Browsing by Author "Lai, Ching-Yi"

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A Complete MacWilliams Theorem for Convolutional Codes
(2014-01-01)
Lai, Ching-Yi
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Hsieh, Min-Hsiu
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Lu, Hsiao-feng
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電機工程學系
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Department of Electrical and Computer Engineering
In this paper, we prove a MacWilliams identity for the weight adjacency matrices based on the constraint codes of a convolutional code (CC) and its dual. Our result improves upon a recent result by Gluesing-Luerssen and Schneider, where the requirement of a minimal encoder is assumed. We can also establish the MacWilliams identity for the input-parity weight adjacency matrices of a systematic CC and its dual. Most importantly, we show that a type of Hamming weight enumeration functions of all codewords of a CC can be derived from the weight adjacency matrix, which thus provides a connection between these two very different notions of weight enumeration functions in the convolutional code literature. Finally, the relations between various enumeration functions of a CC and its dual are summarized in a diagram. This explains why no MacWilliams identity exists for the free-distance enumerators.
Carrying an arbitrarily large amount of information using a single quantum particle
(2020-08-25)
Hsu, Li-Yi
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Lai, Ching-Yi
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Chang, You-Chia
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Wu, Chien-Ming
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Lee, Ray-Kuang
Theoretically speaking, a photon can travel arbitrarily long before it enters into a detector, resulting in a click. How much information can a photon carry? We study a bipartite asymmetric "two-way signaling" protocol as an extension of that proposed by Del Santo and Dakic. Suppose that Alice and Bob are distant from each other and each of them has an n-bit string. They are tasked to exchange the information of their local n-bit strings with each other, using only a single photon during the communication. It has been shown that the superposition of different spatial locations in a Mach-Zehnder (MZ) interferometer enables bipartite local encodings. We show that, after the travel of a photon through a cascade of n-level MZ interferometers in our protocol, the one of Alice and Bob whose detector clicks can access the other's full information of the n-bit string, while the other can gain one bit of information. That is, the wave-particle duality makes two-way signaling possible, and a single photon can carry an arbitrarily large (but finite) amount of information.
Constant depth fault-tolerant Clifford circuits for multi-qubit large block codes
(2020-10-01)
Zheng, Yi-Cong
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Lai, Ching-Yi
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Brun, Todd A.
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Kwek, Leong-Chuan
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電信工程研究所
Fault-tolerant quantum computation (FTQC) schemes using large block codes that encodek> 1 qubits innphysical qubits can potentially reduce the resource overhead to a great extent because of their high encoding rate. However, the fault-tolerant (FT) logical operations for the encoded qubits are difficult to find and implement, which usually takes not only a very large resource overhead but also longin situcomputation time. In this paper, we focus on Calderbank-Shor-Steane [[n,k,d]] (CSS) codes and their logical FT Clifford circuits. We show that the depth of an arbitrary logical Clifford circuit can be implemented fault-tolerantly inO(1) stepsin situvia either Knill or Steane syndrome measurement circuit, with the qualified ancilla states efficiently prepared. Particularly, for those codes satisfyingk/n similar to Theta(1), the resource scaling for Clifford circuits implementation on the logical level can be the same as on the physical level up to a constant, which is independent of code distanced. With a suitable pipeline to produce ancilla states, our scheme requires only a modest resource cost in physical qubits, physical gates, and computation time for very large scale FTQC.
Interactive Leakage Chain Rule for Quantum Min-entropy
(2019-01-01)
Lai, Ching-Yi
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Chung, Kai-Min
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電信工程研究所
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Institute of Communications Engineering
The leakage chain rule for quantum min-entropy quantifies the change of min-entropy when one party gets additional leakage about the information source. Herein we provide an interactive version that quantifies the change of min-entropy between two parties, who share an initial classical-quantum state and are allowed to run a two-party protocol. As an application, we prove new versions of lower bounds on the complexity of quantum communication of classical information.
ON STATISTICALLY-SECURE QUANTUM HOMOMORPHIC ENCRYPTION
(2018-08-01)
Lai, Ching-Yi
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Chung, Kai-Min
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電信工程研究所
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Institute of Communications Engineering
Homomorphic encryption is an encryption scheme that allows computations to be evaluated on encrypted inputs without knowledge of their raw messages. Recently Ouyang et al. constructed a quantum homomorphic encryption (QHE) scheme for Clifford circuits with statistical security (or information-theoretic security (IT-security)). It is desired to see whether an information-theoretically-secure (ITS) quantum FHE exists. If not, what other nontrivial class of quantum circuits can be homomorphically evaluated with IT-security? We provide a limitation for the first question that an ITS quantum FHE necessarily incurs exponential overhead. As for the second one, we propose a QHE scheme for the instantaneous quantum polynomial-time (IQP) circuits. Our QHE scheme for IQP circuits follows from the one-time pad.
On the MacWilliams Identity for Classical and Quantum Convolutional Codes
(2016-08)
Lai, Ching-Yi
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Hsieh, Min-Hsiu
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Lu, Hsiao-Feng
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電機學院
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College of Electrical and Computer Engineering
The weight generating functions associated with convolutional codes (CCs) are based on state space realizations or the weight adjacency matrices (WAMs). The MacWilliams identity for CCs on the WAMs was first established by Gluesing-Luerssen and Schneider in the case of minimal encoders, and generalized by Forney. We consider this problem in the viewpoint of constraint codes and obtain a simple and direct proof of this MacWilliams identity in the case of minimal encoders. For our purpose, we choose a different representation for the exact weight generating function (EWGF) of a block code, by defining it as a linear combination of orthonormal vectors in Dirac bra-ket notation. This representation provides great flexibility so that general split weight generating functions and their MacWilliams identities can be easily obtained from the MacWilliams identity for EWGFs. As a result, we also obtain the MacWilliams identity for the input-parity WAMs of a systematic convolutional code and its dual. Finally, paralleling the development of the classical case, we establish the MacWilliams identity for quantum CCs.
Quantum Data-Syndrome Codes
(2020-03-01)
Ashikhmin, Alexei
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Lai, Ching-Yi
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Brun, Todd A.
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傳播研究所
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Institute of Communication Studies
Performing active quantum error correction to protect fragile quantum states highly depends on the correctness of measured error syndromes. To obtain reliable error syndromes using imperfect physical circuits, we propose syndrome measurement (SM) and quantum data-syndrome (DS) codes. SM codes protect syndrome with linearly dependent redundant stabilizer measurements. DS codes generalize this idea for simultaneous correction of both data qubits and syndrome bits errors. We study fundamental properties of quantum DS codes, including split weight enumerators, generalized MacWilliams identities, and linear programming bounds. In particular, we derive Singleton and Hamming-type upper bounds on the minimum distance of degenerate quantum DS codes. Then we study random DS codes and show that random DS codes with a relatively small additional syndrome measurements achieve the Gilbert-Varshamov bound of stabilizer codes. Finally, we propose a family of CSS-type quantum DS codes based on classical cyclic codes, which include the Steane code and the quantum Golay code.
The Encoding and Decoding Complexities of Entanglement-Assisted Quantum Stabilizer Codes
(2019-01-01)
Kuo, Kao-Yueh
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Lai, Ching-Yi
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電信工程研究所
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Institute of Communications Engineering
Quantum error-correcting codes are used to protect quantum information from decoherence. A raw state is mapped, by an encoding circuit, to a codeword so that the most likely quantum errors from a noisy quantum channel can be removed after a decoding process. A good encoding circuit should have some desired features, such as low depth, few gates, and so on. In this paper, we show how to practically implement an encoding circuit of gate complexity O(n(n - k + c)/ log n) for an [[n, k; c]] quantum stabilizer code with the help of c pairs of maximally-entangled states. For the special case of an [[n, k]] stabilizer code with c = 0, the encoding complexity is O(n(n - k)= log n), which is previously known to be O(n(2) / log n). For c > 0; this suggests that the benefits from shared entanglement come at an additional cost of encoding complexity. Finally we discuss decoding of entanglement-assisted quantum stabilizer codes and extend previously known computational hardness results on decoding quantum stabilizer codes.