For the treatment of the quantum effect of charge distribution in nanoscale MOSFETs,a quantum correction model using Levenberg-Marquardt back-propagation neural networks is presented that can predict the quantum densi...For the treatment of the quantum effect of charge distribution in nanoscale MOSFETs,a quantum correction model using Levenberg-Marquardt back-propagation neural networks is presented that can predict the quantum density from the classical density. The training speed and accuracy of neural networks with different hidden layers and numbers of neurons are studied. We conclude that high training speed and accuracy can be obtained using neural networks with two hidden layers,but the number of neurons in the hidden layers does not have a noticeable effect, For single and double-gate nanoscale MOSFETs, our model can easily predict the quantum charge density in the silicon layer,and it agrees closely with the Schrodinger-Poisson approach.展开更多
In this article, the authors study the exact traveling wave solutions of modified Zakharov equations for plasmas with a quantum correction by hyperbolic tangent function expansion method, hyperbolic secant expansion m...In this article, the authors study the exact traveling wave solutions of modified Zakharov equations for plasmas with a quantum correction by hyperbolic tangent function expansion method, hyperbolic secant expansion method, and Jacobi elliptic function ex- pansion method. They obtain more exact traveling wave solutions including trigonometric function solutions, rational function solutions, and more generally solitary waves, which are called classical bright soliton, W-shaped soliton, and M-shaped soliton.展开更多
We study the absorption probability and Hawking radiation of the scalar field in a d-dimensional black hole with quantum correction arising from the polymer quantization. We find that the quantum length scale k （i.e....We study the absorption probability and Hawking radiation of the scalar field in a d-dimensional black hole with quantum correction arising from the polymer quantization. We find that the quantum length scale k （i.e., the bounce radius） modifies the standard results in greybody factors and Hawking radiation on the brahe and into the bulk. For the black hole with the larger mass M the effects of the parameter k in the four-dimensional black hole spacetime are entirely different from those in the high dimensional cases. When the mass of black hole M becomes very small, we also find that only the sign of the change rate of the greybody factors on the brahe with respect to the dimensional number depends sharply on the bounce radius k. These information can help us know more about the extra dimension and the black holes with quantum correction.展开更多
We propose a quantization procedure for the nucleon-scMar meson system, in which an arbitrary mean scalar meson field Ф is introduced. The equivalence of this procedure with the usual one is proven for any given valu...We propose a quantization procedure for the nucleon-scMar meson system, in which an arbitrary mean scalar meson field Ф is introduced. The equivalence of this procedure with the usual one is proven for any given value of qS. By use of this procedure, the scalar meson field in the Walecka＇s MFA and in Chin＇s RHA are quantized around the mean field, Its corrections on these theories are considered by perturbation up to the second order. The arbitrariness of Ф makes us free to fix it at any stage in the calculation. When we fix it in the way of Walecka＇s MFA, the quantum corrections are big, and the result does not converge. When we fix it in the way of Chin＇s RHA, the quantum correction is negligibly small, and the convergence is excellent. It shows that RHA covers the leading part of quantum field theory for nuclear systems and is an excellent zeroth order approximation for further quantum corrections, while the Walecka＇s MFA does not. We suggest to fix the parameter Ф at the end of the whole calculation by minimizing the total energy per-nucleon for the nuclear matter or the total energy for the finite nucleus, to make the quantized relativistic mean field theory （QRMFT） a variational method.展开更多
Quantum computing has the potential to solve complex problems that are inefficiently handled by classical computation.However,the high sensitivity of qubits to environmental interference and the high error rates in cu...Quantum computing has the potential to solve complex problems that are inefficiently handled by classical computation.However,the high sensitivity of qubits to environmental interference and the high error rates in current quantum devices exceed the error correction thresholds required for effective algorithm execution.Therefore,quantum error correction technology is crucial to achieving reliable quantum computing.In this work,we study a topological surface code with a two-dimensional lattice structure that protects quantum information by introducing redundancy across multiple qubits and using syndrome qubits to detect and correct errors.However,errors can occur not only in data qubits but also in syndrome qubits,and different types of errors may generate the same syndromes,complicating the decoding task and creating a need for more efficient decoding methods.To address this challenge,we used a transformer decoder based on an attention mechanism.By mapping the surface code lattice,the decoder performs a self-attention process on all input syndromes,thereby obtaining a global receptive field.The performance of the decoder was evaluated under a phenomenological error model.Numerical results demonstrate that the decoder achieved a decoding accuracy of 93.8%.Additionally,we obtained decoding thresholds of 5%and 6.05%at maximum code distances of 7 and 9,respectively.These results indicate that the decoder used demonstrates a certain capability in correcting noise errors in surface codes.展开更多
Quantum error correction is essential for realizing fault-tolerant quantum computing,where both the efficiency and accuracy of the decoding algorithms play critical roles.In this work,we introduce the implementation o...Quantum error correction is essential for realizing fault-tolerant quantum computing,where both the efficiency and accuracy of the decoding algorithms play critical roles.In this work,we introduce the implementation of the PLANAR algorithm,a software framework designed for fast and exact decoding of quantum codes with a planar structure.The algorithm first converts the optimal decoding of quantum codes into a partition function computation problem of an Ising spin glass model.Then it utilizes the exact Kac–Ward formula to solve it.In this way,PLANAR offers the exact maximum likelihood decoding in polynomial complexity for quantum codes with a planar structure,including the surface code with independent code-capacity noise and the quantum repetition code with circuit-level noise.Unlike traditional minimumweight decoders such as minimum-weight perfect matching(MWPM),PLANAR achieves theoretically optimal performance while maintaining polynomial-time efficiency.In addition,to demonstrate its capabilities,we exemplify the implementation using the rotated surface code,a commonly used quantum error correction code with a planar structure,and show that PLANAR achieves a threshold of approximately p_(uc)≈0.109 under the depolarizing error model,with a time complexity scaling of O(N^(0.69)),where N is the number of spins in the Ising model.展开更多
We investigate in this work a quantum error correction on a five-qubits graph state used for secret sharing through five noisy channels. We describe the procedure for the five, seven and nine qubits codes. It is known...We investigate in this work a quantum error correction on a five-qubits graph state used for secret sharing through five noisy channels. We describe the procedure for the five, seven and nine qubits codes. It is known that the three codes always allow error recovery if only one among the sent qubits is disturbed in the transmitting channel. However, if two qubits and more are disturbed, then the correction will depend on the used code. We compare in this paper the three codes by computing the average fidelity between the sent secret and that measured by the receivers. We will treat the case where, at most, two qubits are affected in each one of five depolarizing channels.展开更多
We calculate photon sphere r_(ph) and critical curve b_(c) for a quantum corrected Schwarzschild black hole,finding that they violate universal inequalities proved for asymptotically flat black holes that satisfy the ...We calculate photon sphere r_(ph) and critical curve b_(c) for a quantum corrected Schwarzschild black hole,finding that they violate universal inequalities proved for asymptotically flat black holes that satisfy the null energy condition in the framework of Einstein gravity.This violation seems to be a common phenomenon when considering quantum modification of Einstein gravity.Furthermore,we study the shadows,lensing rings,and photon rings in the quantum corrected Schwarzschild black hole.The violation leads to a larger bright lensing ring in the observational appearance of the thin disk emission near the black hole compared with the classical Schwarzschild black hole.Our analysis may provide observational evidence for the quantum effect of general relativity.展开更多
We calculate the thermodynamic quantities in the quantum corrected Reissner-Nordstr?m-AdS(RN-AdS)black hole,and examine their quantum corrections.By analyzing the mass and heat capacity,we give the critical state and ...We calculate the thermodynamic quantities in the quantum corrected Reissner-Nordstr?m-AdS(RN-AdS)black hole,and examine their quantum corrections.By analyzing the mass and heat capacity,we give the critical state and the remnant state,respectively,and discuss their consistency.Then,we investigate the quantum tunneling from the event horizon of massless scalar particle by using the null geodesic method,and charged massive boson W^(±)and fermions by using the Hamilton-Jacob method.It is shown that the same Hawking temperature can be obtained from these tunneling processes of different particles and methods.Next,by using the generalized uncertainty principle(GUP),we study the quantum corrections to the tunneling and the temperature.Then the logarithmic correction to the black hole entropy is obtained.展开更多
By considering an asymmetric thin-shell wormhole(ATSW)surrounded by an optically and geometrically thin disk,we investigate the luminosity distribution of this ATSW with the spacetime on two sides encoded with the ren...By considering an asymmetric thin-shell wormhole(ATSW)surrounded by an optically and geometrically thin disk,we investigate the luminosity distribution of this ATSW with the spacetime on two sides encoded with the renormalization group improved(RGI)parameters(Ω,γ).Although some light rays are absorbed into the throat in the vicinity of the wormhole,they return through the throat with certain conditions,unlike in the case of black holes.The spacetime on one side of the wormhole can capture the additional photons emitted from the thin disk,resulting in several interesting observable features of the wormhole.The results in this paper show that there are two additional orbit numbers n in the ATSW and six transfer functions,rather than three as in the black hole case.In this case,the ATSW indeed has a more complex observable structure,where some additional light rings arise naturally.For instance,there are two additional photon rings for the emitted Model 1.Moreover,we also find a new wide hump between the first and second additional photon rings in Model 2.The effects of Ω and γ on the observed images are clearly addressed throughout this study,and the influence of Ω is found to be larger.Finally,we conclude that the observations of the RGI-ATSW can help further distinguish it from other ATSWs and black holes when a thin accretion disk exists around it.展开更多
In this work,we apply tunneling formalism to analyze charged particles tunneling across a hairy black hole horizon.Such black hole solutions are essential for frameworks based on Horndeski's gravity theory.Applyin...In this work,we apply tunneling formalism to analyze charged particles tunneling across a hairy black hole horizon.Such black hole solutions are essential for frameworks based on Horndeski's gravity theory.Applying a semi-classical technique,we examine the tunneling of charged particles from a hairy black hole and derive the generic tunneling spectrum of released particles,ignoring self-gravitational and interaction.It is studied to ignore the back-reaction impact of the radiated particle on the hairy black hole.We analyze the properties of the black hole,such as temperature and entropy,under the influence of quantum gravity and also observe that the firstorder correction is present.We study tunneling radiation produced by a charged field equation in the presence of a generalized uncertainty effect.We modify the semi-classical technique by using the generalized uncertainty principle,the WKB approximation,and surface gravity.展开更多
Measurement-based quantum computation with continuous variables,which realizes computation by performing measurement and feedforward of measurement results on a large scale Gaussian cluster state,provides a feasible w...Measurement-based quantum computation with continuous variables,which realizes computation by performing measurement and feedforward of measurement results on a large scale Gaussian cluster state,provides a feasible way to implement quantum computation.Quantum error correction is an essential procedure to protect quantum information in quantum computation and quantum communication.In this review,we briefly introduce the progress of measurement-based quantum computation and quantum error correction with continuous variables based on Gaussian cluster states.We also discuss the challenges in the fault-tolerant measurement-based quantum computation with continuous variables.展开更多
For applying the perfect code to transmit quantum information over a noise channel,the standard protocol contains four steps:the encoding,the noise channel,the error-correction operation,and the decoding.In present wo...For applying the perfect code to transmit quantum information over a noise channel,the standard protocol contains four steps:the encoding,the noise channel,the error-correction operation,and the decoding.In present work,we show that this protocol can be simplified.The error-correction operation is not necessary if the decoding is realized by the so-called complete unitary transformation.We also offer a quantum circuit,which can correct the arbitrary single-qubit errors.展开更多
Quantum error correction technology is an important solution to solve the noise interference generated during the operation of quantum computers.In order to find the best syndrome of the stabilizer code in quantum err...Quantum error correction technology is an important solution to solve the noise interference generated during the operation of quantum computers.In order to find the best syndrome of the stabilizer code in quantum error correction,we need to find a fast and close to the optimal threshold decoder.In this work,we build a convolutional neural network(CNN)decoder to correct errors in the toric code based on the system research of machine learning.We analyze and optimize various conditions that affect CNN,and use the RestNet network architecture to reduce the running time.It is shortened by 30%-40%,and we finally design an optimized algorithm for CNN decoder.In this way,the threshold accuracy of the neural network decoder is made to reach 10.8%,which is closer to the optimal threshold of about 11%.The previous threshold of 8.9%-10.3%has been slightly improved,and there is no need to verify the basic noise.展开更多
Quantum metrology provides a fundamental limit on the precision of multi-parameter estimation,called the Heisenberg limit,which has been achieved in noiseless quantum systems.However,for systems subject to noises,it i...Quantum metrology provides a fundamental limit on the precision of multi-parameter estimation,called the Heisenberg limit,which has been achieved in noiseless quantum systems.However,for systems subject to noises,it is hard to achieve this limit since noises are inclined to destroy quantum coherence and entanglement.In this paper,a combined control scheme with feedback and quantum error correction(QEC)is proposed to achieve the Heisenberg limit in the presence of spontaneous emission,where the feedback control is used to protect a stabilizer code space containing an optimal probe state and an additional control is applied to eliminate the measurement incompatibility among three parameters.Although an ancilla system is necessary for the preparation of the optimal probe state,our scheme does not require the ancilla system to be noiseless.In addition,the control scheme in this paper has a low-dimensional code space.For the three components of a magnetic field,it can achieve the highest estimation precision with only a 2-dimensional code space,while at least a4-dimensional code space is required in the common optimal error correction protocols.展开更多
The loss of a quantum channel leads to an irretrievable particle loss as well as information. In this paper, the loss of quantum channel is analysed and a method is put forward to recover the particle and information ...The loss of a quantum channel leads to an irretrievable particle loss as well as information. In this paper, the loss of quantum channel is analysed and a method is put forward to recover the particle and information loss effectively using universal quantum error correction. Then a secure direct communication scheme is proposed, such that in a loss channel the information that an eavesdropper can obtain would be limited to arbitrarily small when the code is properly chosen and the correction operation is properly arranged.展开更多
The present study delves into the application of investigating quantum state behaviour,particularly focusing on coherent and superposition states.These states,characterized by their remarkable stability and precision,...The present study delves into the application of investigating quantum state behaviour,particularly focusing on coherent and superposition states.These states,characterized by their remarkable stability and precision,have found extensive utility in various domains of quantum mechanics and quantum information processing.Coherent states are valuable for manipulating quantum systems with accuracy.Superposition states allow quantum systems to exist in numerous configurations at the same time,which paves the way for quantum computing’s capacity for parallel processing.The research accentuates the crucial role of quantum error correction(QEC)in ensuring the stability and reliability of quantum information processing systems.Quantum systems are prone to errors from decoherence and environmental noise,making QEC essential for ensuring accurate results by employing the Shor code,an error-correcting code devised by Peter Shor,it becomes feasible to detect and rectify errors that may arise during quantum computations.The Shor code detects and corrects both bit-flip and phase-flip errors,greatly enhancing the robustness of quantum information systems.This research offers insights into the multifaceted utility of MZI(Mach-Zehnder interferometer)and its relevance in the advancement of quantum technology.By integrating QEC with the capabilities of MZI,this study offers a holistic approach to advancing the precision and reliability of quantum technologies.展开更多
To improve the decoding performance of quantum error-correcting codes in asymmetric noise channels,a neural network-based decoding algorithm for bias-tailored quantum codes is proposed.The algorithm consists of a bias...To improve the decoding performance of quantum error-correcting codes in asymmetric noise channels,a neural network-based decoding algorithm for bias-tailored quantum codes is proposed.The algorithm consists of a biased noise model,a neural belief propagation decoder,a convolutional optimization layer,and a multi-objective loss function.The biased noise model simulates asymmetric error generation,providing a training dataset for decoding.The neural network,leveraging dynamic weight learning and a multi-objective loss function,mitigates error degeneracy.Additionally,the convolutional optimization layer enhances early-stage convergence efficiency.Numerical results show that for bias-tailored quantum codes,our decoder performs much better than the belief propagation(BP)with ordered statistics decoding(BP+OSD).Our decoder achieves an order of magnitude improvement in the error suppression compared to higher-order BP+OSD.Furthermore,the decoding threshold of our decoder for surface codes reaches a high threshold of 20%.展开更多
Quantum error-correcting codes are essential for fault-tolerant quantum computing,as they effectively detect and correct noise-induced errors by distributing information across multiple physical qubits.The subsystem s...Quantum error-correcting codes are essential for fault-tolerant quantum computing,as they effectively detect and correct noise-induced errors by distributing information across multiple physical qubits.The subsystem surface code with three-qubit check operators demonstrates significant application potential due to its simplified measurement operations and low logical error rates.However,the existing minimum-weight perfect matching(MWPM)algorithm exhibits high computational complexity and lacks flexibility in large-scale systems.Therefore,this paper proposes a decoder based on a graph attention network(GAT),representing error syndromes as undirected graphs with edge weights,and employing a multihead attention mechanism to efficiently aggregate node features and enable parallel computation.Compared to MWPM,the GAT decoder exhibits linear growth in computational complexity,adapts to different quantum code structures,and demonstrates stronger robustness under high physical error rates.The experimental results demonstrate that the proposed decoder achieves an overall accuracy of 89.95%under various small code lattice sizes(L=2,3,4,5),with the logical error rate threshold increasing to 0.0078,representing an improvement of approximately 13.04%compared to the MWPM decoder.This result significantly outperforms traditional methods,showcasing superior performance under small code lattice sizes and providing a more efficient decoding solution for large-scale quantum error correction.展开更多
For the quantum error correction and noisy intermediate-scale quantum algorithms to function with high efficiency,the raw fidelity of quantum logic gates on physical qubits needs to satisfy strict requirements.The neu...For the quantum error correction and noisy intermediate-scale quantum algorithms to function with high efficiency,the raw fidelity of quantum logic gates on physical qubits needs to satisfy strict requirements.The neutral atom quantum computing equipped with Rydberg blockade gates has made impressive progress recently,which makes it worthwhile to explore its potential in the two-qubit entangling gates,including the controlledphase gate,and in particular,the CZ gate.Provided the quantum coherence is well preserved,improving the fidelity of Rydberg blockade gates calls for special mechanisms to deal with adverse effects caused by realistic experimental conditions.Here,the heralded very-high-fidelity Rydberg blockade controlled-phase gate is designed to address these issues,which contains self-correction and projection as the key steps.This trailblazing method builds upon the previously established buffer-atom-mediated gate framework,with a special form of symmetry under parity–time transformation playing a crucial role in the process.We further analyze the performance with respect to a few typical sources of imperfections.This procedure can also be regarded as quantum hardware error correction or mitigation.While this paper by itself does not cover every single subtle issue and still contains many oversimplifications,we find it reasonable to anticipate a very-high-fidelity two-qubit quantum logic gate operated in the sense of heralded but probabilistic,whose gate error can be reduced to the level of 10^(-4)–10^(-6)or even lower with reasonably high possibilities.展开更多
文摘For the treatment of the quantum effect of charge distribution in nanoscale MOSFETs,a quantum correction model using Levenberg-Marquardt back-propagation neural networks is presented that can predict the quantum density from the classical density. The training speed and accuracy of neural networks with different hidden layers and numbers of neurons are studied. We conclude that high training speed and accuracy can be obtained using neural networks with two hidden layers,but the number of neurons in the hidden layers does not have a noticeable effect, For single and double-gate nanoscale MOSFETs, our model can easily predict the quantum charge density in the silicon layer,and it agrees closely with the Schrodinger-Poisson approach.
基金Supported by the National Natural Science Foundation of China (10871075)Natural Science Foundation of Guangdong Province,China (9151064201000040)
文摘In this article, the authors study the exact traveling wave solutions of modified Zakharov equations for plasmas with a quantum correction by hyperbolic tangent function expansion method, hyperbolic secant expansion method, and Jacobi elliptic function ex- pansion method. They obtain more exact traveling wave solutions including trigonometric function solutions, rational function solutions, and more generally solitary waves, which are called classical bright soliton, W-shaped soliton, and M-shaped soliton.
基金Supported by the National Natural Science Foundation of China under Grant No. 11275065the NCET under Grant No. 10-0165+1 种基金the PCSIRT under Grant No. IRT0964the construct program of key disciplines in Hunan Province
文摘We study the absorption probability and Hawking radiation of the scalar field in a d-dimensional black hole with quantum correction arising from the polymer quantization. We find that the quantum length scale k （i.e., the bounce radius） modifies the standard results in greybody factors and Hawking radiation on the brahe and into the bulk. For the black hole with the larger mass M the effects of the parameter k in the four-dimensional black hole spacetime are entirely different from those in the high dimensional cases. When the mass of black hole M becomes very small, we also find that only the sign of the change rate of the greybody factors on the brahe with respect to the dimensional number depends sharply on the bounce radius k. These information can help us know more about the extra dimension and the black holes with quantum correction.
基金Supported by the Nature Science Foundation of China under Grant Nos.10875003 and 10811240152the calculations are supported by CERNET High Performance Computing Center in China
文摘We propose a quantization procedure for the nucleon-scMar meson system, in which an arbitrary mean scalar meson field Ф is introduced. The equivalence of this procedure with the usual one is proven for any given value of qS. By use of this procedure, the scalar meson field in the Walecka＇s MFA and in Chin＇s RHA are quantized around the mean field, Its corrections on these theories are considered by perturbation up to the second order. The arbitrariness of Ф makes us free to fix it at any stage in the calculation. When we fix it in the way of Walecka＇s MFA, the quantum corrections are big, and the result does not converge. When we fix it in the way of Chin＇s RHA, the quantum correction is negligibly small, and the convergence is excellent. It shows that RHA covers the leading part of quantum field theory for nuclear systems and is an excellent zeroth order approximation for further quantum corrections, while the Walecka＇s MFA does not. We suggest to fix the parameter Ф at the end of the whole calculation by minimizing the total energy per-nucleon for the nuclear matter or the total energy for the finite nucleus, to make the quantized relativistic mean field theory （QRMFT） a variational method.
基金Project supported by the Natural Science Foundation of Shandong Province,China(Grant No.ZR2021MF049)Joint Fund of Natural Science Foundation of Shandong Province(Grant Nos.ZR2022LLZ012 and ZR2021LLZ001)the Key R&D Program of Shandong Province,China(Grant No.2023CXGC010901)。
文摘Quantum computing has the potential to solve complex problems that are inefficiently handled by classical computation.However,the high sensitivity of qubits to environmental interference and the high error rates in current quantum devices exceed the error correction thresholds required for effective algorithm execution.Therefore,quantum error correction technology is crucial to achieving reliable quantum computing.In this work,we study a topological surface code with a two-dimensional lattice structure that protects quantum information by introducing redundancy across multiple qubits and using syndrome qubits to detect and correct errors.However,errors can occur not only in data qubits but also in syndrome qubits,and different types of errors may generate the same syndromes,complicating the decoding task and creating a need for more efficient decoding methods.To address this challenge,we used a transformer decoder based on an attention mechanism.By mapping the surface code lattice,the decoder performs a self-attention process on all input syndromes,thereby obtaining a global receptive field.The performance of the decoder was evaluated under a phenomenological error model.Numerical results demonstrate that the decoder achieved a decoding accuracy of 93.8%.Additionally,we obtained decoding thresholds of 5%and 6.05%at maximum code distances of 7 and 9,respectively.These results indicate that the decoder used demonstrates a certain capability in correcting noise errors in surface codes.
基金supported by the National Natural Science Foundation of China(Grant Nos.12325501,12047503,and 12247104)the Chinese Academy of Sciences(Grant No.ZDRW-XX-2022-3-02)P.Z.is partially supported by the Innovation Program for Quantum Science and Technology(Grant No.2021ZD0301900).
文摘Quantum error correction is essential for realizing fault-tolerant quantum computing,where both the efficiency and accuracy of the decoding algorithms play critical roles.In this work,we introduce the implementation of the PLANAR algorithm,a software framework designed for fast and exact decoding of quantum codes with a planar structure.The algorithm first converts the optimal decoding of quantum codes into a partition function computation problem of an Ising spin glass model.Then it utilizes the exact Kac–Ward formula to solve it.In this way,PLANAR offers the exact maximum likelihood decoding in polynomial complexity for quantum codes with a planar structure,including the surface code with independent code-capacity noise and the quantum repetition code with circuit-level noise.Unlike traditional minimumweight decoders such as minimum-weight perfect matching(MWPM),PLANAR achieves theoretically optimal performance while maintaining polynomial-time efficiency.In addition,to demonstrate its capabilities,we exemplify the implementation using the rotated surface code,a commonly used quantum error correction code with a planar structure,and show that PLANAR achieves a threshold of approximately p_(uc)≈0.109 under the depolarizing error model,with a time complexity scaling of O(N^(0.69)),where N is the number of spins in the Ising model.
文摘We investigate in this work a quantum error correction on a five-qubits graph state used for secret sharing through five noisy channels. We describe the procedure for the five, seven and nine qubits codes. It is known that the three codes always allow error recovery if only one among the sent qubits is disturbed in the transmitting channel. However, if two qubits and more are disturbed, then the correction will depend on the used code. We compare in this paper the three codes by computing the average fidelity between the sent secret and that measured by the receivers. We will treat the case where, at most, two qubits are affected in each one of five depolarizing channels.
基金J.P.is supported by the China Scholarship Council.M.G.is supported by National Natural Science Foundation of China(NSFC)(11947210)funded by China Postdoctoral Science Foundation(2019M660278)X.H.F.is supported by NSFC(11905157,11935009)。
文摘We calculate photon sphere r_(ph) and critical curve b_(c) for a quantum corrected Schwarzschild black hole,finding that they violate universal inequalities proved for asymptotically flat black holes that satisfy the null energy condition in the framework of Einstein gravity.This violation seems to be a common phenomenon when considering quantum modification of Einstein gravity.Furthermore,we study the shadows,lensing rings,and photon rings in the quantum corrected Schwarzschild black hole.The violation leads to a larger bright lensing ring in the observational appearance of the thin disk emission near the black hole compared with the classical Schwarzschild black hole.Our analysis may provide observational evidence for the quantum effect of general relativity.
基金Project supported by the Natural Science Foundation of Zhejiang Province,China (Grant No.LY14A030001)。
文摘We calculate the thermodynamic quantities in the quantum corrected Reissner-Nordstr?m-AdS(RN-AdS)black hole,and examine their quantum corrections.By analyzing the mass and heat capacity,we give the critical state and the remnant state,respectively,and discuss their consistency.Then,we investigate the quantum tunneling from the event horizon of massless scalar particle by using the null geodesic method,and charged massive boson W^(±)and fermions by using the Hamilton-Jacob method.It is shown that the same Hawking temperature can be obtained from these tunneling processes of different particles and methods.Next,by using the generalized uncertainty principle(GUP),we study the quantum corrections to the tunneling and the temperature.Then the logarithmic correction to the black hole entropy is obtained.
基金Supported by the National Natural Science Foundation of China(11903025)the Science and Technology Program of Sichuan Province,China(2023ZYD0023)+2 种基金the Youth Science and Technology Innovation Research Team of Sichuan Province,China(21CXTD0038)the Natural Science Foundation of Sichuan Province,China(2022NSFSC1833)by the Central Guidance on the Local Science and Technology Development Fund of SiChuan Province,China(24ZYZYTS0188)。
文摘By considering an asymmetric thin-shell wormhole(ATSW)surrounded by an optically and geometrically thin disk,we investigate the luminosity distribution of this ATSW with the spacetime on two sides encoded with the renormalization group improved(RGI)parameters(Ω,γ).Although some light rays are absorbed into the throat in the vicinity of the wormhole,they return through the throat with certain conditions,unlike in the case of black holes.The spacetime on one side of the wormhole can capture the additional photons emitted from the thin disk,resulting in several interesting observable features of the wormhole.The results in this paper show that there are two additional orbit numbers n in the ATSW and six transfer functions,rather than three as in the black hole case.In this case,the ATSW indeed has a more complex observable structure,where some additional light rings arise naturally.For instance,there are two additional photon rings for the emitted Model 1.Moreover,we also find a new wide hump between the first and second additional photon rings in Model 2.The effects of Ω and γ on the observed images are clearly addressed throughout this study,and the influence of Ω is found to be larger.Finally,we conclude that the observations of the RGI-ATSW can help further distinguish it from other ATSWs and black holes when a thin accretion disk exists around it.
基金funded by the National Natural Science Foundation of China under Grant No.11975145。
文摘In this work,we apply tunneling formalism to analyze charged particles tunneling across a hairy black hole horizon.Such black hole solutions are essential for frameworks based on Horndeski's gravity theory.Applying a semi-classical technique,we examine the tunneling of charged particles from a hairy black hole and derive the generic tunneling spectrum of released particles,ignoring self-gravitational and interaction.It is studied to ignore the back-reaction impact of the radiated particle on the hairy black hole.We analyze the properties of the black hole,such as temperature and entropy,under the influence of quantum gravity and also observe that the firstorder correction is present.We study tunneling radiation produced by a charged field equation in the presence of a generalized uncertainty effect.We modify the semi-classical technique by using the generalized uncertainty principle,the WKB approximation,and surface gravity.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11834010,11804001,and 11904160)the Natural Science Foundation of Anhui Province,China(Grant No.1808085QA11)+1 种基金the Program of Youth Sanjin Scholar,National Key R&D Program of China(Grant No.2016YFA0301402)the Fund for Shanxi"1331 Project"Key Subjects Construction.
文摘Measurement-based quantum computation with continuous variables,which realizes computation by performing measurement and feedforward of measurement results on a large scale Gaussian cluster state,provides a feasible way to implement quantum computation.Quantum error correction is an essential procedure to protect quantum information in quantum computation and quantum communication.In this review,we briefly introduce the progress of measurement-based quantum computation and quantum error correction with continuous variables based on Gaussian cluster states.We also discuss the challenges in the fault-tolerant measurement-based quantum computation with continuous variables.
文摘For applying the perfect code to transmit quantum information over a noise channel,the standard protocol contains four steps:the encoding,the noise channel,the error-correction operation,and the decoding.In present work,we show that this protocol can be simplified.The error-correction operation is not necessary if the decoding is realized by the so-called complete unitary transformation.We also offer a quantum circuit,which can correct the arbitrary single-qubit errors.
基金the National Natural Science Foundation of China(Grant Nos.11975132 and 61772295)the Natural Science Foundation of Shandong Province,China(Grant No.ZR2019YQ01)the Project of Shandong Province Higher Educational Science and Technology Program,China(Grant No.J18KZ012).
文摘Quantum error correction technology is an important solution to solve the noise interference generated during the operation of quantum computers.In order to find the best syndrome of the stabilizer code in quantum error correction,we need to find a fast and close to the optimal threshold decoder.In this work,we build a convolutional neural network(CNN)decoder to correct errors in the toric code based on the system research of machine learning.We analyze and optimize various conditions that affect CNN,and use the RestNet network architecture to reduce the running time.It is shortened by 30%-40%,and we finally design an optimized algorithm for CNN decoder.In this way,the threshold accuracy of the neural network decoder is made to reach 10.8%,which is closer to the optimal threshold of about 11%.The previous threshold of 8.9%-10.3%has been slightly improved,and there is no need to verify the basic noise.
基金Project supported by the National Natural Science Foundation of China(Grant No.61873251)。
文摘Quantum metrology provides a fundamental limit on the precision of multi-parameter estimation,called the Heisenberg limit,which has been achieved in noiseless quantum systems.However,for systems subject to noises,it is hard to achieve this limit since noises are inclined to destroy quantum coherence and entanglement.In this paper,a combined control scheme with feedback and quantum error correction(QEC)is proposed to achieve the Heisenberg limit in the presence of spontaneous emission,where the feedback control is used to protect a stabilizer code space containing an optimal probe state and an additional control is applied to eliminate the measurement incompatibility among three parameters.Although an ancilla system is necessary for the preparation of the optimal probe state,our scheme does not require the ancilla system to be noiseless.In addition,the control scheme in this paper has a low-dimensional code space.For the three components of a magnetic field,it can achieve the highest estimation precision with only a 2-dimensional code space,while at least a4-dimensional code space is required in the common optimal error correction protocols.
基金Project supported by the National Natural Science Foundation of China （Grant No 10504042）.Acknowledgments We would like to thank Liu Wei-Tao, Wu Wei and Gao Ming for useful discussions.
文摘The loss of a quantum channel leads to an irretrievable particle loss as well as information. In this paper, the loss of quantum channel is analysed and a method is put forward to recover the particle and information loss effectively using universal quantum error correction. Then a secure direct communication scheme is proposed, such that in a loss channel the information that an eavesdropper can obtain would be limited to arbitrarily small when the code is properly chosen and the correction operation is properly arranged.
文摘The present study delves into the application of investigating quantum state behaviour,particularly focusing on coherent and superposition states.These states,characterized by their remarkable stability and precision,have found extensive utility in various domains of quantum mechanics and quantum information processing.Coherent states are valuable for manipulating quantum systems with accuracy.Superposition states allow quantum systems to exist in numerous configurations at the same time,which paves the way for quantum computing’s capacity for parallel processing.The research accentuates the crucial role of quantum error correction(QEC)in ensuring the stability and reliability of quantum information processing systems.Quantum systems are prone to errors from decoherence and environmental noise,making QEC essential for ensuring accurate results by employing the Shor code,an error-correcting code devised by Peter Shor,it becomes feasible to detect and rectify errors that may arise during quantum computations.The Shor code detects and corrects both bit-flip and phase-flip errors,greatly enhancing the robustness of quantum information systems.This research offers insights into the multifaceted utility of MZI(Mach-Zehnder interferometer)and its relevance in the advancement of quantum technology.By integrating QEC with the capabilities of MZI,this study offers a holistic approach to advancing the precision and reliability of quantum technologies.
基金supported by the National Natural Science Foundation of China(Grant Nos.62371240,61802175,62401266,and 12201300)the National Key R&D Program of China(Grant No.2022YFB3103800)+2 种基金the Natural Science Foundation of Jiangsu Province(Grant No.BK20241452)the Fundamental Research Funds for the Central Universities(Grant No.30923011014)the fund of Laboratory for Advanced Computing and Intelligence Engineering(Grant No.2023-LYJJ-01-009)。
文摘To improve the decoding performance of quantum error-correcting codes in asymmetric noise channels,a neural network-based decoding algorithm for bias-tailored quantum codes is proposed.The algorithm consists of a biased noise model,a neural belief propagation decoder,a convolutional optimization layer,and a multi-objective loss function.The biased noise model simulates asymmetric error generation,providing a training dataset for decoding.The neural network,leveraging dynamic weight learning and a multi-objective loss function,mitigates error degeneracy.Additionally,the convolutional optimization layer enhances early-stage convergence efficiency.Numerical results show that for bias-tailored quantum codes,our decoder performs much better than the belief propagation(BP)with ordered statistics decoding(BP+OSD).Our decoder achieves an order of magnitude improvement in the error suppression compared to higher-order BP+OSD.Furthermore,the decoding threshold of our decoder for surface codes reaches a high threshold of 20%.
基金Project supported by the Natural Science Foundation of Shandong Province,China(Grant No.ZR2021MF049)the Joint Fund of the Natural Science Foundation of Shandong Province,China(Grant Nos.ZR2022LLZ012 and ZR2021LLZ001)the Key Research and Development Program of Shandong Province,China(Grant No.2023CXGC010901)。
文摘Quantum error-correcting codes are essential for fault-tolerant quantum computing,as they effectively detect and correct noise-induced errors by distributing information across multiple physical qubits.The subsystem surface code with three-qubit check operators demonstrates significant application potential due to its simplified measurement operations and low logical error rates.However,the existing minimum-weight perfect matching(MWPM)algorithm exhibits high computational complexity and lacks flexibility in large-scale systems.Therefore,this paper proposes a decoder based on a graph attention network(GAT),representing error syndromes as undirected graphs with edge weights,and employing a multihead attention mechanism to efficiently aggregate node features and enable parallel computation.Compared to MWPM,the GAT decoder exhibits linear growth in computational complexity,adapts to different quantum code structures,and demonstrates stronger robustness under high physical error rates.The experimental results demonstrate that the proposed decoder achieves an overall accuracy of 89.95%under various small code lattice sizes(L=2,3,4,5),with the logical error rate threshold increasing to 0.0078,representing an improvement of approximately 13.04%compared to the MWPM decoder.This result significantly outperforms traditional methods,showcasing superior performance under small code lattice sizes and providing a more efficient decoding solution for large-scale quantum error correction.
基金supported by the Science and Technology Commission of Shanghai Municipality(Grant No.24DP2600202)the National Key R&D Program of China(Grant No.2024YFB4504002)the National Natural Science Foundation of China(Grant No.92165107)。
文摘For the quantum error correction and noisy intermediate-scale quantum algorithms to function with high efficiency,the raw fidelity of quantum logic gates on physical qubits needs to satisfy strict requirements.The neutral atom quantum computing equipped with Rydberg blockade gates has made impressive progress recently,which makes it worthwhile to explore its potential in the two-qubit entangling gates,including the controlledphase gate,and in particular,the CZ gate.Provided the quantum coherence is well preserved,improving the fidelity of Rydberg blockade gates calls for special mechanisms to deal with adverse effects caused by realistic experimental conditions.Here,the heralded very-high-fidelity Rydberg blockade controlled-phase gate is designed to address these issues,which contains self-correction and projection as the key steps.This trailblazing method builds upon the previously established buffer-atom-mediated gate framework,with a special form of symmetry under parity–time transformation playing a crucial role in the process.We further analyze the performance with respect to a few typical sources of imperfections.This procedure can also be regarded as quantum hardware error correction or mitigation.While this paper by itself does not cover every single subtle issue and still contains many oversimplifications,we find it reasonable to anticipate a very-high-fidelity two-qubit quantum logic gate operated in the sense of heralded but probabilistic,whose gate error can be reduced to the level of 10^(-4)–10^(-6)or even lower with reasonably high possibilities.
