Quantifying the nonlinearity of a quantum oscillator

We address the quantification of nonlinearity for quantum oscillators and introduce two measures based on the properties of the ground state rather than on the form of the potential itself. The first measure is a fidelity-based one, and corresponds to the renormalized Bures distance between the ground state of the considered oscillator and the ground state of a reference harmonic oscillator. Then, in order to avoid the introduction of this auxiliary oscillator, we introduce a different measure based on the non-Gaussianity (nG) of the ground state. The two measures are evaluated for a sample of significant nonlinear potentials and their properties are discussed in some detail. We show that the two measures are monotone functions of each other in most cases, and this suggests that the nG-based measure is a suitable choice to capture the anharmonic nature of a quantum oscillator, and to quantify its nonlinearity independently on the specific features of the potential. We also provide examples of potentials where the Bures measure cannot be defined, due to the lack of a proper reference harmonic potential, while the nG-based measure properly quantify their nonlinear features. Our results may have implications in experimental applications where access to the effective potential is limited, e.g., in quantum control, and protocols rely on information about the ground or thermal state.Comment: 8 pages, 5 figures, published versio

Extending quantum probabilistic error cancellation by noise scaling

We propose a general framework for quantum error mitigation that combines and generalizes two techniques: probabilistic error cancellation (PEC) and zero-noise extrapolation (ZNE). Similar to PEC, the proposed method represents ideal operations as linear combinations of noisy operations that are implementable on hardware. However, instead of assuming a fixed level of hardware noise, we extend the set of implementable operations by noise scaling. By construction, this method encompasses both PEC and ZNE as particular cases and allows us to investigate a larger set of hybrid techniques. For example, gate extrapolation can be used to implement PEC without requiring knowledge of the device's noise model, e.g., avoiding gate-set tomography. Alternatively, probabilistic error reduction can be used to estimate expectation values at intermediate virtual noise strengths (below the hardware level), leading to partially mitigated results at a lower sampling cost. Moreover, multiple results obtained with different noise-reduction factors can be further postprocessed with ZNE to better approximate the zero-noise limit

Testing Platform-independent Quantum Error Mitigation on Noisy Quantum Computers

We apply quantum error mitigation techniques to a variety of benchmark problems and quantum computers to evaluate the performance of quantum error mitigation in practice. To do so, we define an empirically motivated, resource-normalized metric of the improvement of error mitigation which we call the improvement factor, and calculate this metric for each experiment we perform. The experiments we perform consist of zero-noise extrapolation and probabilistic error cancellation applied to two benchmark problems run on IBM, IonQ, and Rigetti quantum computers, as well as noisy quantum computer simulators. Our results show that error mitigation is on average more beneficial than no error mitigation — even when normalized by the additional resources used — but also emphasize that the performance of quantum error mitigation depends on the underlying computer

Zero noise extrapolation on logical qubits by scaling the error correction code distance

In this work, we migrate the quantum error mitigation technique of Zero-Noise Extrapolation (ZNE) to fault-tolerant quantum computing. We employ ZNE on \emph{logically encoded} qubits rather than \emph{physical} qubits. This approach will be useful in a regime where quantum error correction (QEC) is implementable but the number of qubits available for QEC is limited. Apart from illustrating the utility of a traditional ZNE approach (circuit-level unitary folding) for the QEC regime, we propose a novel noise scaling ZNE method specifically tailored to QEC: \emph{distance scaled ZNE (DS-ZNE)}. DS-ZNE scales the distance of the error correction code, and thereby the resulting logical error rate, and utilizes this code distance as the scaling `knob' for ZNE. Logical qubit error rates are scaled until the maximum achievable code distance for a fixed number of physical qubits, and lower error rates (i.e., effectively higher code distances) are achieved via extrapolation techniques migrated from traditional ZNE. Furthermore, to maximize physical qubit utilization over the ZNE experiments, logical executions at code distances lower than the maximum allowed by the physical qubits on the quantum device are parallelized to optimize device utilization. We validate our proposal with numerical simulation and confirm that ZNE lowers the logical error rates and increases the effective code distance beyond the physical capability of the quantum device. For instance, at a physical code distance of 11, the DS-ZNE effective code distance is 17, and at a physical code distance of 13, the DS-ZNE effective code distance is 21. When the proposed technique is compared against unitary folding ZNE under the constraint of a fixed number of executions of the quantum device, DS-ZNE outperforms unitary folding by up to 92\% in terms of the post-ZNE logical error rate.Comment: 8 pages, 5 figure

Middle East Respiratory Syndrome Corona Virus (MERS-CoV): Levels of Knowledge and Awareness in Bahrain

The Middle East respiratory syndrome coronavirus (MERS−CoV) was first identified in the Kingdom of Saudi Arabia (KSA) in 2012 that accounts 80% of the global cases. On 10th of April 2016, Bahrain notified WHO of a first fatal case. Hence, as a public health research and practice, the authors sought to assess the knowledge and awareness of MERS-CoV in Bahrain. A cross-sectional, conveniently sampled study was carried out through face-to-face interviews using a structured Arabic questionnaire among 498 Bahraini adults. While, 95% had a travel history to KSA, around 50% had the knowledge and awareness of MERS CoV being a viral lethal disease and its associated symptoms. Stratifying by socio-demographics, the authors found that the levels ofeducation, occupation, history of travel to KSA were significantly associated with the knowledge and awareness of MERS CoV (p < 0.05). On the preventive measures of MERS CoV, occupation and history of travel to KSA were significantly associated (p < 0.05). Considering the first notified case from Bahrain, proximity and travel history to KSA of 95% of the Bahrainis, the knowledge and awareness of MERS CoV is found to be inadequate. Therefore, the knowledge and awareness campaign on MERS CoV is pivotal as a good public health practice. Keywords: MERS-CoV, Knowledge, Awareness, Bahrai

Impact of time-correlated noise on zero-noise extrapolation

Zero-noise extrapolation is a quantum error mitigation technique that has typically been studied under the ideal approximation that the noise acting on a quantum device is not time correlated. In this paper, we investigate the feasibility and performance of zero-noise extrapolation in the presence of time-correlated noise. We show that, in contrast to white noise, time-correlated noise is harder to mitigate via zero-noise extrapolation because it is difficult to scale the noise level without also modifying its spectral distribution. This limitation is particularly strong if "local"gate-level methods are applied for noise scaling. However, we find that "global"noise-scaling methods, e.g., global unitary folding, can be sufficiently reliable even in the presence of time-correlated noise

Mitiq: A software package for error mitigation on noisy quantum computers

We introduce Mitiq, a Python package for error mitigation on noisy quantum computers. Error mitigation techniques can reduce the impact of noise on near-term quantum computers with minimal overhead in quantum resources by relying on a mixture of quantum sampling and classical post-processing techniques. Mitiq is an extensible toolkit of different error mitigation methods, including zero-noise extrapolation, probabilistic error cancellation, and Clifford data regression. The library is designed to be compatible with generic backends and interfaces with different quantum software frameworks. We describe Mitiq using code snippets to demonstrate usage and discuss features and contribution guidelines. We present several examples demonstrating error mitigation on IBM and Rigetti superconducting quantum processors as well as on noisy simulators

Mitiq : a software package for error mitigation on noisy quantum computers

We introduce Mitiq, a Python package for error mitigation on noisy quantum computers. Error mitigation techniques can reduce the impact of noise on near-term quantum computers with minimal overhead in quantum resources by relying on a mixture of quantum sampling and classical post-processing techniques. Mitiq is an extensible toolkit of different error mitigation methods, including zero-noise extrapolation, probabilistic error cancellation, and Clifford data regression. The library is designed to be compatible with generic backends and interfaces with different quantum software frameworks. We describe Mitiq using code snippets to demonstrate usage and discuss features and contribution guidelines. We present several examples demonstrating error mitigation on IBM and Rigetti superconducting quantum processors as well as on noisy simulators

"Much ado about nothing"? The historical journey towards financial inclusion for Zimbabwe's low-earning consumers

An investigation into the debt relief measures available to consumer debtors in Zimbabwe reveals that the former and now repealed insolvency statutes did not cater for debtors with smaller estates such as No-Income-No Asset (NINA) debtors. Given the dire state of the Zimbabwean economy due to a multiplicity of economic and political reasons fuelled by other factors such as the COVID-19 pandemic, this category of Zimbabwean consumer debtors found themselves in a lifelong debt trap. However, in 2018, Zimbabwe introduced a new Insolvency Act that, among others, provides for a pre-liquidation composition procedure that could benefit those debtors who do not qualify for the liquidation of assets process. Against the backdrop of the historical development and the plight of indigent debtors, the authors consider the new measure and conclude that although being a step in the right direction, it may still provide too little protection for NINA debtors.https://www.jicl.org.uk2024-12-01hj2024Mercantile LawSDG-16:Peace,justice and strong institution