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16-qubit IBM universal quantum computer can be fully entangled
Yuanhao Wang, Ying Li, Zhang-qi Yin, Bei Zeng
TL;DR
The paper asks whether a 16-qubit quantum processor can produce highly entangled states, an important indicator of quantum-device capability. It prepares 8- to 16-qubit ring graph states on IBM’s ibmqx5 using optimized low-depth circuits and finds that the states are fully entangled, including across all 16 qubits.
Problem
Demonstrating highly entangled states is an important step in assessing the quantumness and performance of quantum processors.
Method
The paper prepares 8- to 16-qubit graph states on the 16-qubit ibmqx5 through IBM’s cloud service using optimized low-depth circuits.
Results
The prepared graph states are not biseparable with respect to any fixed partition, achieving full entanglement using all 16 qubits.
Takeaways & Limitations
The results demonstrate that ibmqx5 can generate highly entangled states involving all of its 16 qubits.
Abstract
from arXiv · showhide
Entanglement is an important evidence that a quantum device can potentially solve problems intractable for classical computers. In this paper, we prepare connected graph states involving 8 to 16 qubits on ibmqx5, a 16-qubit superconducting quantum processor accessible via IBM cloud,using low-depth circuits. We demonstrate that the prepared state is fully entangled, i.e. the state is inseparable with respect to any fixed partition.
I. INTRODUCTION
The paper uses highly entangled graph states to assess the quantumness of IBM’s 16-qubit ibmqx5 processor, despite error accumulation in faulty gates. It prepares 8- to 16-qubit states with optimized low-depth circuits and demonstrates full entanglement.
- Entanglement is a critical resource for quantum information processing and an important step toward demonstrating quantumness in quantum processors.
- Faulty-gate error accumulation makes producing highly entangled states on quantum processors highly non-trivial.
- The study assesses the 16-qubit ibmqx5 by producing graph states, an important class of many-body entangled states.
- 8- to 16-qubit ring graph states are generated on ibmqx5 using optimized low-depth circuits tailored to its universal gate set.
- The prepared states are fully entangled: they involve all physical qubits and are inseparable with respect to any fixed partition.
A. Graph states and entanglement
The paper defines graph states through graph-controlled operations and develops an efficient reduced-density-matrix approach to test full entanglement. For ring states, pairwise subsystem entanglement can rule out every fixed bipartition with linearly many circuit configurations.
- Linear cluster states are selected because they remain entangled after tracing out many qubits and are more robust against decoherence than GHZ and 2-D graph states.
- A graph state is associated with an undirected graph whose vertices represent qubits and whose edges specify control-Z operations.
- An n-qubit graph state can be prepared by initializing all qubits in |+⟩ and applying a control-Z gate for every graph edge.
- Subsystem entanglement detected in reduced density matrices constrains which qubits can lie on opposite sides of a possible fixed bipartition.
- For an n-qubit ring, showing that n −1 selected qubit pairs must remain on the same side rules out every fixed separation and establishes full entanglement.
- The method requires 3⁄4 (n −1) circuit configurations, growing linearly with n rather than exponentially as full n-qubit tomography does.
B. Graph states on ibmqx5
The experiment targets ring graph states on ibmqx5, choosing even rings that fit the processor connectivity and permit low-depth preparation. The paper prepares states from 8 through 16 qubits and reports full entanglement across all 16 qubits.
- ibmqx5 is a 16-qubit superconducting processor whose connectivity restricts which directed CNOT operations are allowed.
- The experiment uses five ring graph states with 8, 10, 12, 14, and 16 qubits embedded in progressively larger subsets of ibmqx5.
- The selected graph states are genuinely entangled and were chosen for robustness against decoherence, making entanglement more likely to persist in larger states.
- Even rings are two-edge-colorable, enabling their preparation with low-depth circuits on ibmqx5.
- The preparation circuit starts from the graph-state definition, implements control-Z gates with CNOT and Hadamard gates, and is optimized by reordering operations and removing redundant Hadamards.
C. Experimental Results
Low-depth local operations and partial tomography were used to test connected 8- to 16-qubit ring graph states. The measured negativities support full entanglement for the 8-, 10-, 12-, 14-, and 16-qubit states.
- Measurement and analysis: Each ring state was tested through n partial tomographies of neighboring four-qubit subsystems, with 2048 measurements per experimental configuration.The four-qubit density matrices were obtained using maximum likelihood reconstruction.
- Measurement and analysis: Local operations on the outer qubits of each four-qubit chain reduced the subsystem to two qubits whose negativity was measured.For an ideal graph state, the resulting two-qubit state is maximally entangled, so a close experimental state should yield positive negativity.
- 12-qubit state: 12-qubit data showed 10 of 12 significantly nonzero negativities, while a targeted four-qubit test measured 0.0391±0.0039 and ruled out the remaining possible separation.The authors therefore concluded that the 12-qubit graph state is fully entangled.
- 14-qubit state: 14-qubit data showed 12 of 14 significantly positive negativities, and a targeted test measured 0.0698 ± 0.0048, ruling out the remaining possible separation.The state was consequently concluded to be fully entangled.
- 16-qubit state: 15 of 16 measured negativities were significantly positive for the 16-qubit state, supporting full entanglement of all 16 qubits in ibmqx5.The authors interpret the result as showing the state is not biseparable with respect to a fixed partition.
- Experimental caveat: The {q8, q9, q10, q11} subsystem produced close-to-zero negativity in 3 of 4 experiments, potentially because q10 and q11 had relatively high gate and readout errors.The reported readout errors for q10 and q11 were above the average level of 6.5%.
D. Further Exploration of the 16-qubit State
The 16-qubit data were further analyzed to localize entanglement between physically separated qubits using ideal local operations and negativity measurements. Localized entanglement was identified for many qubit pairs at distances two and three.
- Method: The authors use ideal local operations on the 16-qubit state to investigate localized entanglement between qubits at distances two and three.The analysis uses the same experimental data and evaluates negativity in selected two-qubit subsystems.
- Distance-three analysis: For a six-qubit chain, the procedure applies operations to the endpoints, postselects zeros, traces out four qubits, and calculates negativity for the remaining pair.For a perfect 16-qubit state, the resulting two-qubit system would be maximally entangled.
- Distance-two pairs: 13 of 16 qubit pairs at distance two showed identified localized entanglement.The corresponding negativities were calculated for each six-qubit subsystem and reported in Table 1.
- Distance-three pairs: Localized entanglement was identified in 6 of 16 qubit pairs at distance three.The results were presented in Table 2.
III. DISCUSSION
The experiments prepared 8- to 16-qubit graph states on ibmqx5 and demonstrated full entanglement across any fixed partition. They also detected localized entanglement at qubit distances 3 and 4, using reduced density matrices of at most four qubits despite fidelity limitations.
- 8-, 10-, 12-, 14-, and 16-qubit graph states were prepared on the 16-qubit ibmqx5 processor.
- The prepared states were shown to be non-biseparable with respect to any fixed partition, including full entanglement across all 16 qubits.
- Localized entanglement was demonstrated between qubit pairs separated by distances 3 and 4 within the 16-qubit entangled state.
- The detection method requires measuring reduced density matrices of at most four qubits, whose size does not scale with the total qubit number.
- Graph-state fidelity remained limited; for example, the 12-qubit graph state had fidelity below 0.44.
- The 4-qubit reduced-density-matrix negativity decayed gently as qubit number increased, indicating that error per qubit weakly depended on qubit number.
Funding
The work received support from Chinese and Canadian research funding organizations.
- Y.L. was supported by NSAF Grant U1730449.
- Z.-Q.Y. was supported by National Natural Science Foundation of China Grants 61771278, 11574176, and 11474177.
- B.Z. was supported by NSERC and CIFAR.
Figures
The figures document ibmqx5’s connectivity and calibration, the graph-state circuits and their hardware-adapted implementation, and negativity measurements for graph states from 8 to 16 qubits.
- The experiment uses five graph states spanning 8, 10, 12, 14, and 16 qubits.
- The graph-state preparation begins from the definition-implied circuit and uses low-depth even-ring states.
- The implemented circuits are optimized for ibmqx5’s connectivity and shown for the larger graph states.
- Negativity measurements are plotted for the graph states, with 95% confidence intervals estimated by bootstrapping.
Tables
The tables report negativities for pairs of qubits separated by distances two and three in the 16-qubit state.
- Table 1 reports negativities of qubits with distance 2 in the 16-qubit state.
- Table 2 reports negativities of qubits with distance 3 in the 16-qubit state.