scholarly journals Quantum Error Mitigation using Symmetry Expansion

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 548
Author(s):  
Zhenyu Cai
Keyword(s):  
Wide Spectrum ◽  
Physical Problem ◽  
Estimation Bias ◽  
Energy Estimation ◽  
Practical Applications ◽  
Error Mitigation ◽  
Sampling Cost ◽  
Limited Scale ◽  
Near Term ◽  
Quantum Error

Even with the recent rapid developments in quantum hardware, noise remains the biggest challenge for the practical applications of any near-term quantum devices. Full quantum error correction cannot be implemented in these devices due to their limited scale. Therefore instead of relying on engineered code symmetry, symmetry verification was developed which uses the inherent symmetry within the physical problem we try to solve. In this article, we develop a general framework named symmetry expansion which provides a wide spectrum of symmetry-based error mitigation schemes beyond symmetry verification, enabling us to achieve different balances between the estimation bias and the sampling cost of the scheme. We show that certain symmetry expansion schemes can achieve a smaller estimation bias than symmetry verification through cancellation between the biases due to the detectable and undetectable noise components. A practical way to search for such a small-bias scheme is introduced. By numerically simulating the Fermi-Hubbard model for energy estimation, the small-bias symmetry expansion we found can achieve an estimation bias 6 to 9 times below what is achievable by symmetry verification when the average number of circuit errors is between 1 to 2. The corresponding sampling cost for random shot noise reduction is just 2 to 6 times higher than symmetry verification. Beyond symmetries inherent to the physical problem, our formalism is also applicable to engineered symmetries. For example, the recent scheme for exponential error suppression using multiple noisy copies of the quantum device is just a special case of symmetry expansion using the permutation symmetry among the copies.

scholarly journals Multi-exponential error extrapolation and combining error mitigation techniques for NISQ applications

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Zhenyu Cai
Keyword(s):  
Estimation Accuracy ◽  
Quantum Computers ◽  
Practical Application ◽  
Combined Method ◽  
Error Mitigation ◽  
Sampling Cost ◽  
Mitigation Techniques ◽  
Near Term ◽  
Quantum Error ◽  
Error Count

AbstractNoise in quantum hardware remains the biggest roadblock for the implementation of quantum computers. To fight the noise in the practical application of near-term quantum computers, instead of relying on quantum error correction which requires large qubit overhead, we turn to quantum error mitigation, in which we make use of extra measurements. Error extrapolation is an error mitigation technique that has been successfully implemented experimentally. Numerical simulation and heuristic arguments have indicated that exponential curves are effective for extrapolation in the large circuit limit with an expected circuit error count around unity. In this Article, we extend this to multi-exponential error extrapolation and provide more rigorous proof for its effectiveness under Pauli noise. This is further validated via our numerical simulations, showing orders of magnitude improvements in the estimation accuracy over single-exponential extrapolation. Moreover, we develop methods to combine error extrapolation with two other error mitigation techniques: quasi-probability and symmetry verification, through exploiting features of these individual techniques. As shown in our simulation, our combined method can achieve low estimation bias with a sampling cost multiple times smaller than quasi-probability while without needing to be able to adjust the hardware error rate as required in canonical error extrapolation.

scholarly journals Unified approach to data-driven quantum error mitigation

2021 ◽  
Vol 3 (3) ◽  
Author(s):  
Angus Lowe ◽  
Max Hunter Gordon ◽  
Piotr Czarnik ◽  
Andrew Arrasmith ◽  
Patrick J. Coles ◽  
...  
Keyword(s):  
Data Driven ◽  
Unified Approach ◽  
Error Mitigation ◽  
Quantum Error

scholarly journals Temperature and Relative Humidity Profile Retrieval from Fengyun-3D/HIRAS in the Arctic Region

2021 ◽  
Vol 13 (10) ◽  
pp. 1884
Author(s):  
Jingjing Hu ◽  
Yansong Bao ◽  
Jian Liu ◽  
Hui Liu ◽  
George P. Petropoulos ◽  
...  
Keyword(s):  
Relative Humidity ◽  
Real Time ◽  
Wide Spectrum ◽  
Warm Season ◽  
Arctic Region ◽  
Cold Season ◽  
The Arctic ◽  
Practical Applications ◽  
A New Technique ◽  
The Arctic Region

The acquisition of real-time temperature and relative humidity (RH) profiles in the Arctic is of great significance for the study of the Arctic’s climate and Arctic scientific research. However, the operational algorithm of Fengyun-3D only takes into account areas within 60°N, the innovation of this work is that a new technique based on Neural Network (NN) algorithm was proposed, which can retrieve these parameters in real time from the Fengyun-3D Hyperspectral Infrared Radiation Atmospheric Sounding (HIRAS) observations in the Arctic region. Considering the difficulty of obtaining a large amount of actual observation (such as radiosonde) in the Arctic region, collocated ERA5 data from European Centre for Medium-Range Weather Forecasts (ECMWF) and HIRAS observations were used to train the neural networks (NNs). Brightness temperature and training targets were classified using two variables: season (warm season and cold season) and surface type (ocean and land). NNs-based retrievals were compared with ERA5 data and radiosonde observations (RAOBs) independent of the NN training sets. Results showed that (1) the NNs retrievals accuracy is generally higher on warm season and ocean; (2) the root-mean-square error (RMSE) of retrieved profiles is generally slightly higher in the RAOB comparisons than in the ERA5 comparisons, but the variation trend of errors with height is consistent; (3) the retrieved profiles by the NN method are closer to ERA5, comparing with the AIRS products. All the results demonstrated the potential value in time and space of NN algorithm in retrieving temperature and relative humidity profiles of the Arctic region from HIRAS observations under clear-sky conditions. As such, the proposed NN algorithm provides a valuable pathway for retrieving reliably temperature and RH profiles from HIRAS observations in the Arctic region, providing information of practical value in a wide spectrum of practical applications and research investigations alike.All in all, our work has important implications in broadening Fengyun-3D’s operational implementation range from within 60°N to the Arctic region.

scholarly journals Error mitigation with Clifford quantum-circuit data

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 592
Author(s):  
Piotr Czarnik ◽  
Andrew Arrasmith ◽  
Patrick J. Coles ◽  
Lukasz Cincio
Keyword(s):  
State Energy ◽  
Quantum Computer ◽  
Quantum Circuit ◽  
Training Data ◽  
Quantum Circuits ◽  
Accurate Estimation ◽  
Error Mitigation ◽  
Order Of Magnitude ◽  
Quantum Observables ◽  
Near Term

Achieving near-term quantum advantage will require accurate estimation of quantum observables despite significant hardware noise. For this purpose, we propose a novel, scalable error-mitigation method that applies to gate-based quantum computers. The method generates training data {Xinoisy,Xiexact} via quantum circuits composed largely of Clifford gates, which can be efficiently simulated classically, where Xinoisy and Xiexact are noisy and noiseless observables respectively. Fitting a linear ansatz to this data then allows for the prediction of noise-free observables for arbitrary circuits. We analyze the performance of our method versus the number of qubits, circuit depth, and number of non-Clifford gates. We obtain an order-of-magnitude error reduction for a ground-state energy problem on 16 qubits in an IBMQ quantum computer and on a 64-qubit noisy simulator.

scholarly journals Physical Implementability of Linear Maps and Its Application in Error Mitigation

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 600
Author(s):  
Jiaqing Jiang ◽  
Kun Wang ◽  
Xin Wang
Keyword(s):  
General Linear ◽  
Local Error ◽  
Decomposition Technique ◽  
Completely Positive ◽  
Linear Map ◽  
Quantum Operations ◽  
Error Mitigation ◽  
Linear Maps ◽  
Analytic Expressions ◽  
Sampling Cost

Completely positive and trace-preserving maps characterize physically implementable quantum operations. On the other hand, general linear maps, such as positive but not completely positive maps, which can not be physically implemented, are fundamental ingredients in quantum information, both in theoretical and practical perspectives. This raises the question of how well one can simulate or approximate the action of a general linear map by physically implementable operations. In this work, we introduce a systematic framework to resolve this task using the quasiprobability decomposition technique. We decompose a target linear map into a linear combination of physically implementable operations and introduce the physical implementability measure as the least amount of negative portion that the quasiprobability must pertain, which directly quantifies the cost of simulating a given map using physically implementable quantum operations. We show this measure is efficiently computable by semidefinite programs and prove several properties of this measure, such as faithfulness, additivity, and unitary invariance. We derive lower and upper bounds in terms of the Choi operator's trace norm and obtain analytic expressions for several linear maps of practical interests. Furthermore, we endow this measure with an operational meaning within the quantum error mitigation scenario: it establishes the lower bound of the sampling cost achievable via the quasiprobability decomposition technique. In particular, for parallel quantum noises, we show that global error mitigation has no advantage over local error mitigation.

scholarly journals Scalable thermoelectric fibers for multifunctional textile-electronics

2020 ◽  
Vol 11 (1) ◽  
Author(s):  
Tianpeng Ding ◽  
Kwok Hoe Chan ◽  
Yi Zhou ◽  
Xiao-Qiao Wang ◽  
Yin Cheng ◽  
...  
Keyword(s):  
Energy Harvesting ◽  
Green Energy ◽  
Process Efficiency ◽  
Robotic Arm ◽  
Practical Applications ◽  
Flexible Devices ◽  
Fiber Fabrication ◽  
Mechanical Compliance ◽  
Limited Scale ◽  
High Scalability

AbstractTextile electronics are poised to revolutionize future wearable applications due to their wearing comfort and programmable nature. Many promising thermoelectric wearables have been extensively investigated for green energy harvesting and pervasive sensors connectivity. However, the practical applications of the TE textile are still hindered by the current laborious p/n junctions assembly of limited scale and mechanical compliance. Here we develop a gelation extrusion strategy that demonstrates the viability of digitalized manufacturing of continuous p/n TE fibers at high scalability and process efficiency. With such alternating p/n-type TE fibers, multifunctional textiles are successfully woven to realize energy harvesting on curved surface, multi-pixel touch panel for writing and communication. Moreover, modularized TE garments are worn on a robotic arm to fulfill diverse active and localized tasks. Such scalable TE fiber fabrication not only brings new inspiration for flexible devices, but also sets the stage for a wide implementation of multifunctional textile-electronics.

scholarly journals Heisenberg-limited single-mode quantum metrology in a superconducting circuit

2019 ◽  
Vol 10 (1) ◽  
Author(s):  
W. Wang ◽  
Y. Wu ◽  
Y. Ma ◽  
W. Cai ◽  
L. Hu ◽  
...  
Keyword(s):  
Single Mode ◽  
Coherence Time ◽  
Microwave Cavity ◽  
Phase Estimation ◽  
Quantum Metrology ◽  
Practical Applications ◽  
Infinite Dimensional ◽  
Noise Limit ◽  
Quantum Error ◽  
Shot Noise Limit

Abstract Two-mode interferometers lay the foundations for quantum metrology. Instead of exploring quantum entanglement in the two-mode interferometers, a single bosonic mode also promises a measurement precision beyond the shot-noise limit (SNL) by taking advantage of the infinite-dimensional Hilbert space of Fock states. Here, we demonstrate a single-mode phase estimation that approaches the Heisenberg limit (HL) unconditionally. Due to the strong dispersive nonlinearity and long coherence time of a microwave cavity, quantum states of the form $$\left( {\left| 0 \right\rangle + \left| N \right\rangle } \right)/\sqrt 2$$ 0 + N ∕ 2 can be generated, manipulated and detected with high fidelities, leading to an experimental phase estimation precision scaling as ∼N−0.94. A 9.1 dB enhancement of the precision over the SNL at N = 12 is achieved, which is only 1.7 dB away from the HL. Our experimental architecture is hardware efficient and can be combined with quantum error correction techniques to fight against decoherence, and thus promises quantum-enhanced sensing in practical applications.

scholarly journals Quantum Error Mitigation With Artificial Neural Network

IEEE Access ◽  
2020 ◽  
Vol 8 ◽  
pp. 188853-188860
Author(s):  
Changjun Kim ◽  
Kyungdeock Daniel Park ◽  
June-Koo Rhee
Keyword(s):  
Neural Network ◽  
Artificial Neural Network ◽  
Error Mitigation ◽  
Artificial Neural ◽  
Quantum Error

scholarly journals Dynamical Manipulation of Surface Plasmon Polaritons

2019 ◽  
Vol 9 (16) ◽  
pp. 3297 ◽  
Author(s):  
Wang ◽  
Zhao ◽  
Li
Keyword(s):  
Electromagnetic Field ◽  
Metal Surface ◽  
Surface Plasmon ◽  
Surface Plasmon Polaritons ◽  
Wide Spectrum ◽  
Future Perspectives ◽  
Practical Applications ◽  
Fundamental Research ◽  
Dielectric Structures ◽  
Plasmon Polaritons

As the fundamental and promising branch of nanophotonics, surface plasmon polaritons (SPP) with the ability of manipulating the electromagnetic field on the subwavelength scale are of interest to a wide spectrum of scientists. Composed of metallic or dielectric structures whose shape and position are carefully engineered on the metal surface, traditional SPP devices are generally static and lack tunability. Dynamical manipulation of SPP is meaningful in both fundamental research and practical applications. In this article, the achievements in dynamical SPP excitation, SPP focusing, SPP vortex, and SPP nondiffracting beams are presented. The mechanisms of dynamical SPP devices are revealed and compared, and future perspectives are discussed.

UV Nano-Imprint Lithography for Manufacturing Applications

2007 ◽  
Author(s):  
Jin Choi ◽  
S. V. Sreenivasan ◽  
Doug Resnick
Keyword(s):  
Uv Curing ◽  
Magnetic Storage ◽  
Imprint Lithography ◽  
Practical Applications ◽  
Drop On Demand ◽  
Defect Repair ◽  
Manufacturing Applications ◽  
Near Term ◽  
Layer Control ◽  
Nano Imprint

Researchers have demonstrated that imprint lithography techniques have remarkable replication resolution and can pattern sub-5nm structures. However, a fully capable lithography approach needs to address several challenges in order to be useful in nano-manufacturing applications. This paper presents the key technical challenges as well as the progress achieved to-date in these areas. A promising nanoimprint technique that has been previously discussed in the literature is a UV curing technique known as Step and Flash Imprint Lithography (S-FIL). In this article, a variant of the S-FIL process — known as drop-on-demand UV nano-imprint process — that addresses many of the key manufacturing challenges is discussed. This process has the ability to address challenges such as process repeatability in residual layer control, low defectivity, ability to fully automate the lithography process, nano-resolution alignment, and the ability to handle pattern density variations. All nano-imprint lithography techniques essentially replicate the patterns present in a master mold (or template). One of the demanding challenges is the creation of this template. Patterning, metrology, inspection, and defect repair issues relevant to template fabrication are discussed. Finally, with a brief discussion of near-term practical applications in the areas of photonics, magnetic storage, and CMOS devices is presented.

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