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Search Results: 1 - 10 of 1150 matches for " Yuichiro Fujiwara "
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Parsing a sequence of qubits
Yuichiro Fujiwara
Mathematics , 2012, DOI: 10.1109/TIT.2013.2272695
Abstract: We develop a theoretical framework for frame synchronization, also known as block synchronization, in the quantum domain which makes it possible to attach classical and quantum metadata to quantum information over a noisy channel even when the information source and sink are frame-wise asynchronous. This eliminates the need of frame synchronization at the hardware level and allows for parsing qubit sequences during quantum information processing. Our framework exploits binary constant-weight codes that are self-synchronizing. Possible applications may include asynchronous quantum communication such as a self-synchronizing quantum network where one can hop into the channel at any time, catch the next coming quantum information with a label indicating the sender, and reply by routing her quantum information with control qubits for quantum switches all without assuming prior frame synchronization between users.
Even-freeness of cyclic 2-designs
Yuichiro Fujiwara
Mathematics , 2012,
Abstract: A Steiner 2-design of block size k is an ordered pair (V, B) of finite sets such that B is a family of k-subsets of V in which each pair of elements of V appears exactly once. A Steiner 2-design is said to be r-even-free if for every positive integer i =< r it contains no set of i elements of B in which each element of V appears exactly even times. We study the even-freeness of a Steiner 2-design when the cyclic group acts regularly on V. We prove the existence of infinitely many nontrivial Steiner 2-designs of large block size which have the cyclic automorphisms and higher even-freeness than the trivial lower bound but are not the points and lines of projective geometry.
Self-synchronizing pulse position modulation with error tolerance
Yuichiro Fujiwara
Mathematics , 2013, DOI: 10.1109/TIT.2013.2262094
Abstract: Pulse position modulation (PPM) is a popular signal modulation technique which creates M-ary data by means of the position of a pulse within a time interval. While PPM and its variations have great advantages in many contexts, this type of modulation is vulnerable to loss of synchronization, potentially causing a severe error floor or throughput penalty even when little or no noise is assumed. Another disadvantage is that this type of modulation typically offers no error correction mechanism on its own, making them sensitive to intersymbol interference and environmental noise. In this paper we propose a coding theoretic variation of PPM that allows for significantly more efficient symbol and frame synchronization as well as strong error correction. The proposed scheme can be divided into a synchronization layer and a modulation layer. This makes our technique compatible with major existing techniques such as standard PPM, multipluse PPM, and expurgated PPM as well in that the scheme can be realized by adding a simple synchronization layer to one of these standard techniques. We also develop a generalization of expurgated PPM suited for the modulation layer of the proposed self-synchronizing modulation scheme. This generalized PPM can also be used as stand-alone error-correcting PPM with a larger number of available symbols.
Using arbitrary parity-check matrices for quantum error correction assisted by less noisy qubits
Yuichiro Fujiwara
Mathematics , 2014,
Abstract: Recently a framework for assisted quantum error correction was proposed in which a specific type of error is allowed to occur on auxiliary qubits, which is in contrast to standard entanglement assistance that requires noiseless auxiliary qubits. However, while the framework maintains the ability to import any binary or quaternary linear code without sacrificing active error correction power, it requires the code designer to turn a parity-check matrix of the underlying classical code into an equivalent one in standard form. This means that classical coding theoretic techniques that require parity-check matrices to be in specific form may not fully be exploitable. Another issue of the recently proposed scheme is that the error correction capabilities for bit errors and phase errors are generally equal, which is not ideal for asymmetric error models. This paper addresses these two problems. We generalize the framework in such a way that any parity-check matrix of any binary or quaternary linear code can be exploited. Our generalization also allows for importing a pair of distinct linear codes so that error correction capabilities become suitably asymmetric.
Ability of stabilizer quantum error correction to protect itself from its own imperfection
Yuichiro Fujiwara
Mathematics , 2014, DOI: 10.1103/PhysRevA.90.062304
Abstract: The theory of stabilizer quantum error correction allows us to actively stabilize quantum states and simulate ideal quantum operations in a noisy environment. It is critical is to correctly diagnose noise from its syndrome and nullify it accordingly. However, hardware that performs quantum error correction itself is inevitably imperfect in practice. Here, we show that stabilizer codes possess a built-in capability of correcting errors not only on quantum information but also on faulty syndromes extracted by themselves. Shor's syndrome extraction for fault-tolerant quantum computation is naturally improved. This opens a path to realizing the potential of stabilizer quantum error correction hidden within an innocent looking choice of generators and stabilizer operators that have been deemed redundant.
Instantaneous Quantum Channel Estimation during Quantum Information Processing
Yuichiro Fujiwara
Mathematics , 2014,
Abstract: We present a nonintrusive method for reliably estimating the noise level during quantum computation and quantum communication protected by quantum error-correcting codes. As preprocessing of quantum error correction, our scheme estimates the current noise level through a negligible amount of classical computation using error syndromes and updates the decoder's knowledge on the spot before inferring the locations of errors. This preprocessing requires no additional quantum interaction or modification in the system. The estimate can be of higher quality than the maximum likelihood estimate based on perfect knowledge of channel parameters, thereby eliminating the need of the unrealistic assumption that the decoder accurately knows channel parameters a priori. Simulations demonstrate that not only can the decoder pick up on a change of channel parameters, but even if the channel stays the same, a quantum low-density parity-check code can perform better when the decoder exploits the on-the-spot estimates instead of the true error probabilities of the quantum channel.
Block synchronization for quantum information
Yuichiro Fujiwara
Mathematics , 2012, DOI: 10.1103/PhysRevA.87.022344
Abstract: Locating the boundaries of consecutive blocks of quantum information is a fundamental building block for advanced quantum computation and quantum communication systems. We develop a coding theoretic method for properly locating boundaries of quantum information without relying on external synchronization when block synchronization is lost. The method also protects qubits from decoherence in a manner similar to conventional quantum error-correcting codes, seamlessly achieving synchronization recovery and error correction. A family of quantum codes that are simultaneously synchronizable and error-correcting is given through this approach.
Quantum synchronizable codes from finite geometries
Yuichiro Fujiwara,Peter Vandendriessche
Computer Science , 2013, DOI: 10.1109/TIT.2014.2357029
Abstract: Quantum synchronizable error-correcting codes are special quantum error-correcting codes that are designed to correct both the effect of quantum noise on qubits and misalignment in block synchronization. It is known that in principle such a code can be constructed through a combination of a classical linear code and its subcode if the two are both cyclic and dual-containing. However, finding such classical codes that lead to promising quantum synchronizable error-correcting codes is not a trivial task. In fact, although there are two families of classical codes that are proved to produce quantum synchronizable codes with good minimum distances and highest possible tolerance against misalignment, their code lengths have been restricted to primes and Mersenne numbers. In this paper, examining the incidence vectors of projective spaces over the finite fields of characteristic $2$, we give quantum synchronizable codes from cyclic codes whose lengths are not primes or Mersenne numbers. These projective geometric codes achieve good performance in quantum error correction and possess the best possible ability to recover synchronization, thereby enriching the variety of good quantum synchronizable codes. We also extend the current knowledge of cyclic codes in classical coding theory by explicitly giving generator polynomials of the finite geometric codes and completely characterizing the minimum weight nonzero codewords. In addition to the codes based on projective spaces, we carry out a similar analysis on the well-known cyclic codes from Euclidean spaces that are known to be majority logic decodable and determine their exact minimum distances.
A characterization of entanglement-assisted quantum low-density parity-check codes
Yuichiro Fujiwara,Vladimir D. Tonchev
Mathematics , 2011, DOI: 10.1109/TIT.2013.2247461
Abstract: As in classical coding theory, quantum analogues of low-density parity-check (LDPC) codes have offered good error correction performance and low decoding complexity by employing the Calderbank-Shor-Steane (CSS) construction. However, special requirements in the quantum setting severely limit the structures such quantum codes can have. While the entanglement-assisted stabilizer formalism overcomes this limitation by exploiting maximally entangled states (ebits), excessive reliance on ebits is a substantial obstacle to implementation. This paper gives necessary and sufficient conditions for the existence of quantum LDPC codes which are obtainable from pairs of identical LDPC codes and consume only one ebit, and studies the spectrum of attainable code parameters.
High-rate self-synchronizing codes
Yuichiro Fujiwara,Vladimir D. Tonchev
Mathematics , 2012, DOI: 10.1109/TIT.2012.2234501
Abstract: Self-synchronization under the presence of additive noise can be achieved by allocating a certain number of bits of each codeword as markers for synchronization. Difference systems of sets are combinatorial designs which specify the positions of synchronization markers in codewords in such a way that the resulting error-tolerant self-synchronizing codes may be realized as cosets of linear codes. Ideally, difference systems of sets should sacrifice as few bits as possible for a given code length, alphabet size, and error-tolerance capability. However, it seems difficult to attain optimality with respect to known bounds when the noise level is relatively low. In fact, the majority of known optimal difference systems of sets are for exceptionally noisy channels, requiring a substantial amount of bits for synchronization. To address this problem, we present constructions for difference systems of sets that allow for higher information rates while sacrificing optimality to only a small extent. Our constructions utilize optimal difference systems of sets as ingredients and, when applied carefully, generate asymptotically optimal ones with higher information rates. We also give direct constructions for optimal difference systems of sets with high information rates and error-tolerance that generate binary and ternary self-synchronizing codes.
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