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Synthesis of Reversible Logic Circuits
, 2003
"... Reversible or informationlossless circuits have applications in digital signal processing, communication, computer graphics and cryptography. They are also a fundamental requirement in the emerging field of quantum computation. We investigate the synthesis of reversible circuits that employ a minim ..."
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Cited by 87 (6 self)
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Reversible or informationlossless circuits have applications in digital signal processing, communication, computer graphics and cryptography. They are also a fundamental requirement in the emerging field of quantum computation. We investigate the synthesis of reversible circuits that employ a minimum number of gates and contain no redundant inputoutput linepairs (temporary storage channels). We prove constructively that every even permutation can be implemented without temporary storage using NOT, CNOT and TOFFOLI gates. We describe an algorithm for the synthesis of optimal circuits and study the reversible functions on three wires, reporting the distribution of circuit sizes. Finally, in an application important to quantum computing, we synthesize oracle circuits for Grover's search algorithm, and show a significant improvement over a previously proposed synthesis algorithm.
Quantum Programming
 In Mathematics of Program Construction
, 1999
"... In this paper a programming language is presented for the expression of quantum algorithms. It contains the features required to program a `universal' quantum computer (including initialisation and observation), has a formal semantics and body of laws, and provides a renement calculus supportin ..."
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Cited by 80 (3 self)
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In this paper a programming language is presented for the expression of quantum algorithms. It contains the features required to program a `universal' quantum computer (including initialisation and observation), has a formal semantics and body of laws, and provides a renement calculus supporting the verication and derivation of programs against their specications. A representative selection of quantum algorithms are expressed in the language and one of them is derived from its specication. 1 1 Introduction The purpose of this paper is to present a programming language for quantum computation. So far quantum algorithms have been described by pseudo code or quantum network [6, 0]. To a computer scientist the former has little attraction. The latter provides a dataow view of computation and so is useful when considering implementation in terms of gates (a view which is perhaps slightly premature since we have little idea what might constitute the primitive gates). Whilst it expre...
Optimal synthesis of multiple output Boolean functions using a set of quantum gates by symbolic reachability analysis
 IEEE Trans. on CAD of Integrated Circuits and Systems
, 2006
"... Abstract—This paper proposes an approach to optimally synthesize quantum circuits by symbolic reachability analysis, where the primary inputs and outputs are basis binary and the internal signals can be nonbinary in a multiplevalued domain. The authors present an optimal synthesis method to minimiz ..."
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Cited by 48 (5 self)
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Abstract—This paper proposes an approach to optimally synthesize quantum circuits by symbolic reachability analysis, where the primary inputs and outputs are basis binary and the internal signals can be nonbinary in a multiplevalued domain. The authors present an optimal synthesis method to minimize quantum cost and some speedup methods with nonoptimal quantum cost. The methods here are applicable to small reversible functions. Unlike previous works that use permutative reversible gates, a lower level library that includes nonpermutative quantum gates is used here. The proposed approach obtains the minimum cost quantum circuits for Miller gate, half adder, and full adder, which are better than previous results. This cost is minimum for any circuit using the set of quantum gates in this paper, where the control qubit of 2qubit gates is always basis binary. In addition, the minimum quantum cost in the same manner for Fredkin, Peres, and Toffoli gates is proven. The method can also find the best conversion from an irreversible function to a reversible circuit as a byproduct of the generality of its formulation, thus synthesizing in principle arbitrary multioutput Boolean functions with quantum gate library. This paper constitutes the first successful experience of applying formal methods and satisfiability to quantum logic synthesis. Index Terms—Formal verification, logic synthesis, model checking, quantum computing, reversible logic, satisfiability. I.
Reversible Logic Circuit Synthesis
 In International Conference on Computer Aided Design
, 2002
"... Reversible, or informationlossless, circuits have applications in digital signal processing, communication, computer graphics and cryptography. They are also a fundamental requirement for quantum computation. We investigate the synthesis of reversible circuits that employ a minimum number of gates ..."
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Cited by 42 (2 self)
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Reversible, or informationlossless, circuits have applications in digital signal processing, communication, computer graphics and cryptography. They are also a fundamental requirement for quantum computation. We investigate the synthesis of reversible circuits that employ a minimum number of gates and contain no redundant inputoutput linepairs (temporary storage channels). We propose new constructions for reversible circuits composed of NOT, ControlledNOT, and TOFFOLI gates (the CNT gate library) based on permutation theory. A new algorithm is given to synthesize optimal reversible circuits using an arbitrary gate library, and we describe much faster heuristic algorithms. We also pursue applications of the proposed techniques to the synthesis of quantum circuits.
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
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
Synthesis of quantum logic circuits
 IEEE Trans. on ComputerAided Design
"... The pressure of fundamental limits on classical computation and the promise of exponential speedups from quantum effects have recently brought quantum circuits [10] to the attention of the Electronic Design Automation community [18, 28, 7, 27, 17]. We discuss efficient quantum logic circuits which p ..."
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Cited by 28 (5 self)
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The pressure of fundamental limits on classical computation and the promise of exponential speedups from quantum effects have recently brought quantum circuits [10] to the attention of the Electronic Design Automation community [18, 28, 7, 27, 17]. We discuss efficient quantum logic circuits which perform two tasks: (i) implementing generic quantum computations and (ii) initializing quantum registers. In contrast to conventional computing, the latter task is nontrivial because the statespace of an nqubit register is not finite and contains exponential superpositions of classical bit strings. Our proposed circuits are asymptotically optimal for respective tasks and improve earlier published results by at least a factor of two. The circuits for generic quantum computation constructed by our algorithms are the most efficient known today in terms of the number of most expensive gates (quantum controlledNOTs). They are based on an analogue of the Shannon decomposition of Boolean functions and a new circuit block, quantum multiplexor, that generalizes several known constructions. A theoretical lower bound implies that our circuits cannot be improved by more than a factor of two. We additionally show how to accommodate the severe architectural limitation of using only nearestneighbor gates that is representative of current implementation technologies. This increases the number of gates by almost an order of magnitude, but preserves the asymptotic optimality of gate counts. 1
Toward a software architecture for quantum computing design tools
 Proceedings of the 2nd International Workshop on Quantum Programming Languages (QPL
, 2004
"... Compilers and computeraided design tools are essential for finegrained control of nanoscale quantummechanical systems. A proposed fourphase design flow assists with computations by transforming a quantum algorithm from a highlevel language program into precisely scheduled physical actions. Quan ..."
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Cited by 20 (3 self)
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Compilers and computeraided design tools are essential for finegrained control of nanoscale quantummechanical systems. A proposed fourphase design flow assists with computations by transforming a quantum algorithm from a highlevel language program into precisely scheduled physical actions. Quantum computers have the potential to solve certain computational problems—for example, factoring composite numbers or comparing an unknown image against a large database— more efficiently than modern computers. They are also indispensable in controlling quantummechanical systems in emergent nanotechnology applications, such as secure optical communication, in which modern computers cannot natively operate on quantum data. Despite convincing laboratory demonstrations of
Evolving Quantum Circuits Using Genetic Algorithms
 Proc. 4th NASA/DoD EHW
, 2002
"... Abstract: In this paper we focus on a general approach of using genetic algorithm (GA) to evolve Quantum circuits (QC). We propose a generic GA to evolve arbitrary quantum circuit specified by a (target) unitary matrix as well as a specific encoding that reduces the time of calculating the resultant ..."
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Cited by 19 (5 self)
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Abstract: In this paper we focus on a general approach of using genetic algorithm (GA) to evolve Quantum circuits (QC). We propose a generic GA to evolve arbitrary quantum circuit specified by a (target) unitary matrix as well as a specific encoding that reduces the time of calculating the resultant unitary matrices of chromosomes. We demonstrate that, in contrast to previous approaches, our encoding allows synthesis of small quantum circuits of arbitrary type, using standard genetic operators. 1.