Quantum Mixed State Compiling

Abstract

The task of learning a quantum circuit to prepare a given mixed state is a fundamental quantum subroutine. We present a variational quantum algorithm (VQA) to learn mixed states which is suitable for near-term hardware. Our algorithm represents a generalization of previous VQAs that aimed at learning preparation circuits for pure states. We consider two different ansätze for compiling the target state; the first is based on learning a purification of the state and the second on representing it as a convex combination of pure states. In both cases, the resources required to store and manipulate the compiled state grow with the rank of the approximation. Thus, by learning a lower rank approximation of the target state, our algorithm provides a means of compressing a state for more efficient processing. As a byproduct of our algorithm, one effectively learns the principal components of the target state, and hence our algorithm further provides a new method for principal component analysis. We investigate the efficacy of our algorithm through extensive numerical implementations, showing that typical random states and thermal states of many body systems may be learnt this way. Additionally, we demonstrate on quantum hardware how our algorithm can be used to study hardware noise-induced states.

arXiv comment17 main + 17 appendix pages, 6 main + 9 appendix figures

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• Adaptive variational low-rank dynamics for open quantum systems
• Hückel Molecular Orbital Theory on a Quantum Computer: A Scalable System-Agnostic Variational Implementation with Compact Encoding
• Quantum density estimation with density matrices: Application to quantum anomaly detection
• The topology of data hides in quantum thermal states
• QSlack: A slack-variable approach for variational quantum semi-definite programming
• Rigorous noise reduction with quantum autoencoders
• Efficient quantum algorithms for testing symmetries of open quantum systems
• Low-Rank Variational Quantum Algorithm for the Dynamics of Open Quantum Systems
• Dual-VQE: A quantum algorithm to lower bound the ground-state energy
• Multi-target quantum compilation algorithm
• Variational-toolbox-based separability detection of multiqubit states
• Schmidt quantum compressor
• Finite Gaussian assistance protocols and a conic metric for extremizing spacelike vacuum entanglement