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79
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 264 (5 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.
Simulating quantum mechanics on a quantum computer
 PHYSICA D
, 1998
"... Algorithms are described for efficiently simulating quantum mechanical systems on quantum computers. A class of algorithms for simulating the Schrödinger equation for interacting manybody systems are presented in some detail. These algorithms would make it possible to simulate nonrelativistic quant ..."
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Cited by 51 (3 self)
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Algorithms are described for efficiently simulating quantum mechanical systems on quantum computers. A class of algorithms for simulating the Schrödinger equation for interacting manybody systems are presented in some detail. These algorithms would make it possible to simulate nonrelativistic quantum systems on a quantum computer with an exponential speedup compared to simulations on classical computers. Issues involved in simulating relativistic systems of Dirac or gauge particles are discussed.
Improving gatelevel simulation of quantum circuits
 Quantum Information Processing
"... While thousands of experimental physicists and chemists are currently trying to build scalable quantum computers, it appears that simulation of quantum computation will be at least as critical as circuit simulation in classical VLSI design. However, since the work of Richard Feynman in the early 198 ..."
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Cited by 35 (8 self)
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While thousands of experimental physicists and chemists are currently trying to build scalable quantum computers, it appears that simulation of quantum computation will be at least as critical as circuit simulation in classical VLSI design. However, since the work of Richard Feynman in the early 1980s little progress was made in practical quantum simulation. Most researchers focused on polynomialtime simulation of restricted types of quantum circuits that fall short of the full power of quantum computation [7]. Simulating quantum computing devices and useful quantum algorithms on classical hardware now requires excessive computational resources, making many important simulation tasks infeasible. In this work we propose a new technique for gatelevel simulation of quantum circuits which greatly reduces the difficulty and cost of such simulations. The proposed technique is implemented in a simulation tool called the Quantum Information Decision Diagram (QuIDD) and evaluated by simulating Grover’s quantum search algorithm [8]. The backend of our package, QuIDD Pro, is based on Binary Decision Diagrams, wellknown for their ability to efficiently represent many seemingly intractable combinatorial structures. This reliance on a wellestablished area of research allows us to take advantage of existing software for BDD manipulation and achieve unparalleled empirical results for quantum simulation. 1
Introduction to Quantum Algorithms
, 2001
"... Abstract. These notes discuss the quantum algorithms we know of that can solve problems significantly faster than the corresponding classical algorithms. ..."
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Cited by 23 (0 self)
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Abstract. These notes discuss the quantum algorithms we know of that can solve problems significantly faster than the corresponding classical algorithms.
Quantum Computation
, 1998
"... In the last few years, theoretical study of quantum systems serving as computational devices has achieved tremendous progress. We now have strong theoretical evidence that quantum computers, if built, might be used as a dramatically powerful computational tool, capable of performing tasks which see ..."
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Cited by 17 (0 self)
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In the last few years, theoretical study of quantum systems serving as computational devices has achieved tremendous progress. We now have strong theoretical evidence that quantum computers, if built, might be used as a dramatically powerful computational tool, capable of performing tasks which seem intractable for classical computers. This review is about to tell the story of theoretical quantum computation. I left out the developing topic of experimental realizations of the model, and neglected other closely related topics which are quantum information and quantum communication. As a result of narrowing the scope of this paper, I hope it has gained the benefit of being an almost self contained introduction to the exciting field of quantum computation.
Level reduction and the quantum threshold theorem
 PH.D. THESIS, CALTECH, 2007, EPRINT ARXIV:QUANTPH/0703230
, 2007
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A Fault Tolerant, Area Efficient Architecture for Shor’s Factoring Algorithm
"... We optimize the area and latency of Shor’s factoring while simultaneously improving fault tolerance through: (1) balancing the use of ancilla generators, (2) aggressive optimization of error correction, and (3) tuning the core adder circuits. Our custom CAD flow produces detailed layouts of the phys ..."
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Cited by 15 (3 self)
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We optimize the area and latency of Shor’s factoring while simultaneously improving fault tolerance through: (1) balancing the use of ancilla generators, (2) aggressive optimization of error correction, and (3) tuning the core adder circuits. Our custom CAD flow produces detailed layouts of the physical components and utilizes simulation to analyze circuits in terms of area, latency, and success probability. We introduce a metric, called ADCR, which is the probabilistic equivalent of the classic AreaDelay product. Our error correction optimization can reduce ADCR by an order of magnitude or more. Contrary to conventional wisdom, we show that the area of an optimized quantum circuit is not dominated exclusively by error correction. Further, our adder evaluation shows that quantum carrylookahead adders (QCLA) beat ripplecarry adders in ADCR, despite being larger and more complex. We conclude with what we believe is one of most accurate estimates of the area and latency required for 1024bit Shor’s factorization: 7659 mm 2 for the smallest circuit and 6 × 10 8 seconds for the fastest circuit.
Quantum algorithms for quantum field theories, Science 336
, 2012
"... Quantum field theory reconciles quantum mechanics and special relativity, and plays a central role in many areas of physics. We developed a quantum algorithm to compute relativistic scattering probabilities in a massive quantum field theory with quartic selfinteractions (f4 theory) in spacetime of ..."
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Cited by 15 (4 self)
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Quantum field theory reconciles quantum mechanics and special relativity, and plays a central role in many areas of physics. We developed a quantum algorithm to compute relativistic scattering probabilities in a massive quantum field theory with quartic selfinteractions (f4 theory) in spacetime of four and fewer dimensions. Its run time is polynomial in the number of particles, their energy, and the desired precision, and applies at both weak and strong coupling. In the strongcoupling and highprecision regimes, our quantum algorithm achieves exponential speedup over the fastest known classical algorithm. Thequestion whether quantum field theoriescan be efficiently simulated by quantumcomputers was first posed by Feynman three decades ago when he introduced the notion of quantum computers (1). Since then, efficient quantum algorithms for simulating the dynamics of quantum manybody systems have been developed theoretically (2–4) and demonstrated experimentally (5–7). Quantum field theory, which applies quantum mechanics to functions of space
Quantum computing: Pro and con
 Proc. Royal Soc. London A
, 1997
"... I assess the potential of quantum computation. Broad and important applications must be found to justify construction of a quantum computer; I review some of the known quantum algorithms and consider the prospects for finding new ones. Quantum computers are notoriously susceptible to making errors; ..."
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Cited by 12 (0 self)
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I assess the potential of quantum computation. Broad and important applications must be found to justify construction of a quantum computer; I review some of the known quantum algorithms and consider the prospects for finding new ones. Quantum computers are notoriously susceptible to making errors; I discuss recently developed faulttolerant procedures that enable a quantum computer with noisy gates to perform reliably. Quantum computing hardware is still in its infancy; I comment on the specifications that should be met by future hardware. Over the past few years, work on quantum computation has erected a new classification of computational complexity, has generated profound insights into the nature of decoherence, and has stimulated the formulation of new techniques in highprecision experimental physics. A broad interdisciplinary effort will be needed if quantum computers are to fulfil their destiny as the world's fastest computing devices. This paper is an expanded version of remarks that were prepared for a panel discussion