Realizable Universal Quantum Logic Gates

Sleator, Tycho; Weinfurter, Harald

doi:10.1103/physrevlett.74.4087

Cited by 499 publications

(385 citation statements)

References 19 publications

Supporting

Mentioning

377

Contrasting

Unclassified

Order By: Relevance

“…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.…”

mentioning

confidence: 99%

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

Duan

Ying

2013

Phys. Rev. A

View full text Add to dashboard Cite

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...

show abstract

mentioning

confidence: 99%

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

Duan

Ying

2013

Phys. Rev. A

View full text Add to dashboard Cite

show abstract

“…Ever since the pioneering work on quantum computation and quantum error correction [1][2][3][4], there have been many proposed quantum computer (QC) hardware architectures based on different quantum systems [5], such as trapped ions [6], cavity QED [7], liquid state NMR [8], nuclear spins in solids [9], electron spins [10][11][12], superconducting Josephson junctions [13], electrons on He surface [14], etc. Currently, experimental progress has mostly occurred in proposals based on atomic, optical, and NMR physics.…”

mentioning

confidence: 99%

Spin-based quantum computation in multielectron quantum dots

Sarma

2001

Phys. Rev. A

View full text Add to dashboard Cite

In a quantum computer the hardware and software are intrinsically connected because the quantum Hamiltonian (or more precisely its time development) is the code that runs the computer. We demonstrate this subtle and crucial relationship by considering the example of electron-spin-based solid state quantum computer in semiconductor quantum dots. We show that multielectron quantum dots with one valence electron in the outermost shell do not behave simply as an effective single spin system unless special conditions are satisfied. Our work compellingly demonstrates that a delicate synergy between theory and experiment (between software and hardware) is essential for constructing a quantum computer.PACS numbers: 03.67. Lx, 85.30.Vw Ever since the pioneering work on quantum computation and quantum error correction [1][2][3][4] To help overcome these difficulties, more theoretical work is needed to explore the optimal operating regimes, figure out the operational constraints and tolerances, and discover potential sources of errors, just to name a few directions [15][16][17][18]. While the optical and atomic physics based architectures have been crucial in demonstrating the proof of principle for quantum computation, it is generally believed that solid state QC architectures, with their obvious advantage of controllable scale-up possibilities, offer the most promising potential for realistic large scale QC hardwares. The fundamental problem plaguing the solid state QC architectures has been the fact that the basic quantum bit (qubit), the QC building block, has not been compellingly demonstrated in any solid state QC architectures, although there is no reason to doubt that they exist in nature. Thus, the construction of successful QC hardwares has faced the somewhat embarrassing dichotomy: the architectures (ion traps, etc.) demonstrating existence of quantum bits cannot be easily scaled up, while the architectures (solid state QCs) which may be easily scaled up have not yet experimentally demonstrated quantum bits! Quantum computation with fermionic spins is considered to be a potentially promising prospect for solid state quantum computers [9][10][11][12]19]. Among the many proposed solid state QC architectures the spin quantum computer has several intrinsic advantages: (1) A fermionic spin, being a quantum two-level system, is a natural qubit with its spin up and down states; (2) it is fairly straightforward to carry out single-qubit operations on spin up and down levels by applying suitable magnetic fields (or through a purely exchange-based scheme [15]); (3) two-qubit operations can, in principle, be carried out rather easily (in theory, at least) by using the exchange interaction between two neighboring spins; (4) quantum spin is fairly robust and does not decohere easily (typical electron spin relaxation times in solids are many orders of magnitude longer [20] than the momentum relaxation time)-in particular, electron spin relaxation times could be microseconds in semiconductors [21].Our work presented in this...

show abstract

“…form an universal set of quantum gates [110][111][112], i.e. any arbitrary large unitary transformation can be represented as operations on one or two q-bits.…”

Section: Brief Introduction On Quantum Computationmentioning

confidence: 99%

Deep nuclear resonant tunneling thermal rate constant calculations

Mandrà

Valleau

Ceotto

2013

Int J of Quantum Chemistry

View full text Add to dashboard Cite

A fast and robust time‐independent method to calculate thermal rate constants in the deep resonant tunneling regime for scattering reactions is presented. The method is based on the calculation of the cumulative reaction probability which, once integrated, gives the thermal rate constant. We tested our method with both continuous (single and double Eckart barriers) and discontinuous first derivative potentials (single and double rectangular barriers). Our results show that the presented method is robust enough to deal with extreme resonating conditions such as multiple barrier potentials. Finally, the calculation of the thermal rate constant for double Eckart potentials with several quasi‐bound states and the comparison with the time‐independent log‐derivative method are reported. An implementation of the method using the Mathematica Suite is included in the Supporting Information. © 2013 Wiley Periodicals, Inc.

show abstract

Realizable Universal Quantum Logic Gates

Cited by 499 publications

References 19 publications

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

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

Spin-based quantum computation in multielectron quantum dots

Deep nuclear resonant tunneling thermal rate constant calculations

Contact Info

Product

Resources

About