We investigate the quantum speed limit time （QSLT） of a two-level atom under quantum-jump-based feedback control or homodyne-based feedback control. Our results show that the two different feedback control schemes h...We investigate the quantum speed limit time （QSLT） of a two-level atom under quantum-jump-based feedback control or homodyne-based feedback control. Our results show that the two different feedback control schemes have different influences on the evolutionary speed. By adjusting the feedback parameters, the quantum-jump-based feedback control can induce speedup of the atomic evolution from an excited state, but the homodyne-based feedback control cannot change the evolutionary speed. Additionally, the QSLT for the whole dynamical process is explored. Under the quantum-jump-based feedback control, the QSLT displays oscillatory behaviors, which implies multiple speed-up and speed-down processes during the evolution. While, the homodyne-based feedback control can accelerate the speed-up process and improve the uniform speed in the uniform evolution process.展开更多
We present a comprehensive mathematical framework establishing the foundations of holographic quantum computing, a novel paradigm that leverages holographic phenomena to achieve superior error correction and algorithm...We present a comprehensive mathematical framework establishing the foundations of holographic quantum computing, a novel paradigm that leverages holographic phenomena to achieve superior error correction and algorithmic efficiency. We rigorously demonstrate that quantum information can be encoded and processed using holographic principles, establishing fundamental theorems characterizing the error-correcting properties of holographic codes. We develop a complete set of universal quantum gates with explicit constructions and prove exponential speedups for specific classes of computational problems. Our framework demonstrates that holographic quantum codes achieve a code rate scaling as O(1/logn), superior to traditional quantum LDPC codes, while providing inherent protection against errors via geometric properties of the code structures. We prove a threshold theorem establishing that arbitrary quantum computations can be performed reliably when physical error rates fall below a constant threshold. Notably, our analysis suggests certain algorithms, including those involving high-dimensional state spaces and long-range interactions, achieve exponential speedups over both classical and conventional quantum approaches. This work establishes the theoretical foundations for a new approach to quantum computation that provides natural fault tolerance and scalability, directly addressing longstanding challenges of the field.展开更多
Quantum image processing has long been a fascinating field,but establishing the existence of quantum speedup for all images remains challenging.In this study,we aim to identify a subset of images for which a quantum a...Quantum image processing has long been a fascinating field,but establishing the existence of quantum speedup for all images remains challenging.In this study,we aim to identify a subset of images for which a quantum algorithm can be developed with a guaranteed advantage.Specifically,we present a quantum image filtering algorithm that exhibits an exponential speedup for efficiently encoded images with a lower-bounded signal-to-noise ratio.Our approach relies on a fixed-point Grover's search to emulate the effect of Hadamard multiplication with the filtering function.To demonstrate its effectiveness,we apply our method to three typical filtering problems.Additionally,we emphasize the significance of the efficient-encoding assumption by illustrating that the quantum speedup may diminish for images lacking efficient encoding.Our work underscores the importance of exploring image types and features to realize potential quantum advantages in image processing.展开更多
The role the quantum entanglement plays in quantum computation speedup has been widely disputed. Some believe that quantum computation's speedup over classical computation is impossible if entan-glement is absent,...The role the quantum entanglement plays in quantum computation speedup has been widely disputed. Some believe that quantum computation's speedup over classical computation is impossible if entan-glement is absent,while others claim that the presence of entanglement is not a necessary condition for some quantum algorithms. This paper discusses this problem systematically. Simulating quantum computation with classical resources is analyzed and entanglement in known algorithms is reviewed. It is concluded that the presence of entanglement is a necessary but not sufficient condition in the pure state or pseudo-pure state quantum computation speedup. The case with the mixed state remains open. Further work on quantum computation will benefit from the presented results.展开更多
The interference has been measured by the visibility in two-level systems, which, however, does not work for multi-level systems. We generalize a measure of the interference based on decoherence process, consistent wi...The interference has been measured by the visibility in two-level systems, which, however, does not work for multi-level systems. We generalize a measure of the interference based on decoherence process, consistent with the visibility in qubit systems. By taking duster states as examples, we show in the one-way quantum computation that the gate fidelity is proportional to the interference of the measured qubit and is inversely proportional to the interference of all register qubits. We also find that the interference increases with the number of the computing steps. So we conjecture that the interference may be the source of the speedup of the one-way quantum computation.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant No.11374096)Hunan Provincial Innovation Foundation for Postgraduate,China(Grant No.CX2017B177)the Scientific Research Project of Hunan Provincial Education Department,China(Grant No.16C0949)
文摘We investigate the quantum speed limit time （QSLT） of a two-level atom under quantum-jump-based feedback control or homodyne-based feedback control. Our results show that the two different feedback control schemes have different influences on the evolutionary speed. By adjusting the feedback parameters, the quantum-jump-based feedback control can induce speedup of the atomic evolution from an excited state, but the homodyne-based feedback control cannot change the evolutionary speed. Additionally, the QSLT for the whole dynamical process is explored. Under the quantum-jump-based feedback control, the QSLT displays oscillatory behaviors, which implies multiple speed-up and speed-down processes during the evolution. While, the homodyne-based feedback control can accelerate the speed-up process and improve the uniform speed in the uniform evolution process.
文摘We present a comprehensive mathematical framework establishing the foundations of holographic quantum computing, a novel paradigm that leverages holographic phenomena to achieve superior error correction and algorithmic efficiency. We rigorously demonstrate that quantum information can be encoded and processed using holographic principles, establishing fundamental theorems characterizing the error-correcting properties of holographic codes. We develop a complete set of universal quantum gates with explicit constructions and prove exponential speedups for specific classes of computational problems. Our framework demonstrates that holographic quantum codes achieve a code rate scaling as O(1/logn), superior to traditional quantum LDPC codes, while providing inherent protection against errors via geometric properties of the code structures. We prove a threshold theorem establishing that arbitrary quantum computations can be performed reliably when physical error rates fall below a constant threshold. Notably, our analysis suggests certain algorithms, including those involving high-dimensional state spaces and long-range interactions, achieve exponential speedups over both classical and conventional quantum approaches. This work establishes the theoretical foundations for a new approach to quantum computation that provides natural fault tolerance and scalability, directly addressing longstanding challenges of the field.
基金supported by the National Natural Science Foundation of China(Grant No.92265208)the National Key R&D Program of China(Grant No.2018YFA0306703)startup funding supported by the University of Massachusetts,Boston。
文摘Quantum image processing has long been a fascinating field,but establishing the existence of quantum speedup for all images remains challenging.In this study,we aim to identify a subset of images for which a quantum algorithm can be developed with a guaranteed advantage.Specifically,we present a quantum image filtering algorithm that exhibits an exponential speedup for efficiently encoded images with a lower-bounded signal-to-noise ratio.Our approach relies on a fixed-point Grover's search to emulate the effect of Hadamard multiplication with the filtering function.To demonstrate its effectiveness,we apply our method to three typical filtering problems.Additionally,we emphasize the significance of the efficient-encoding assumption by illustrating that the quantum speedup may diminish for images lacking efficient encoding.Our work underscores the importance of exploring image types and features to realize potential quantum advantages in image processing.
基金Supported by the National Natural Science Foundation for Distinguished Young Scholars of China (Grant No. 60625204)the Key Project of the National Natural Science Foundation of China (Grant No. 60496324)+2 种基金the National 973 Fundamental Research and Development Program of China (Grant No. 2002CB312004)the National 863 High-Tech Project of China (Grant No. 2006AA01Z155)the Knowledge Innovation Program of the Chinese Academy of Sciences and MADIS
文摘The role the quantum entanglement plays in quantum computation speedup has been widely disputed. Some believe that quantum computation's speedup over classical computation is impossible if entan-glement is absent,while others claim that the presence of entanglement is not a necessary condition for some quantum algorithms. This paper discusses this problem systematically. Simulating quantum computation with classical resources is analyzed and entanglement in known algorithms is reviewed. It is concluded that the presence of entanglement is a necessary but not sufficient condition in the pure state or pseudo-pure state quantum computation speedup. The case with the mixed state remains open. Further work on quantum computation will benefit from the presented results.
文摘The interference has been measured by the visibility in two-level systems, which, however, does not work for multi-level systems. We generalize a measure of the interference based on decoherence process, consistent with the visibility in qubit systems. By taking duster states as examples, we show in the one-way quantum computation that the gate fidelity is proportional to the interference of the measured qubit and is inversely proportional to the interference of all register qubits. We also find that the interference increases with the number of the computing steps. So we conjecture that the interference may be the source of the speedup of the one-way quantum computation.
