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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 38 (6 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
Quantum Weakest Preconditions
 UNDER CONSIDERATION FOR PUBLICATION IN MATH. STRUCT. IN COMP. SCIENCE
, 2005
"... We develop a notion of predicate transformer and, in particular, the weakest precondition, appropriate for quantum computation. We show that there is a Stonetype duality between the usual statetransformer semantics and the weakest precondition semantics. Rather than trying to reduce quantum comput ..."
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Cited by 36 (2 self)
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We develop a notion of predicate transformer and, in particular, the weakest precondition, appropriate for quantum computation. We show that there is a Stonetype duality between the usual statetransformer semantics and the weakest precondition semantics. Rather than trying to reduce quantum computation to probabilistic programming we develop a notion that is directly taken from concepts used in quantum computation. The proof that weakest preconditions exist for completely positive maps follows immediately from the Kraus representation theorem. As an example we give the semantics of Selinger’s language in terms of our weakest preconditions. We also cover some specific situations and exhibit an interesting link with stabilizers.
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
Towards faulttolerant quantum computing with trapped ions
 Nature Physics
, 2008
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Quantum circuit simplification using templates
 in Proc
, 2005
"... Optimal synthesis of quantum circuits is intractable and heuristic methods must be employed. Templates are a general approach to reversible and quantum circuit simplification. In this paper, we consider the use of templates to simplify a quantum circuit initially found by other means. We present a ..."
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Cited by 32 (10 self)
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Optimal synthesis of quantum circuits is intractable and heuristic methods must be employed. Templates are a general approach to reversible and quantum circuit simplification. In this paper, we consider the use of templates to simplify a quantum circuit initially found by other means. We present and analyze templates in the general case, and then provide particular details for circuits composed of NOT, CNOT and controlledsqrtofNOT gates. We introduce templates for this set of gates and apply them to simplify both known quantum realizations of Toffoli gates and circuits found by earlier heuristic Fredkin and Toffoli gate synthesis algorithms. While the number of templates is quite small, the reduction in quantum cost is often significant. 1.
Research on hidden variable theories: a review of recent progresses
, 2007
"... Quantum Mechanics (QM) is one of the pillars of modern physics: an impressive amount of experiments have confirmed this theory and many technological applications are based on it. Nevertheless, at one century since its development, various aspects concerning its very foundations still remain to be c ..."
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Cited by 28 (2 self)
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Quantum Mechanics (QM) is one of the pillars of modern physics: an impressive amount of experiments have confirmed this theory and many technological applications are based on it. Nevertheless, at one century since its development, various aspects concerning its very foundations still remain to be clarified. Among them, the transition from a microscopic probabilistic world into a macroscopic deterministic one and quantum nonlocality. A possible way out from these problems would be if QM represents a statistical approximation of an unknown deterministic theory. This review is addressed to present the most recent progresses on the studies related to Hidden Variable Theories (HVT), both from an experimental and a theoretical point of view, giving a larger emphasis to results with a direct experimental application. More in details, the first part of the review is a historical introduction to this problem. The EinsteinPodolskyRosen argument and the first discussions about
Techniques for the synthesis of reversible Toffoli networks
 ACM TRANS. DESIGN AUTOM. ELECTR. SYST
, 2006
"... This paper presents novel techniques for the synthesis of reversible networks of Toffoli gates, as well as improvements to previous methods. Gate count and a technology oriented cost metrices are used. Our synthesis techniques are independent of the cost metrics. Two new iterative synthesis procedur ..."
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Cited by 28 (3 self)
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This paper presents novel techniques for the synthesis of reversible networks of Toffoli gates, as well as improvements to previous methods. Gate count and a technology oriented cost metrices are used. Our synthesis techniques are independent of the cost metrics. Two new iterative synthesis procedure employing ReedMuller spectra are introduced and shown to complement earlier synthesis approaches. The template simplification introduced in earlier work is enhanced and new templates of sizes 7 and 9 are presented. A novel “resynthesis” approach is introduced wherein a sequence of gates is chosen from a network, and the reversible specification it realizes is resynthesized as an independent problem in hopes of reducing the network cost. Empirical results are presented to show that the methods are effective both in terms of the realization of all 3 × 3 reversible functions and larger reversible benchmark specifications.
On mutually unbiased bases
 D O I : 10.1142/S0219749910006502. URL http://dx.doi.org/10.1142/S0219749910006502
, 2010
"... Mutually unbiased bases for quantum degrees of freedom are central to all theoretical investigations and practical exploitations of complementary properties. Much is known about mutually unbiased bases, but there are also a fair number of important questions that have not been answered in full as y ..."
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Cited by 25 (1 self)
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Mutually unbiased bases for quantum degrees of freedom are central to all theoretical investigations and practical exploitations of complementary properties. Much is known about mutually unbiased bases, but there are also a fair number of important questions that have not been answered in full as yet. In particular, one can ¯nd maximal sets of N þ 1 mutually unbiased bases in Hilbert spaces of primepower dimensionN pm, with p prime and m a positive integer, and there is a continuum of mutually unbiased bases for a continuous degree of freedom, such as motion along a line. But not a single example of a maximal set is known if the dimension is another composite number (N 6; 10; 12;...). In this review, we present a uni¯ed approach in which the basis states are labeled by numbers 0; 1; 2;...;N 1 that are both elements of a Galois ¯eld and ordinary integers. This dual nature permits a compact systematic construction of maximal sets of mutually unbiased bases when they are known to exist but throws no light on the open existence problem in other cases.We show how to use the thus constructed mutually unbiased bases in quantuminformatics applications,
Simulations in Coalgebra
 THEOR. COMP. SCI
, 2003
"... A new approach to simulations is proposed within the theory of coalgebras by taking a notion of order on a functor as primitive. Such an order forms a basic building block for a "lax relation lifting", or "relator" as used by other authors. Simulations appear as coalgebras of thi ..."
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Cited by 24 (2 self)
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A new approach to simulations is proposed within the theory of coalgebras by taking a notion of order on a functor as primitive. Such an order forms a basic building block for a "lax relation lifting", or "relator" as used by other authors. Simulations appear as coalgebras of this lifted functor, and similarity as greatest simulation. Twoway similarity is then similarity in both directions. In general, it is different from bisimilarity (in the usual coalgebraic sense), but a su#cient condition is formulated (and illustrated) to ensure that bisimilarity and twoway similarity coincide. Also, suitable conditions are identified which ensures that similarity on a final coalgebra forms an (algebraic) dcpo structure. This involves a close investigation of the iterated applications F (#) and F (1) of a functor F with an order to the initial and final sets.