Using negated control signals in quantum computing circuits

Moraga, Claudio

doi:10.2298/fuee1103423m

Cited by 12 publications

(8 citation statements)

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“…The first experimental realization of the quantum Toffoli gate was presented in an ion-trap quantum computer, in 2009 at the University of Innsbruck, Austria [20]. Then, the Toffoli gate was realized in linear optics [21] and superconducting circuits [22,31,32].Due to its significance in quantum computing, the theoretical pursuit of efficient implementation of the Toffoli gate using a sequence of single-and two-qubit gates has a quite long history [7,8,11,12,[33][34][35][36][37]. It was explicitly stated as an open problem by Nielsen and Chuang in their influential textbook on quantum computation [14]: How many general two-qubit gates (or CNOT gates) are required to implement the Toffoli gate (see [14], p. 213, Problem 4.4)?…”

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confidence: 99%

“…However, the optimal simulation of the Toffoli gate by using general bipartite quantum logical gates remains unknown. This problem has attracted attention from many researchers in the last two decades [8,11,12,[34][35][36][37]. In this Rapid Communication, we address this problem by showing that five two-qubit gates are necessary for implementing the Toffoli gate.…”

mentioning

confidence: 99%

“…Due to its significance in quantum computing, the theoretical pursuit of efficient implementation of the Toffoli gate using a sequence of single-and two-qubit gates has a quite long history [7,8,11,12,[33][34][35][36][37]. It was explicitly stated as an open problem by Nielsen and Chuang in their influential textbook on quantum computation [14]: How many general two-qubit gates (or CNOT gates) are required to implement the Toffoli gate (see [14], p. 213, Problem 4.4)?…”

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Five two-qubit gates are necessary for implementing the Toffoli gate

Duan

Ying

2013

Phys. Rev. A

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In this Rapid Communication, we consider the open problem of the minimum cost of two-qubit gates for simulating the Toffoli gate and show that five two-qubit gates are necessary. Before our work, it was known that five two-qubit gates are sufficient to implement the Toffoli gate, and numerical evidence indicates that five two-qubit gates are also necessary. The idea introduced here can also be used to solve the problem of optimal simulation of Deutsch three-qubit gates. Since quantum computation provides the possibility of solving certain problems much faster than any classical computer using the best currently known algorithms [1][2][3][4][5], a huge amount of effort has been devoted to building functional and scalable quantum computers over the last two decades. The quantum circuit model is one popular model of quantum computer hardware [6][7][8][9][10][11][12][13][14][15][16][17][18]. In order to be a general purpose computational device, a quantum computer must implement a small set of quantum logical gates [14], which are universal, that is, can serve as the basic building blocks of quantum circuits, in the same way as do classical logical gates for conventional digital circuits. It is quite natural to choose certain gates operating on a small number of qubits as the basic gates.Theoretically, any two-qubit gate that can create entanglement, like the controlled-NOT (CNOT) gate, together with all single-qubit gates, is universal [18]. It has also been experimentally demonstrated that two-qubit gates can be realized with high fidelity using the current technology, for example, two-qubit gates with superconducting qubits have been presented with fidelities higher than 90% [19]. Finding more efficient ways to implement quantum gates may allow small-scale quantum computing tasks to be demonstrated on a shorter time scale. More precisely, it would be quite helpful for defeating quantum decoherence to realize multiqubit gates with the least number of possible basic gates. Thus an important problem is how to implement multiqubit gates using only two-qubit gates. Indeed, a study of the minimum cost of two-qubit gates for simulating a multiqubit gate is not only of theoretical importance, but also an experimental requirement: to accomplish a quantum algorithm, even at a small size, one has to implement a relatively high level of control over the multiqubit quantum system. A lot of experiments demonstrate multiqubit controlled-NOT gates in ion traps [20] Making controlled unitaries is an essential task for many algorithms in quantum computing [1]. Among all quantum controlled gates, those highly controlled unitaries (i.e., unitaries controlled on more than one other qubit) are useful in numerous quantum algorithms including the oracle in the * nengkunyu@gmail.com binary welded tree algorithm [5] and quantum simulation [24]. The Toffoli gate is perhaps one of the most important highly controlled unitaries for three reasons: (1) The Toffoli gate is universal for classical reversible computation in the sense that all con...

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Five two-qubit gates are necessary for implementing the Toffoli gate

Duan

Ying

2013

Phys. Rev. A

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“…Thus another unitary transformation is used to exchange |000 to |001 and vice-versa, leaving all other basis states unaffected. This transformation can be constructed using a negated Toffoli gate [6], here depicted as a Toffoli with four NOT gates between P 3 and P 4 . The last gate exchanges the 2nd and 3rd qubits just to move the ancilla out of the way.…”

Section: Constructing a Quantum Probability Splittermentioning

confidence: 99%

A quantum probability splitter and its application to qubit preparation

Sgarbas

2012

Quantum Inf Process

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This paper presents a quantum probability splitter, i.e. a quantum circuit that modifies the probability amplitudes of a qubit so that the probability on the selected basis state is halved. It also presents a potential application of this circuit related to qubit preparation: it shows how a qubit is prepared to a superposition of any valid pair of basis states probabilities, by repeated application of the quantum probability splitter.

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“…Some notable approaches to the minimization of incompletely specified reversible function include the cube sharing and reordering [7], [14], [17], adding ancilla bits [1], [12], [15], using Toffoli gates with mixed control bits [7], [13], [16], [20] and designing circuits using Fredkin and Peres gates [3], [19].…”

Section: Introductionmentioning

confidence: 99%

Minimizing Reversible Circuits in the 2n Scheme Using Two and Three Bits Patterns

Lukáč

Hawash

Kameyama

et al. 2014

2014 17th Euromicro Conference on Digital System Design

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In this paper we present improvements to the cost of quantum circuits implemented with 2n-lines circuit implementation. The 2n-line circuit implementation is intended for the linear nearest neighbor quantum circuits and implements any quantum circuits in such manner that they can be directly mapped to quantum implementations. In this paper we propose a replacement strategy for 2-and 3-qubit patterns detected on the control lines. It is demonstrated that application of this strategy leads to a considerable reduction of circuit cost.

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Using negated control signals in quantum computing circuits

Cited by 12 publications

References 12 publications

Five two-qubit gates are necessary for implementing the Toffoli gate

Five two-qubit gates are necessary for implementing the Toffoli gate

A quantum probability splitter and its application to qubit preparation

Minimizing Reversible Circuits in the 2n Scheme Using Two and Three Bits Patterns

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