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arXiv:1812.07821 · npj Quantum Information

Benchmarks of nonclassicality for qubit arrays

Mordecai Waegell, Justin Dressel

Published Aug 1, 2019• 11 citations
arXivHTMLPDF

Abstract

Abstract We present a set of practical benchmarks for N-qubit arrays that economically test the fidelity of achieving multi-qubit nonclassicality. The benchmarks are measurable correlators similar to two-qubit Bell correlators, and are derived from a particular set of geometric structures from the N-qubit Pauli group. These structures prove the Greenberger–Horne–Zeilinger (GHZ) theorem, while the derived correlators witness genuine N-partite entanglement and establish a tight lower bound on the fidelity of particular stabilizer state preparations. The correlators need only M ≤ N + 1 distinct measurement settings, as opposed to the 22N − 1 settings that would normally be required to tomographically verify their associated stabilizer states. We optimize the measurements of these correlators for a physical array of qubits that can be nearest-neighbor-coupled using a circuit of controlled-Z gates with constant gate depth to form N-qubit linear cluster states. We numerically simulate the provided circuits for a realistic scenario with N = 3, …, 9 qubits, using ranges of T1 energy relaxation times, T2 dephasing times, and controlled-Z gate-fidelities consistent with Google’s 9-qubit superconducting chip. The simulations verify the tightness of the fidelity bounds and witness nonclassicality for all nine qubits, while also showing ample room for improvement in chip performance.

DOI
10.1038/s41534-019-0181-8

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Abstract We present a set of practical benchmarks for N-qubit arrays that economically test the fidelity of achieving multi-qubit nonclassicality. The benchmarks are measurable correlators similar to two-qubit Bell correlators, and are derived from a particular set of geometric structures from the N-qubit Pauli group. These structures prove the Greenberger–Horne–Zeilinger (GHZ) theorem, while the derived correlators witness genuine N-partite entanglement and establish a tight lower bound on the fidelity of particular stabilizer state preparations. The correlators need only M ≤ N + 1 distinct measurement settings, as opposed to the 22N − 1 settings that would normally be required to tomographically verify their associated stabilizer states. We optimize the measurements of these correlators for a physical array of qubits that can be nearest-neighbor-coupled using a circuit of controlled-Z gates with constant gate depth to form N-qubit linear cluster states. We numerically simulate the provided circuits for a realistic scenario with N = 3, …, 9 qubits, using ranges of T1 energy relaxation times, T2 dephasing times, and controlled-Z gate-fidelities consistent with Google’s 9-qubit superconducting chip. The simulations verify the tightness of the fidelity bounds and witness nonclassicality for all nine qubits, while also showing ample room for improvement in chip performance.
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
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.
Entanglement is the quintessential quantum phenomenon and a key enabler of quantum algorithms. The ability to faithfully entangle many distinct particles is often used as a benchmark for the quality of hardware and control in a quantum computer. Greenberger-Horne-Zeilinger (GHZ) states, also known as Schrödinger cat states, are useful for this task. They are easy to verify, but difficult to prepare due to their high sensitivity to noise. In this Letter we report on the largest GHZ state prepared to date consisting of 120 superconducting qubits. We do this via a combination of optimized compilation, low-overhead error detection and temporary uncomputation. We use an automated compiler to maximize error-detection in state preparation circuits subject to arbitrary qubit connectivity constraints and variations in error rates. We measure a GHZ fidelity of 0.56(3) with a post-selection rate of 28%. We certify the fidelity of our GHZ states using multiple methods and show that they are all equivalent, albeit with different practical considerations.
I report a hands-on, systematic investigation of Greenberger–Horne–Zeilinger (GHZ) state generation on a 127-qubit supercon-ducting quantum processor, covering system sizes from 4 to 80 qubits. I measured both computational-basis populations andglobal Pauli-X parity oscillations to decompose the state fidelity into its population purity and phase-coherence components. Mydata reveal an exponential collapse of fidelity with qubit number: a 4-qubit GHZ state achieves a fidelity of F = 0.9307, wellabove the threshold for entanglement-based quantum key distribution, yet by 32 qubits the fidelity has plummeted to 0.0963 andthe parity signal is extinguished. At 80 qubits, the state is indistinguishable from a maximally mixed state (F = 0.0453). I isolatethe dominant noise channels—CNOT gate errors, dephasing, readout crosstalk—and map the current usability frontier for rawmultipartite entanglement. I then contrast my results with mitigation-enhanced benchmarks from other platforms, showing thatadaptive compilation and dynamical decoupling can recover fidelity above the genuine multipartite entanglement (GME) thresholdeven at 120 qubits. This work provides a deeply personal, quantitative perspective on the challenges and near-term solutions forscaling entanglement in quantum communication, sensing, and error-mitigated computation.
The nonclassical properties of the noisy three-qubit Greenberger-Horne-Zeilinger (GHZ) states, ${\ensuremath{\rho}}_{v}=v|\text{GHZ}\ensuremath{\rangle}\ensuremath{\langle}\text{GHZ}|+(1\ensuremath{-}v)\mathbb{1}/8$ parameterized by the visibility $0\ensuremath{\le}v\ensuremath{\le}1$ are investigated. Based on the violation of the $2\ifmmode\times\else\texttimes\fi{}2\ifmmode\times\else\texttimes\fi{}2$-setting Mermin inequality, ${\ensuremath{\rho}}_{v}$ is nonclassical for the parameter range $1/2<v\ensuremath{\le}1$. It has been posed whether additional settings would allow to lower the threshold visibility. Here we report on Bell inequalities giving a threshold value smaller than v=1/2v=1/2v=1/2. This rules out the possibility of a local hidden variable model in the limit of v=1/2v=1/2v=1/2. In particular, the lowest threshold visibility we found is v=0.496057v=0.496\phantom{\rule{0.16em}{0ex}}057v=0.496057, attainable with $5\ifmmode\times\else\texttimes\fi{}5\ifmmode\times\else\texttimes\fi{}5$ settings, whereas the most economical one in number of settings corresponds to $3\ifmmode\times\else\texttimes\fi{}3\ifmmode\times\else\texttimes\fi{}4$ settings. The method which enabled us to obtain these results, and in particular the about 10 000 tight Bell inequalities giving v<1/2v<1/2v<1/2, are also discussed in detail.
Abstract We benchmark the decoherence of superconducting transmon qubits to examine the temporal stability of energy relaxation, dephasing, and qubit transition frequency. By collecting statistics during measurements spanning multiple days, we find the mean parameters T1‾\overline {T_1}T1​​ T 1 ¯ = 49 μs and T2∗‾\overline {T_2^ \ast }T2∗​​ T 2 * ¯ = 95 μs; however, both of these quantities fluctuate, explaining the need for frequent re-calibration in qubit setups. Our main finding is that fluctuations in qubit relaxation are local to the qubit and are caused by instabilities of near-resonant two-level-systems (TLS). Through statistical analysis, we determine sub-millihertz switching rates of these TLS and observe the coherent coupling between an individual TLS and a transmon qubit. Finally, we find evidence that the qubit’s frequency stability produces a 0.8 ms limit on the pure dephasing which we also observe. These findings raise the need for performing qubit metrology to examine the reproducibility of qubit parameters, where these fluctuations could affect qubit gate fidelity.