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148
The Computational Complexity of Linear Optics
 in Proceedings of STOC 2011
"... We give new evidence that quantum computers—moreover, rudimentary quantumcomputers built entirely out of linearoptical elements—cannotbeefficientlysimulatedbyclassical computers. In particular, we define a model of computation in which identical photons are generated, sent through a linearoptical n ..."
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Cited by 32 (8 self)
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We give new evidence that quantum computers—moreover, rudimentary quantumcomputers built entirely out of linearoptical elements—cannotbeefficientlysimulatedbyclassical computers. In particular, we define a model of computation in which identical photons are generated, sent through a linearoptical network, then nonadaptively measured to count the number of photons in each mode. This model is not known or believed to be universal for quantum computation, and indeed, we discuss the prospects for realizing the model using current technology. On the other hand, we prove that the model is able to solve sampling problems and search problems that are classically intractable under plausible assumptions. Our first result says that, if there exists a polynomialtime classical algorithm that samples from the same probability distribution as a linearoptical network, then P #P = BPP NP, and hence the polynomial hierarchy collapses to the third level. Unfortunately, this result assumes an extremely accurate simulation. Our main result suggests that even an approximate or noisy classical simulation would already imply a collapse of the polynomial hierarchy. For this, we need two unproven conjectures: the PermanentofGaussians Conjecture, which says that it is #Phard to approximate the permanent of a matrixAofindependentN (0,1)Gaussianentries, withhigh probability over A; and the Permanent AntiConcentration Conjecture, which says that Per(A)  ≥ √ n!/poly(n) with high probability over A. We present evidence for these conjectures, both of which seem interesting even apart from our application. For the 96page full version, see www.scottaaronson.com/papers/optics.pdf
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 27 (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.
Quantum Circuit Simplification and Level Compaction
 in IEEE Transactions on ComputerAided Design of Integrated Circuits and Systems, 2008
"... Abstract—Quantum circuits are timedependent diagrams describing the process of quantum computation. Usually, a quantum algorithm must be mapped into a quantum circuit. Optimal synthesis of quantum circuits is intractable, and heuristic methods must be employed. With the use of heuristics, the optim ..."
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Cited by 24 (4 self)
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Abstract—Quantum circuits are timedependent diagrams describing the process of quantum computation. Usually, a quantum algorithm must be mapped into a quantum circuit. Optimal synthesis of quantum circuits is intractable, and heuristic methods must be employed. With the use of heuristics, the optimality of circuits is no longer guaranteed. In this paper, we consider a local optimization technique based on templates to simplify and reduce the depth of nonoptimal quantum circuits. We present and analyze templates in the general case and provide particular details for the circuits composed of NOT, CNOT, and controlledsqrtofNOT gates. We apply templates to optimize various common circuits implementing multiple control Toffoli gates and quantum Boolean arithmetic circuits. We also show how templates can be used to compact the number of levels of a quantum circuit. The runtime of our implementation is small, whereas the reduction in the number of quantum gates and number of levels is significant. Index Terms—Circuit optimization, quantum circuits, time optimization. I.
Circuit for Shor’s algorithm using 2n+3 qubits
 54
, 2002
"... We try to minimize the number of qubits needed to factor an integer of n bits using Shor’s algorithm on a quantum computer. We introduce a circuit which uses 2n+3 qubits and O(n 3 lg(n)) elementary quantum gates in a depth of O(n 3) to implement the factorization algorithm. The circuit is computable ..."
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Cited by 20 (0 self)
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We try to minimize the number of qubits needed to factor an integer of n bits using Shor’s algorithm on a quantum computer. We introduce a circuit which uses 2n+3 qubits and O(n 3 lg(n)) elementary quantum gates in a depth of O(n 3) to implement the factorization algorithm. The circuit is computable in polynomial time on a classical computer and is completely general as it does not rely on any property of the number to be factored. 1
The Effect of Communication Costs in SolidState Quantum Computing Architectures
, 2003
"... Quantum computation has become an intriguing technology with which to attack difficult problems and to enhance system security. Quantum algorithms, however, have been analyzed under idealized assumptions without important physical constraints in mind. In this paper, we analyze two key constraints: t ..."
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Cited by 17 (3 self)
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Quantum computation has become an intriguing technology with which to attack difficult problems and to enhance system security. Quantum algorithms, however, have been analyzed under idealized assumptions without important physical constraints in mind. In this paper, we analyze two key constraints: the short spatial distance of quantum interactions and the short temporal life of quantum data. In particular, quantum computations must make use of extremely robust error correction techniques to extend the life of quantum data. We present optimized spatial layouts of quantum error correction circuits for quantum bits embedded in silicon. We analyze the complexity of error correction under the constraint that interaction between these bits is near neighbor and data must be propagated via swap operations from one part of the circuit to another. We discover two interesting results from our quantum layouts. First, the recursive nature of quantum error correction circuits requires a additional communication technique more powerful than nearneighbor swaps – too much error accumulates if we attempt to swap over long distances. We show that quantum teleportation can be used to implement recursive structures. We also show that the reliability of the quantum swap operation is the limiting factor in solidstate quantum computation.
Quantum computing with trapped ions
, 2008
"... Quantum computers hold the promise to solve certain computational task much more efficiently than classical computers. We review the recent experimental advancements towards a quantum computer with trapped ions. In particular, various implementations of qubits, quantum gates and some key experiments ..."
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Cited by 16 (2 self)
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Quantum computers hold the promise to solve certain computational task much more efficiently than classical computers. We review the recent experimental advancements towards a quantum computer with trapped ions. In particular, various implementations of qubits, quantum gates and some key experiments are discussed. Furthermore, we review some implementations of quantum algorithms such as a deterministic teleportation of quantum information and an error correction scheme.
RevKit: A Toolkit for Reversible Circuit Design
"... Abstract—In recent years, research in the domain of reversible circuit design has attracted significant attention leading to many different approaches for e.g. synthesis, optimization, simulation, verification, and test. However, most of the resulting tools are not publicly available. In this paper, ..."
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Cited by 15 (10 self)
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Abstract—In recent years, research in the domain of reversible circuit design has attracted significant attention leading to many different approaches for e.g. synthesis, optimization, simulation, verification, and test. However, most of the resulting tools are not publicly available. In this paper, we introduce RevKit, an open source toolkit that aims to make recent developments in reversible circuit design accessible to other researchers. Therefore, a modular and extendable framework is provided which easily enables the addition of new methods and tools. RevKit already provides some of the existing approaches for synthesis, optimization, and verification functionality. I. INTRODUCTION AND BACKGROUND The development of computing machines has found great success in the last decades. Nowadays billions of components are built on a few square centimeters – and this increasing
Implementation of Grover’s quantum search algorithm in a scalable system
 Phys. Rev. A
, 2005
"... For my mom and dad ii ACKNOWLEDGEMENTS My graduate school experience here at Michigan has been amazing and that is due, in large part, to the people that I have met and the friends that I have made along the way. First and foremost I need to thank Chris for letting me work in his lab, Chris, thank y ..."
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Cited by 14 (2 self)
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For my mom and dad ii ACKNOWLEDGEMENTS My graduate school experience here at Michigan has been amazing and that is due, in large part, to the people that I have met and the friends that I have made along the way. First and foremost I need to thank Chris for letting me work in his lab, Chris, thank you so much. In my six years here I have learned more than I could have possibly imagined. When I look back to when I first joined the lab, compared to where I am now the difference, in my mind at least, is unreal. In your lab I had the opportunity to learn about so many different aspects of experimental physics, from microwave sources, to optics and lasers, to atomic physics. Thank you for all of the opportunities you have given me and for supporting me along the way. I feel well prepared for whatever my physics future holds and I am truly grateful. Next I need to thank all my collegues especially Louis, Patty, and Paul with whom I worked and from whom I learned the most. Louis and Patty, thank you for showing
Is the Brain a Quantum Computer?
"... We argue that computation via quantum mechanical processes is irrelevant to explaining how brains produce thought, contrary to the ongoing speculations of many theorists. First, quantum effects do not have the temporal properties required for neural information processing. Second, there are substant ..."
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Cited by 13 (4 self)
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We argue that computation via quantum mechanical processes is irrelevant to explaining how brains produce thought, contrary to the ongoing speculations of many theorists. First, quantum effects do not have the temporal properties required for neural information processing. Second, there are substantial physical obstacles to any organic instantiation of quantum computation. Third, there is no psychological evidence that such mental phenomena as consciousness and mathematical thinking require explanation via quantum theory. We conclude that understanding brain function is unlikely to require quantum computation or similar mechanisms.