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arXiv:2104.05627 · Physical Review Applied

Experimental High-Dimensional Greenberger-Horne-Zeilinger Entanglement with Superconducting Transmon Qutrits

Alba Cervera-Lierta, Mario Krenn, Alán Aspuru‐Guzik, Alexey Galda

Published Feb 23, 2022• 103 citations
arXivHTMLPDF

Abstract

Multipartite entanglement is one of the core concepts in quantum information science with broad applications that span from condensed matter physics to quantum physics foundation tests. Although its most studied and tested forms encompass two-dimensional systems, current quantum platforms technically allow the manipulation of additional quantum levels. We report the experimental demonstration and certification of a high-dimensional multipartite entangled state in a superconducting quantum processor. We generate the three-qutrit Greenberger-Horne-Zeilinger state by designing the necessary pulses to perform high-dimensional quantum operations. We obtain the fidelity of $76\mathrm{%}\ifmmode\pm\else\textpm\fi{}1\mathrm{%}$, proving the generation of a genuine three-partite and three-dimensional entangled state. To this date, only photonic devices have been able to create and certify the entanglement of these high-dimensional states. Our work demonstrates that another platform, superconducting systems, is ready to exploit genuine high-dimensional entanglement and that a programmable quantum device accessed on the cloud can be used to design and execute experiments beyond binary quantum computation.

DOI
10.1103/physrevapplied.17.024062

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Multipartite entanglement is one of the core concepts in quantum information science with broad applications that span from condensed matter physics to quantum physics foundation tests. Although its most studied and tested forms encompass two-dimensional systems, current quantum platforms technically allow the manipulation of additional quantum levels. We report the experimental demonstration and certification of a high-dimensional multipartite entangled state in a superconducting quantum processor. We generate the three-qutrit Greenberger-Horne-Zeilinger state by designing the necessary pulses to perform high-dimensional quantum operations. We obtain the fidelity of 76\mathrm{%}\ifmmode\pm\else\textpm\fi{}1\mathrm{%}, proving the generation of a genuine three-partite and three-dimensional entangled state. To this date, only photonic devices have been able to create and certify the entanglement of these high-dimensional states. Our work demonstrates that another platform, superconducting systems, is ready to exploit genuine high-dimensional entanglement and that a programmable quantum device accessed on the cloud can be used to design and execute experiments beyond binary quantum computation.
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Quantum information science has leaped forward with the exploration of high-dimensional quantum systems, offering greater potential than traditional qubits in quantum communication and quantum computing. To advance the field of high-dimensional quantum technology, a significant effort is underway to progressively enhance the entanglement dimension between two particles. An alternative effective strategy involves not only increasing the dimensionality but also expanding the number of particles that are entangled. We present an experimental study demonstrating multi-partite quantum non-locality beyond qubit constraints, thus moving into the realm of strongly entangled high-dimensional multi-particle quantum systems. In the experiment, quantum states were encoded in the path degree of freedom (DoF) and controlled via polarization, enabling efficient operations in a two-dimensional plane to prepare three- and four-particle Greenberger-Horne-Zeilinger (GHZ) states in three-level systems. Our experimental results reveal ways in which high-dimensional systems can surpass qubits in terms of violating local-hidden-variable theories. Our realization of multiple complex and high-quality entanglement technologies is an important primary step for more complex quantum computing and communication protocols. Experimental demonstrations of genuine high-dimensional multipartite quantum nonlocality have been lacking so far. Here, the authors fill this gap using entangled photons, surpassing qubit-based limits and paving the way for device-independent quantum information processing in more complex systems.
High-dimensional quantum systems, known as qudits with dimension d>2d>2d>2, possess the capability to encode and process more information than traditional two-dimensional qubits. Entangled states serve as crucial resources for both quantum computation and quantum communication. On the basis of circuit quantum electrodynamics (QED) systems, we introduce an efficient scheme to deterministically generate high-dimensional multipartite entangled states of hybrid qutrits (d=3d=3d=3). Assuming a simple initial state has already been prepared with the use of local operations, our method requires only a single step to produce hybrid Greenberger-Horne-Zeilinger (GHZ) entangled states among circuit QED systems consisting of superconducting qutrits and a superconducting cavity. Remarkably, the number of steps and the operational time remain constant as the number of qutrits increases, highlighting the efficiency and scalability of our approach. Using numerical simulations for a three-dimensional hybrid GHZ state of seven qutrits, we demonstrate the feasibility of our scheme and study the effects of various parameters on the fidelity. The importance of this research is in directing the experimental creation of multipartite, high-dimensional, and hybrid GHZ states, which can then be used to enhance quantum communication protocols and computational processes.
High-dimensional qudit (i.e., ddd-level or ddd-state) systems outperform two-dimensional qubit (i.e., 2-level or 2-state) systems in some quantum information processing tasks. We exploit entanglement purification protocols (EPPs) for extracting a subset of high quality arbitrary ddd-dimensional nnn-partite Greenberger-Horne-Zeilinger (GHZ) states from a large set of less entangled GHZ states. In our protocols, qudit-flip and phase-flip errors can be corrected, and the fidelity of the output state can be asymptotically improved to unity by iterating the EPP process. Moreover, the schemes are immune to the number of polluted photons, the fidelity thresholds of the proposed EPPs are developed, and the spatial-based single-qudit operations can be well manipulated with a range of balanced beam splitters, and phase shifters. These features make the proposed schemes offer an alternative method for high-dimensional multipartite entanglement purification.
High-dimensional quantum entangled states exhibit unique properties. While generalizations like qudit Bell, Greenberger-Horne-Zeilinger (GHZ), and Cluster states have been studied, the qudit W states remain underexplored. We discover that a superposition of qudit Dicke states can serve as high-dimensional generalizations of W states, demonstrating their enhanced robustness against qudit loss, and present linearly scalable quantum circuits for their generation. Using a programmable silicon-photonic entanglement generator, we first theoretically and experimentally demonstrate the generation of 3-ququart GHZ and W states using two photons and one ancillary ququart, with fidelities of 0.932 ± 0.009 and 0.901 ± 0.012, respectively. Genuine multipartite entanglement of the GHZ state and the improved resilience of the W state are confirmed. Our findings provide new insights and efficient approaches for qudit-based quantum science and technologies.
Abstract Generating and detecting genuine multipartite entanglement (GME) of sizeable quantum states prepared on physical devices is an important benchmark for highlighting the progress of near-term quantum computers. A common approach to certify GME is to prepare a Greenberger-Horne-Zeilinger (GHZ) state and measure a GHZ fidelity of at least 0.5. We measure the fidelities using multiple quantum coherences of GHZ states on 11 to 27 qubits prepared on the IBM Quantum ibmq_montreal device. Combinations of quantum readout error mitigation (QREM) and parity verification error detection are applied to the states. A fidelity of 0.546 ± 0.017 was recorded for a 27-qubit GHZ state when QREM was used, demonstrating GME across the full device with a confidence level of 98.6%. We benchmarked the effect of parity verification on GHZ fidelity for two GHZ state preparation embeddings on the heavy-hexagon architecture. The results show that the effect of parity verification, while relatively modest, led to a detectable improvement of GHZ fidelity.