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Communications Physics

Open quantum system violates generalized Pauli constraints on quantum device

Irma Avdic, LeeAnn M. Sager-Smith, David A. Mazziotti

Published Jul 17, 2023• 3 citations
Publisher

Abstract

Abstract The Pauli exclusion principle governs the fundamental structure and function of fermionic systems from molecules to materials. Nonetheless, when such a fermionic system is in a pure state, it is subject to additional restrictions known as the generalized Pauli constraints (GPCs). Here we verify experimentally the violation of the GPCs for an open quantum system using data from a superconducting-qubit quantum computer. We prepare states of systems with three-to-seven qubits directly on the quantum device and measure the one-fermion reduced density matrix (1-RDM) from which we can test the GPCs. We find that the GPCs of the 1-RDM are sufficiently sensitive to detect the openness of the 3-to-7 qubit systems in the presence of a single-qubit environment. Results confirm experimentally that the openness of a many-fermion quantum system can be decoded from only a knowledge of the 1-RDM with potential applications from quantum computing and sensing to noise-assisted energy transfer.

DOI
10.1038/s42005-023-01295-w

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Abstract The Pauli exclusion principle governs the fundamental structure and function of fermionic systems from molecules to materials. Nonetheless, when such a fermionic system is in a pure state, it is subject to additional restrictions known as the generalized Pauli constraints (GPCs). Here we verify experimentally the violation of the GPCs for an open quantum system using data from a superconducting-qubit quantum computer. We prepare states of systems with three-to-seven qubits directly on the quantum device and measure the one-fermion reduced density matrix (1-RDM) from which we can test the GPCs. We find that the GPCs of the 1-RDM are sufficiently sensitive to detect the openness of the 3-to-7 qubit systems in the presence of a single-qubit environment. Results confirm experimentally that the openness of a many-fermion quantum system can be decoded from only a knowledge of the 1-RDM with potential applications from quantum computing and sensing to noise-assisted energy transfer.
Abstract “What are the consequences… that Fermi particles cannot get into the same state…” R. P. Feynman wrote of the Pauli exclusion principle, “In fact, almost all the peculiarities of the material world hinge on this wonderful fact.” In 1972 Borland and Dennis showed that there exist powerful constraints beyond the Pauli exclusion principle on the orbital occupations of Fermi particles, providing important restrictions on quantum correlation and entanglement. Here we use computations on quantum computers to experimentally verify the existence of these additional constraints. Quantum many-fermion states are randomly prepared on the quantum computer and tested for constraint violations. Measurements show no violation and confirm the generalized Pauli exclusion principle with an error of one part in one quintillion.
Information about the interaction of a many-electron quantum system with its environment, we show, is encoded within the one-electron density matrix (1-RDM). While the 1-RDM from an ensemble many-electron quantum system must obey the Pauli exclusion principle, the 1-RDM must obey additional constraints known as generalized Pauli conditions when it corresponds to a closed system describable by a single wave function. By examining the 1-RDM's violation of these generalized Pauli conditions, we obtain a sufficient condition at the level of a single electron for a many-electron quantum system's openness. In an application to exciton dynamics in photosynthetic light harvesting we show that the interaction of the system with the environment (quantum noise) relaxes significant constraints imposed on the exciton dynamics by the generalized Pauli conditions. This relaxation provides a geometric (kinematic) interpretation for the role of noise in enhancing exciton transport in quantum systems.
Quantum sensing has highly practical potential applications in fields ranging from fundamental physics and quantum communication to biophysics and bioengineering. However, achieving high fidelity and control of entangled qubits that enables sensing beyond the quantum limit is still a challenging endeavor. In this paper, we present an alternative approach to quantum sensing, which we call open-system quantum sensing, where we exploit a generalization of the Pauli exclusion principle to sense the openness of a multiqubit quantum system from only measurement of the qubit occupations. Qubit occupations of a pure state obey generalized Pauli exclusion constraints that define a convex set known as the Pauli polytope, and hence violation of one of these constraints---a facet of the polytope---reveals a mixed state from the interaction of a quantum system with its environment without performing full-state tomography. We examine experimental ultrafast spectroscopic data from the photosynthetic light-harvesting complex in green sulfur bacteria and show that we can sense and decode the relaxation of the complex due to environmental noise. More generally, we can apply open-system quantum sensing with any general multiqubit quantum system, where it provides a unique, visual approach that promises enhanced sensitivity and fidelity.
The Pauli exclusion principle requires that the occupations of the orbitals lie between zero and one. These Pauli conditions hold for one‐electron reduced density matrices (1‐RDMs) from both open and closed quantum systems. More than 40 years ago, it was recognized that there are additional conditions on the 1‐RDM for closed quantum systems. In this review, we discuss the structure of the 1‐RDM from the generalized Pauli exclusion principle in many‐electron atoms and molecules and the violation of the generalized Pauli principle as a sufficient condition for the openness of a many‐electron quantum system. © 2015 Wiley Periodicals, Inc.
Postulated by Wolfgang Pauli in 1925 to explain the electronic structure of atoms and molecules, the exclusion principle establishes an upper bound of 1 for the fermionic natural occupation numbers (ni ≤ 1), thereby allowing no more than one electron in each quantum state. This is nothing more than a necessary and sufficient condition for a 1-body reduced density matrix to be the contraction of an N-body density matrix, provided that the sum of such occupations equals the number of particles. The pure N-representability problem asks whether given natural occupation numbers can arise from an antisymmetric pure N-particle state. Recent progress on such a problem establishes a systematic approach to a set of stronger constraints on the natural occupation numbers, not implied by the exclusion principle. In fact, for a pure quantum system the natural occupations satisfy a set of linear inequalities, known as generalized Pauli constraints, of the form with . This generalization of the Pauli exclusion principle has been widely used in many-body physics to study the influence of the fermionic exchange symmetry, beyond the original Pauli principle. In this chapter we review recent applications of the generalized Pauli exclusion principle and discuss some of the open problems.
All matter is made up of fermions, one of the fundamental type of particles in nature. Fermions follow the Pauli exclusion principle, stating that two or more identical fermions cannot occupy the same quantum state. Antisymmetry of the fermionic wave function, however, implies additional constraints on the natural occupation numbers. These constraints depend on the dimensionality and purity of the system and have so far not been explored experimentally in a fermionic system to our best knowledge. Here we propose an experiment in a multi-quantum-dot system capable of producing the highly entangled fermionic states necessary to reach the regime, where these additional constraints become dominant and can be probed. The type and strength of the required multifermion entanglement provides barriers to reaching deep into this regime. Transcending these barriers thus serves as a testing ground for the capabilities of future fermionic quantum information processing as well as quantum computer architectures based on fermionic states. All operations in our proposal are based on all-optical gates presented in Li and Akopian [arXiv:2107.05960 (2021)]. We simulate our state preparation procedures in realistic structures, including all main decoherence sources, and find fidelities above 0.97.