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77
Faulttolerant quantum computation
 In Proc. 37th FOCS
, 1996
"... It has recently been realized that use of the properties of quantum mechanics might speed up certain computations dramatically. Interest in quantum computation has since been growing. One of the main difficulties in realizing quantum computation is that decoherence tends to destroy the information i ..."
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Cited by 201 (4 self)
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It has recently been realized that use of the properties of quantum mechanics might speed up certain computations dramatically. Interest in quantum computation has since been growing. One of the main difficulties in realizing quantum computation is that decoherence tends to destroy the information in a superposition of states in a quantum computer, making long computations impossible. A further difficulty is that inaccuracies in quantum state transformations throughout the computation accumulate, rendering long computations unreliable. However, these obstacles may not be as formidable as originally believed. For any quantum computation with t gates, we show how to build a polynomial size quantum circuit that tolerates O(1 / log c t) amounts of inaccuracy and decoherence per gate, for some constant c; the previous bound was O(1 /t). We do this by showing that operations can be performed on quantum data encoded by quantum errorcorrecting codes without decoding this data. 1.
Simulation of topological field theories by quantum computers
 Comm.Math.Phys.227
"... Abstract: Quantum computers will work by evolving a high tensor power of a small (e.g. two) dimensional Hilbert space by local gates, which can be implemented by applying a local Hamiltonian H for a time t. In contrast to this quantum engineering, the most abstract reaches of theoretical physics has ..."
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Cited by 80 (12 self)
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Abstract: Quantum computers will work by evolving a high tensor power of a small (e.g. two) dimensional Hilbert space by local gates, which can be implemented by applying a local Hamiltonian H for a time t. In contrast to this quantum engineering, the most abstract reaches of theoretical physics has spawned “topological models ” having a finite dimensional internal state space with no natural tensor product structure and in which the evolution of the state is discrete, H ≡ 0. These are called topological quantum field theories (TQFTs). These exotic physical systems are proved to be efficiently simulated on a quantum computer. The conclusion is twofold: 1. TQFTs cannot be used to define a model of computation stronger than the usual quantum model “BQP”. 2. TQFTs provide a radically different way of looking at quantum computation. The rich mathematical structure of TQFTs might suggest a new quantum algorithm. 1.
Faulttolerant quantum computation with local gates
 Jour. of Modern Optics
"... I discuss how to perform faulttolerant quantum computation with concatenated codes using local gates in small numbers of dimensions. I show that a threshold result still exists in three, two, or one dimensions when nexttonearestneighbor gates are available, and present explicit constructions. In ..."
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Cited by 31 (0 self)
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I discuss how to perform faulttolerant quantum computation with concatenated codes using local gates in small numbers of dimensions. I show that a threshold result still exists in three, two, or one dimensions when nexttonearestneighbor gates are available, and present explicit constructions. In two or three dimensions, I also show how nearestneighbor gates can give a threshold result. In all cases, I simply demonstrate that a threshold exists, and do not attempt to optimize the error correction circuit or determine the exact value of the threshold. The additional overhead due to the faulttolerance in both space and time is polylogarithmic in the error rate per logical gate. 1
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 26 (1 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
Information and Computation: Classical and Quantum Aspects
 REVIEWS OF MODERN PHYSICS
, 2001
"... Quantum theory has found a new field of applications in the realm of information and computation during the recent years. This paper reviews how quantum physics allows information coding in classically unexpected and subtle nonlocal ways, as well as information processing with an efficiency largely ..."
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Cited by 23 (2 self)
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Quantum theory has found a new field of applications in the realm of information and computation during the recent years. This paper reviews how quantum physics allows information coding in classically unexpected and subtle nonlocal ways, as well as information processing with an efficiency largely surpassing that of the present and foreseeable classical computers. Some outstanding aspects of classical and quantum information theory will be addressed here. Quantum teleportation, dense coding, and quantum cryptography are discussed as a few samples of the impact of quanta in the transmission of information. Quantum logic gates and quantum algorithms are also discussed as instances of the improvement in information processing by a quantum computer. We provide finally some examples of current experimental
Building quantum wires: the long and the short of it
 In Proc. International Symposium on Computer Architecture (ISCA 2003
, 2003
"... As quantum computing moves closer to reality the need for basic architectural studies becomes more pressing. Quantum wires, which transport quantum data, will be a fundamental component in all anticipated silicon quantum architectures. In this paper, we introduce a quantum wire architecture based up ..."
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Cited by 21 (8 self)
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As quantum computing moves closer to reality the need for basic architectural studies becomes more pressing. Quantum wires, which transport quantum data, will be a fundamental component in all anticipated silicon quantum architectures. In this paper, we introduce a quantum wire architecture based upon quantum teleportation. We compare this teleportation channel with the traditional approach to transporting quantum data, which we refer to as the swapping channel. We characterize the latency and bandwidth of these two alternatives in a deviceindependent way and describe how the advanced architecture of the teleportation channel overcomes a basic limit to the maximum communication distance of the swapping channel. In addition, we discover a fundamental tension between the scale of quantum effects and the scale of the classical logic needed to control them. This “pitchmatching ” problem imposes constraints on minimum wire lengths and wire intersections, which in turn imply a sparsely connected architecture of coarsegrained quantum computational elements. This is in direct contrast to the “sea of gates ” architectures presently assumed by most quantum computing studies. 1
Architectural implications of quantum computing technologies
 ACM Journal on Emerging Technologies in Computing Systems (JETC
, 2006
"... In this article we present a classification scheme for quantum computing technologies that is based on the characteristics most relevant to computer systems architecture. The engineering tradeoffs of execution speed, decoherence of the quantum states, and size of systems are described. Concurrency, ..."
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Cited by 17 (4 self)
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In this article we present a classification scheme for quantum computing technologies that is based on the characteristics most relevant to computer systems architecture. The engineering tradeoffs of execution speed, decoherence of the quantum states, and size of systems are described. Concurrency, storage capacity, and interconnection network topology influence algorithmic efficiency, while quantum error correction and necessary quantum state measurement are the ultimate drivers of logical clock speed. We discuss several proposed technologies. Finally, we use our taxonomy to explore architectural implications for common arithmetic circuits, examine the implementation of quantum error correction, and discuss clusterstate quantum computation.
Universal Quantum Computation with the Exchange Interaction
 Nature
"... Experimental implementations of quantum computer architectures are now being investigated in many different physical settings. The full set of requirements that must be met to make quantum computing a reality in the laboratory [1] is daunting, involving capabilities well beyond the present state of ..."
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Cited by 16 (4 self)
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Experimental implementations of quantum computer architectures are now being investigated in many different physical settings. The full set of requirements that must be met to make quantum computing a reality in the laboratory [1] is daunting, involving capabilities well beyond the present state of the art. In this report we develop a significant simplification of these requirements that can be applied in many recent solidstate approaches, using quantum dots [2], and using donoratom nuclear spins [3] or electron spins [4]. In these approaches, the basic twoqubit quantum gate is generated by a tunable Heisenberg interaction (the Hamiltonian is Hij = J(t) ⃗ Si · ⃗ Sj between spins i and j), while the onequbit gates require the control of a local Zeeman field. Compared to the Heisenberg operation, the onequbit operations are significantly slower and require substantially greater materials and device complexity, which may also contribute to increasing the decoherence rate. Here we introduce an explicit scheme in which the Heisenberg interaction alone suffices to exactly implement any quantum computer circuit, at a price of a factor of three in additional qubits and about
Singleshot readout of an individual electron spin in a quantum dot. Nature 430
, 2004
"... a quantum dot ..."
A Quantum LatticeGas Model for Computational Fluid Dynamics
, 1999
"... Quantumcomputing ideas are applied to the practical and ubiquitous problem of fluid dynamics simulation. Hence, this paper addresses two separate areas of physics: quantum mechanics and fluid dynamics (or specially, the computational simulation of fluid dynamics). The quantum algorithm is called a ..."
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Cited by 13 (4 self)
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Quantumcomputing ideas are applied to the practical and ubiquitous problem of fluid dynamics simulation. Hence, this paper addresses two separate areas of physics: quantum mechanics and fluid dynamics (or specially, the computational simulation of fluid dynamics). The quantum algorithm is called a quantum lattice gas. An analytical treatment of the microscopic quantum latticegas system is carried out to predict its behavior at the mesoscopic and macroscopic scales. At the mesoscopic scale, a lattice Boltzmann equation, with a nonlocal collision term that depends on the entire system wavefunction, governs the dynamical system. Numerical results obtained from an exact simulation of a onedimensional quantum latticemodel are included to illustrate the formalism. A symbolic mathematical method is used to implement the quantum mechanical model on a conventional workstation. The numerical simulation indicates that classical viscous damping is not present in the onedimensional quantum la...