Fault-tolerant Quantum Error Correction on Near-term Quantum Processors using Flag and Bridge Qubits

Fault-tolerant (FT) computation by using quantum error correction (QEC) is essential for realizing large-scale quantum algorithms. Devices are expected to have enough qubits to demonstrate aspects of fault tolerance in the near future. However, these near-term quantum processors will only contain a small amount of noisy qubits and allow limited qubit connectivity. Fault-tolerant schemes that not only have low qubit overhead but also comply with geometrical interaction constraints are therefore necessary. In this work, we combine flag fault tolerance with quantum circuit mapping, to enable an efficient flag-bridge approach to implement FT QEC on near-term devices. We further show an example of performing the Steane code error correction on two current superconducting processors and numerically analyze their performance with circuit level noise. The simulation results show that the QEC circuits that measure more stabilisers in parallel have lower logical error rates. We also observe that the Steane code can outperform the distance-3 surface code using flag-bridge error correction. In addition, we foresee potential applications of the flag-bridge approach such as FT computation using lattice surgery and code deformation techniques.Comment: 11 pages, 14 figures, comments are most welcom

Minimising surface-code failures using a color-code decoder

The development of practical, high-performance decoding algorithms reduces the resource cost of fault-tolerant quantum computing. Here we propose a decoder for the surface code that finds low-weight correction operators for errors produced by the depolarising noise model. The decoder is obtained by mapping the syndrome of the surface code onto that of the color code, thereby allowing us to adopt more sophisticated color-code decoding algorithms. Analytical arguments and exhaustive testing show that the resulting decoder can find a least-weight correction for all weight $d/2$ depolarising errors for even code distance $d$. This improves the logical error rate by an exponential factor $O(2^{d/2})$ compared with decoders that treat bit-flip and dephasing errors separately. We demonstrate this improvement with analytical arguments and supporting numerical simulations at low error rates. Of independent interest, we also demonstrate an exponential improvement in logical error rate for our decoder used to correct independent and identically distributed bit-flip errors affecting the color code compared with more conventional color-code decoding algorithms

Timing and resource-aware mapping of quantum circuits to superconducting processors

Quantum algorithms need to be compiled to respect the constraints imposed by quantum processors, which is known as the mapping problem. The mapping procedure will result in an increase of the number of gates and of the circuit latency, decreasing the algorithm's success rate. It is crucial to minimize mapping overhead, especially for Noisy Intermediate-Scale Quantum (NISQ) processors that have relatively short qubit coherence times and high gate error rates. Most of prior mapping algorithms have only considered constraints such as the primitive gate set and qubit connectivity, but the actual gate duration and the restrictions imposed by the use of shared classical control electronics have not been taken into account. In this paper, we present a timing and resource-aware mapper called Qmap to make quantum circuits executable on a scalable superconducting processor named Surface-17 with the objective of achieving the shortest circuit latency. In particular, we propose an approach to formulate the classical control restrictions as resource constraints in a conventional list scheduler with polynomial complexity. Furthermore, we implement a routing heuristic to cope with the connectivity limitation. This router finds a set of movement operations that minimally extends circuit latency. To analyze the mapping overhead and evaluate the performance of different mappers, we map 56 quantum benchmarks onto Surface-17. Compared to a prior mapping strategy that minimizes the number of operations, Qmap can reduce the latency overhead up to 47.3% and operation overhead up to 28.6%, respectively.Comment: Include details on the resource-constrained scheduling algorithm. Comments are most welcom

Code deformation and lattice surgery are gauge fixing

International audienceThe large-scale execution of quantum algorithms requires basic quantum operations to be implemented fault-tolerantly. The most popular technique for accomplishing this, using the devices that can be realized in the near term, uses stabilizer codes which can be embedded in a planar layout. The set of fault-tolerant operations which can be executed in these systems using unitary gates is typically very limited. This has driven the development of measurement-based schemes for performing logical operations in these codes, known as lattice surgery and code deformation. In parallel, gauge fixing has emerged as a measurement-based method for performing universal gate sets in subsystem stabilizer codes. In this work, we show that lattice surgery and code deformation can be expressed as special cases of gauge fixing, permitting a simple and rigorous test for fault-tolerance together with simple guiding principles for the implementation of these operations. We demonstrate the accuracy of this method numerically with examples based on the surface code, some of which are novel

Software mitigation of coherent two-qubit gate errors

Two-qubit gates are important components of quantum computing. However, unwanted interactions between qubits (so-called parasitic gates) can be particularly problematic and degrade the performance of quantum applications. In this work, we present two software methods to mitigate parasitic two-qubit gate errors. The first approach is built upon the Cartan's KAK decomposition and keeps the original unitary decomposition for the error-free native two-qubit gate. It counteracts a parasitic two-qubit gate by only applying single-qubit rotations and therefore has no two-qubit gate overhead. We show the optimal choice of single-qubit mitigation gates. The second approach applies a numerical optimisation algorithm to re-compile a target unitary into the error-parasitic two-qubit gate plus single-qubit gates. We demonstrate these approaches on the CPhase-parasitic iSWAP-like gates. The KAK-based approach helps decrease unitary infidelity by a factor of 3 compared to the noisy implementation without error mitigation. When arbitrary single-qubit rotations are allowed, recompilation could completely mitigate the effect of parasitic errors but may require more native gates than the KAK-based approach. We also compare their average gate fidelity under realistic noise models, including relaxation and depolarising errors. Numerical results suggest that different approaches are advantageous in different error regimes, providing error mitigation guidance for near-term quantum computers

Software mitigation of coherent two-qubit gate errors

Two-qubit gates are important components of quantum computing. However, unwanted interactions between qubits (so-called parasitic gates) can be particularly problematic and degrade the performance of quantum applications. In this work, we present two software methods to mitigate parasitic two-qubit gate errors. The first approach is built upon the Cartan's KAK decomposition and keeps the original unitary decomposition for the error-free native two-qubit gate. It counteracts a parasitic two-qubit gate by only applying single-qubit rotations and therefore has no two-qubit gate overhead. We show the optimal choice of single-qubit mitigation gates. The second approach applies a numerical optimisation algorithm to re-compile a target unitary into the error-parasitic two-qubit gate plus single-qubit gates. We demonstrate these approaches on the CPhase-parasitic iSWAP-like gates. The KAK-based approach helps decrease unitary infidelity by a factor of 3 compared to the noisy implementation without error mitigation. When arbitrary single-qubit rotations are allowed, recompilation could completely mitigate the effect of parasitic errors but may require more native gates than the KAK-based approach. We also compare their average gate fidelity under realistic noise models, including relaxation and depolarising errors. Numerical results suggest that different approaches are advantageous in different error regimes, providing error mitigation guidance for near-term quantum computers

مهارة المحادثة وأسباب ضعف الطلاب الصينيين فيها

هدف البحث إلى تناول مراحل وأهداف وفوائد مهارة المحادثة للمتعلمين الصينين، كما يسعى للكشف عن أسباب ضعف متعلمي اللغة العربية الصينيين في مهارة المحادثة . أستخدم في البحث المنهج الاستقرائي والاستنباطي. توصل البحث إلى العديد من النتائج أهمها:  أن تعليم اللغة العربية في الجامعات الصينية يقتصر إلى حد بعيد على تحفيظ العبارات وتحريرها وترجمتها ، وهذا ما أضعف طلاقة معظم المتعلمين الصينيين للغة العربية في مهارة المحادثة قبل تخرجهم في الجامعات ، فأغلبهم يفضل أن يتعلم اللغة العربية بطرق غير فعالة ، وطرائق التعليم هذه لا تساعدهم في تقوية طاقتهم التعبيرية في المواقف اللغوية التواصلية المختلفة ، وهذا ما يؤدي بالمتعلمين الصينيين إلى سوء الفهم أثناء تبادل وجهات النظر في مناقشة قضية ما مع الناطقين بالعربية، وذلك لأنهم لا يدركون الأهداف الصحيحة من عملية التواصل الشفوي.  يوصي الباحث معلمي اللغة العربية لغير الناطقين بها أن يبتعدوا عن العبارات المحفوظة، وتنمية قدرة المتعلم على المحادثة وأن يكون يغظاً  للخطأ الذي يقوم فيه المتعلم وأن يقدم له التصحيح في الوقت المناسب، بالإضافة إلى توفير معامل اللغة ووضع اختبار معياري دولي دقيق لمهارة المحادثة، يحدد مستوى المتعلم بحسب رصيده اللغوي .     &nbsp

Comparison of prophylactic ipsilateral and bilateral central lymph node dissection in papillary thyroid carcinoma: a meta-analysis

Objective: The scope of surgical resection for paratracheal (level VI) lymph nodes in patients with Papillary Thyroid Carcinoma (PTC) remains debatable. The aim of our study was to evaluate the effectiveness and safety of prophylactic ipsilateral Central Neck lymph node Dissection (CND) versus bilateral CND at the time of total thyroidectomy for Clinically Node-negative (cN0) unilateral PTC. Methods: A systematic retrieval of electronic databases, including Pubmed, Web of Science, and the China Journal Net, was conducted from January 1990 to September 2021. Outcome data of interest included transient hypoparathyroidism, permanent hypoparathyroidism, transient Recurrent Laryngeal Nerve (RLN) injury, permanent RLN injury and local recurrence. We constructed the summary Odds Ratios (ORs) and 95% Confidence Intervals (CIs) for every study with either fixed or random effect models. Results: A full total of 1792 patients from 6 studies were enrolled. Our meta-analysis showed that transient hypoparathyroidism was significantly more frequent in bilateral CND group (OR = 0.58; 95% CI 0.44–0.76). The prevalence of permanent hypoparathyroidism was significantly higher in bilateral CND group patients compared to those in ipsilateral CND group (OR = 0.26; 95% CI 0.15–0.45). On the other hand, our meta-analysis indicated that there were no significant differences in the incidence of transient RLN injury, permanent RLN injury and local recurrence. Conclusions: Compared with bilateral CND, the rate of temporary and permanent hypoparathyroidism in ipsilateral CND is lower, but the local recurrence is similar. It may be presumptuous to suggest that ipsilateral CND is an adequate treatment for cN0 unilateral PTC