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On universal and faulttolerant quantum computing: a novel basis and a new constructive proof of universality for Shor’s basis
 In Proceedings of the 40th Annual Symposium on Foundations of Computer Science
, 1999
"... A novel universal and faulttolerant basis (set of gates) for quantum computation is described. Such a set is necessary to perform quantum computation in a realistic noisy environment. The new basis consists of two singlequbit gates 1 (Hadamard and σz 4), and one doublequbit gate (ControlledNOT). ..."
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Cited by 39 (3 self)
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A novel universal and faulttolerant basis (set of gates) for quantum computation is described. Such a set is necessary to perform quantum computation in a realistic noisy environment. The new basis consists of two singlequbit gates 1 (Hadamard and σz 4), and one doublequbit gate (ControlledNOT). Since the set consisting of ControlledNOT and Hadamard gates is not universal, the new basis achieves universality by including only one additional elementary (in the sense that it does not include angles that are irrational multiples of π) singlequbit gate, and hence, is potentially the simplest universal basis that one can construct. We also provide an alternative proof of universality for the only other known class of universal and faulttolerant basis proposed in [25, 17]. 1
Enlargement of CalderbankShorSteane quantum codes
, 1999
"... It is shown that a classical error correcting code C = [n,k,d] which contains its dual, C ⊥ ⊆ C, and which can be enlarged to C ′ = [n,k ′> k + 1,d ′], can be converted into a quantum code of parameters [[n,k + k ′ − n,min(d, ⌈3d ′ /2⌉)]]. This is a generalisation of a previous construction, it ..."
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Cited by 34 (2 self)
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It is shown that a classical error correcting code C = [n,k,d] which contains its dual, C ⊥ ⊆ C, and which can be enlarged to C ′ = [n,k ′> k + 1,d ′], can be converted into a quantum code of parameters [[n,k + k ′ − n,min(d, ⌈3d ′ /2⌉)]]. This is a generalisation of a previous construction, it enables many new codes of good efficiency to be discovered. Examples based on classical Bose Chaudhuri Hocquenghem (BCH) codes are discussed.
On optimal quantum codes
 Int. J. Quantum Inform
, 2004
"... We present families of quantum errorcorrecting codes which are optimal in the sense that the minimum distance is maximal. These maximum distance separable (MDS) codes are defined over qdimensional quantum systems, where q is an arbitrary prime power. ..."
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Cited by 33 (3 self)
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We present families of quantum errorcorrecting codes which are optimal in the sense that the minimum distance is maximal. These maximum distance separable (MDS) codes are defined over qdimensional quantum systems, where q is an arbitrary prime power.
An evaluation framework and instruction set architecture for iontrap based quantum microarchitectures
 In Proc. 32nd Annual International Symposium on Computer Architecture
, 2005
"... The theoretical study of quantum computation has yielded efficient algorithms for some traditionally hard problems. Correspondingly, experimental work on the underlying physical implementation technology has progressed steadily. However, almost no work has yet been done which explores the architectu ..."
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Cited by 30 (1 self)
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The theoretical study of quantum computation has yielded efficient algorithms for some traditionally hard problems. Correspondingly, experimental work on the underlying physical implementation technology has progressed steadily. However, almost no work has yet been done which explores the architecture design space of large scale quantum computing systems. In this paper, we present a set of tools that enable the quantitative evaluation of architectures for quantum computers. The infrastructure we created comprises a complete compilation and simulation system for computers containing thousands of quantum bits. We begin by compiling complete algorithms into a quantum instruction set. This ISA enables the simple manipulation of quantum state. Another tool we developed automatically transforms quantum software into an equivalent, faulttolerant version required to operate on real quantum devices. Next, our infrastructure transforms the ISA into a set of lowlevel micro architecture specific control operations. In the future, these operations can be used to directly control a quantum computer. For now, our simulation framework quickly uses them to determine the reliability of the application for the target micro architecture. Finally, we propose a simple, regular architecture for iontrap based quantum computers. Using our software infrastructure, we evaluate the design trade offs of this micro architecture. 1
A Quantum Logic Array Microarchitecture: Scalable Quantum Data Movement and Computation
 Proceedings of the 38th International Symposium on Microarchitecture MICRO38
, 2005
"... Recent experimental advances have demonstrated technologies capable of supporting scalable quantum computation. A critical next step is how to put those technologies together into a scalable, faulttolerant system that is also feasible. We propose a Quantum Logic Array (QLA) microarchitecture that f ..."
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Cited by 29 (3 self)
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Recent experimental advances have demonstrated technologies capable of supporting scalable quantum computation. A critical next step is how to put those technologies together into a scalable, faulttolerant system that is also feasible. We propose a Quantum Logic Array (QLA) microarchitecture that forms the foundation of such a system. The QLA focuses on the communication resources necessary to efficiently support faulttolerant computations. We leverage the extensive groundwork in quantum error correction theory and provide analysis that shows that our system is both asymptotically and empirically fault tolerant. Specifically, we use the QLA to implement a hierarchical, arraybased design and a logarithmic expense quantumteleportation communication protocol. Our goal is to overcome the primary scalability challenges of reliability, communication, and quantum resource distribution that plague current proposals for largescale quantum computing. Our work complements recent work by Balenseifer et al [1], which studies the software tool chain necessary to simplify development of quantum applications; here we focus on modeling a fullscale optimized microarchitecture for scalable computing. 1.
Efficient faulttolerant quantum computing
 Nature
, 1999
"... Fault tolerant quantum computing methods which work with efficient quantum error correcting codes are discussed. Several new techniques are introduced to restrict accumulation of errors before or during the recovery. Classes of eligible quantum codes are obtained, and good candidates exhibited. This ..."
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Cited by 26 (4 self)
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Fault tolerant quantum computing methods which work with efficient quantum error correcting codes are discussed. Several new techniques are introduced to restrict accumulation of errors before or during the recovery. Classes of eligible quantum codes are obtained, and good candidates exhibited. This permits a new analysis of the permissible error rates and minimum overheads for robust quantum computing. It is found that, under the standard noise model of ubiquitous stochastic, uncorrelated errors, a quantum computer need be only an order of magnitude larger than the logical machine contained within it in order to be reliable. For example, a scaleup by a factor of 22, with gate error rate of order 10 −5, is sufficient to permit large quantum algorithms such as factorization of thousanddigit numbers.
Convolutional and tailbiting quantum errorcorrecting codes
 IEEE Trans. Inform. Theory
, 2007
"... Rate(n–2)/n unrestricted and CSStype quantum convolutional codes with up to 4096 states and minimum distances up to 10 are constructed as stabilizer codes from classical selforthogonal rate1/n F4linear and binary linear convolutional codes, respectively. These codes generally have higher rate a ..."
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Cited by 23 (4 self)
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Rate(n–2)/n unrestricted and CSStype quantum convolutional codes with up to 4096 states and minimum distances up to 10 are constructed as stabilizer codes from classical selforthogonal rate1/n F4linear and binary linear convolutional codes, respectively. These codes generally have higher rate and less decoding complexity than comparable quantum block codes or previous quantum convolutional codes. Rate(n–2)/n block stabilizer codes with the same rate and errorcorrection capability and essentially the same decoding algorithms are derived from these convolutional codes via tailbiting. Index terms: Quantum errorcorrecting codes, CSStype codes, quantum convolutional codes, quantum tailbiting codes. I.
The Art of Signaling: Fifty Years of Coding Theory
, 1998
"... In 1948 Shannon developed fundamental limits on the efficiency of communication over noisy channels. The coding theorem asserts that there are block codes with code rates arbitrarily close to channel capacity and probabilities of error arbitrarily close to zero. Fifty years later, codes for the Gaus ..."
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Cited by 20 (0 self)
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In 1948 Shannon developed fundamental limits on the efficiency of communication over noisy channels. The coding theorem asserts that there are block codes with code rates arbitrarily close to channel capacity and probabilities of error arbitrarily close to zero. Fifty years later, codes for the Gaussian channel have been discovered that come close to these fundamental limits. There is now a substantial algebraic theory of errorcorrecting codes with as many connections to mathematics as to engineering practice, and the last 20 years have seen the construction of algebraicgeometry codes that can be encoded and decoded in polynomial time, and that beat the Gilbert–Varshamov bound. Given the size of coding theory as a subject, this review is of necessity a personal perspective, and the focus is reliable communication, and not source coding or cryptography. The emphasis is on connecting coding theories for Hamming and Euclidean space and on future challenges, specifically in data networking, wireless communication, and quantum information theory.