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arXiv:2402.00766 · Advanced Quantum Technologies

Benchmarking Multipartite Entanglement Generation with Graph States

René Zander, Colin Kai‐Uwe Becker

Published Oct 9, 2024• 4 citations
arXivHTMLPDF

Abstract

Abstract As quantum computing technology slowly matures and the number of available qubits on a QPU gradually increases, interest in assessing the capabilities of quantum computing hardware in a scalable manner is growing. One of the key properties for quantum computing is the ability to generate multipartite entangled states. In this study, aspects of benchmarking entanglement generation capabilities of noisy intermediate‐scale quantum (NISQ) devices are discussed based on the preparation of graph states and the verification of entanglement in the prepared states. Thereby, entanglement witnesses that are specifically suited for a scalable experiment design are used. This choice of entanglement witnesses can detect A) bipartite entanglement and B) genuine multipartite entanglement for graph states with constant two measurement settings if the prepared graph state is based on a two‐colorable graph, e.g., a square grid graph or one of its subgraphs. With this, it is experimentally verified that a bipartite entangled state comprising all qubits can be prepared on a 127‐qubit IBM Quantum superconducting QPU, and genuine multipartite entanglement can be detected for states of up to 23 qubits with quantum readout error mitigation.

DOI
10.1002/qute.202400239

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As quantum technology advances and the size of quantum computers grow, it becomes increasingly important to understand the extent of quality in the devices. As large-scale entanglement is a quantum resource crucial for achieving quantum advantage, the challenge in its generation makes it a valuable benchmark for measuring the performance of universal quantum devices. In this paper, we study entanglement in Greenberger-Horne-Zeilinger (GHZ) and graph states prepared on the range of IBM Quantum devices. We generate GHZ states and investigate their coherence times with respect to state size and dynamical decoupling techniques. A GHZ fidelity of 0.519 ± 0.014 is measured on a 32-qubit GHZ state, certifying its genuine multipartite entanglement (GME). We show a substantial improvement in GHZ decoherence rates for a seven-qubit GHZ state after implementing dynamical decoupling, and observe a linear trend in the decoherence rate of α = ( 7.13 N + 5.54 ) × 10 − 3 µ s − 1 for up to N = 15 qubits, confirming the absence of superdecoherence. Additionally, we prepare and characterize fully bipartite entangled native-graph states on 22 superconducting quantum devices with qubit counts as high as 414 qubits, all active qubits of the 433-qubit IBM Osprey device. Analysis of the decay of two-qubit entanglement within the prepared states shows suppression of coherent noise signals with the implementation of dynamical decoupling techniques. Additionally, we observe that the entanglement in some qubit pairs oscillates over time, which is likely caused by residual ZZ-interactions. Characterizing entanglement in native-graph states, along with detecting entanglement oscillations, can be an effective approach to low-level device benchmarking that encapsulates two-qubit error rates along with additional sources of noise, with possible applications to quantum circuit compilation. We develop several tools to automate the preparation and entanglement characterization of GHZ and graph states. In particular, a method to characterize graph state bipartite entanglement using just 36 circuits, constant with respect to the number of qubits. Published by the American Physical Society 2024
The ability to prepare sizeable multi-qubit entangled states with full qubit control is a critical milestone for physical platforms upon which quantum computers are built. We investigate the extent to which entanglement is found within a prepared graph state on the 20-qubit superconducting quantum computer IBM Q Poughkeepsie. We prepared a graph state along a path consisting of all twenty qubits within the device and performed full quantum state tomography on all groups of four connected qubits along this path. We determined that each pair of connected qubits was inseparable and hence the prepared state was entangled. Additionally, a genuine multipartite entanglement witness was measured on all qubit subpaths of the graph state and we found genuine multipartite entanglement on chains of up to three qubits. These results represent a demonstration of entanglement in one of the largest solid-state qubit arrays to date and indicate the positive direction of progress towards the goal of implementing complex quantum algorithms relying on such effects.
Abstract Recently, there are tremendous developments on the number of controllable qubits in several quantum computing systems. For these implementations, it is crucial to determine the entanglement structure of the prepared multipartite quantum state as a basis for further information processing tasks. In reality, evaluation of a multipartite state is in general a very challenging task owing to the exponential increase of the Hilbert space with respect to the number of system components. In this work, we propose a systematic method using very few local measurements to detect multipartite entanglement structures based on the graph state—one of the most important classes of quantum states for quantum information processing. Thanks to the close connection between the Schmidt coefficient and quantum entropy in graph states, we develop a family of efficient witness operators to detect the entanglement between subsystems under any partitions and hence the entanglement intactness. We show that the number of local measurements equals to the chromatic number of the underlying graph, which is a constant number, independent of the number of qubits. In reality, the optimization problem involved in the witnesses can be challenging with large system size. For several widely used graph states, such as 1-D and 2-D cluster states and the Greenberger–Horne–Zeilinger state, by taking advantage of the area law of entanglement entropy, we derive analytical solutions for the witnesses, which only employ two local measurements. Our method offers a standard tool for entanglement-structure detection to benchmark multipartite quantum systems.
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.