNN Quantum States for Quantum Lattice Models
• Optimizing Design Choices for Neural Quantum States
• Hamiltonian-Driven Shadow Tomography of Quantum States
• Hybrid convolutional neural network and PEPS wave functions for quantum many-particle states
• Variational Monte Carlo with Large Patched Transformers
• Investigating Topological Order using Recurrent Neural Networks
• Operationally meaningful representations of physical systems in neural networks
• Variational Neural-Network Ansatz for Continuum Quantum Field Theory
• jVMC: Versatile and performant variational Monte Carlo leveraging automated differentiation and GPU acceleration
• Avoiding local minima in Variational Quantum Algorithms with Neural Networks
• Beyond MP2 initialization for unitary coupled cluster quantum circuits
• Neural networks in quantum many-body physics: a hands-on tutorial
• Minimal informationally complete measurements for probability representation of quantum dynamics
• Empirical Sample Complexity of Neural Network Mixed State Reconstruction
• Observing Schrödinger's Cat with Artificial Intelligence: Emergent Classicality from Information Bottleneck
• Tensorized Transformer for Dynamical Systems Modeling
• Time-dependent variational principle for open quantum systems with artificial neural networks
• Simulating quantum circuits using the multi-scale entanglement renormalization ansatz
• Attention to Quantum Complexity
• Finding the Dynamics of an Integrable Quantum Many-Body System via Machine Learning
• Challenges and opportunities in the supervised learning of quantum circuit outputs
• Circuit connectivity boosts by quantum-classical-quantum interfaces