Learning-based quantum error mitigation

If NISQ-era quantum computers are to perform useful tasks, they will need to employ powerful error mitigation techniques. Quasi-probability methods can permit perfect error compensation at the cost of additional circuit executions, provided that the nature of the error model is fully understood and sufficiently local both spatially and temporally. Unfortunately these conditions are challenging to satisfy. Here we present a method by which the proper compensation strategy can instead be learned ab initio. Our training process uses multiple variants of the primary circuit where all non-Clifford gates are substituted with gates that are efficient to simulate classically. The process yields a configuration that is near-optimal versus noise in the real system with its non-Clifford gate set. Having presented a range of learning strategies, we demonstrate the power of the technique both with real quantum hardware (IBM devices) and exactly-emulated imperfect quantum computers. The systems suffer a range of noise severities and types, including spatially and temporally correlated variants. In all cases the protocol successfully adapts to the noise and mitigates it to a high degree.Comment: 28 pages, 19 figure

Error statistics and scalability of quantum error mitigation formulas

Quantum computing promises advantages over classical computing in many problems. Nevertheless, noise in quantum devices prevents most quantum algorithms from achieving the quantum advantage. Quantum error mitigation provides a variety of protocols to handle such noise using minimal qubit resources . While some of those protocols have been implemented in experiments for a few qubits, it remains unclear whether error mitigation will be effective in quantum circuits with tens to hundreds of qubits. In this paper, we apply statistics principles to quantum error mitigation and analyse the scaling behaviour of its intrinsic error. We find that the error increases linearly $O(\epsilon N)$ with the gate number $N$ before mitigation and sub-linearly $O(\epsilon' N^\gamma)$ after mitigation, where $\gamma \approx 0.5$, $\epsilon$ is the error rate of a quantum gate, and $\epsilon'$ is a protocol-dependent factor. The $\sqrt{N}$ scaling is a consequence of the law of large numbers, and it indicates that error mitigation can suppress the error by a larger factor in larger circuits. We propose the importance Clifford sampling as a key technique for error mitigation in large circuits to obtain this result

TETRIS-ADAPT-VQE: An adaptive algorithm that yields shallower, denser circuit ans\"atze

Adaptive quantum variational algorithms are particularly promising for simulating strongly correlated systems on near-term quantum hardware, but they are not yet viable due, in large part, to the severe coherence time limitations on current devices. In this work, we introduce an algorithm called TETRIS-ADAPT-VQE, which iteratively builds up variational ans\"atze a few operators at a time in a way dictated by the problem being simulated. This algorithm is a modified version of the ADAPT-VQE algorithm in which the one-operator-at-a-time rule is lifted to allow for the addition of multiple operators with disjoint supports in each iteration. TETRIS-ADAPT-VQE results in denser but significantly shallower circuits, without increasing the number of CNOT gates or variational parameters. Its advantage over the original algorithm in terms of circuit depths increases with the system size. Moreover, the expensive step of measuring the energy gradient with respect to each candidate unitary at each iteration is performed only a fraction of the time compared to ADAPT-VQE. These improvements bring us closer to the goal of demonstrating a practical quantum advantage on quantum hardware.Comment: 10 pages, 7 figure

Responses of community traits and soil characteristics of Achnatherum inebrians-type degraded grassland to grazing systems in alpine meadows on the Qinghai-Tibet Plateau

IntroductionScientific grazing management is of great significance for the ecological health and sustainable use of alpine meadows.MethodsTo explore appropriate management methods of alpine grasslands of the Qinghai-Tibet Plateau degraded by Achnatherum inebrians (Hance) Keng ex Tzvele presence, we studied the effects of different grazing systems on the A. inebrians population, grassland vegetation community traits, soil characteristics and soil microbial community structure for cold- season grazing plus supplementary feeding pasture (CSF) and four-season open public pasture (FOP) in Tianzhu County, Gansu Province.ResultsCompared with FOP, the CSF site showed significantly inhibited reproduction of A. inebrians, especially the crown width, seed yield and number of reproductive branches per plant were as high as 50%, significantly increased the aboveground biomass of edible forage and soil water content by 57% and 43–55%, better soil nutrients, and significantly reduced soil bulk density by 10– 29%. Different grazing systems affected the composition and diversity of soil microbial communities, with a greater effect on fungi than on bacterial flora. The most abundant phyla of bacteria and fungi were Proteobacteria and Ascomycota for CSF (by 30–38% and 24–28%) and for FOP (by 67–70% and 68–73%), and the relative abundance and species of bacterial and fungal genera were greater for CSF than FOP. The α-diversity indexes of fungi were improved, and the β-diversity of fungi was significant difference between CSF and FOP. However, the grazing utilization time was prolonged in FOP, which reduced the diversity and abundance of soil bacteria and increased soil spatial heterogeneity. The use of A. inebrians-type degraded grassland in the cold season, and as a winter supplementary feeding and resting ground, could effectively inhibit expansion of A. inebrians, promote edible forage growth, enhance grassland productivity and community stability, and improve soil structure. DiscussionThe results guide healthy and sustainable utilization of A. inebrians-type degraded grassland in the Qinghai-Tibet Plateau