Limits on fundamental limits to computation

Markov, Igor L.

doi:10.1038/nature13570

Cited by 362 publications

(255 citation statements)

References 98 publications

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“…Many estimates of computational capacity of physical systems have their starting point in the assumption that T −1 ⊥ * stephen.jordan@nist.gov can be interpreted as a maximum computational clock speed [11,[13][14][15][16][17][18][19][20][21][22][23][24][25]. Related, but distinct, arguments for limits on computational speed related to energy are given in [26][27][28][29].…”

Section: Introductionmentioning

confidence: 99%

Fast quantum computation at arbitrarily low energy

Jordan

2017

Phys. Rev. A

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One version of the energy-time uncertainty principle states that the minimum time T ⊥ for a quantum system to evolve from a given state to any orthogonal state is h/(4∆E) where ∆E is the energy uncertainty. A related bound called the Margolus-Levitin theorem states that T ⊥ ≥ h/(2 E ) where E is the expectation value of energy and the ground energy is taken to be zero. Many subsequent works have interpreted T ⊥ as defining a minimal time for an elementary computational operation and correspondingly a fundamental limit on clock speed determined by a system's energy. Here we present local time-independent Hamiltonians in which computational clock speed becomes arbitrarily large relative to E and ∆E as the number of computational steps goes to infinity. We argue that energy considerations alone are not sufficient to obtain an upper bound on computational speed, and that additional physical assumptions such as limits to information density and information transmission speed are necessary to obtain such a bound.

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Section: Introductionmentioning

confidence: 99%

Fast quantum computation at arbitrarily low energy

Jordan

2017

Phys. Rev. A

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“…The former has a very well developed and working theory, and thus it is expected to dominate informatics for some time. The scientific community is working on several solutions to replace the latter, which has consisted for the past several decades mainly of CMOS (complementary metal oxide semiconductor) architecture [1]. This research is necessary, because the currently available devices are slowly approaching their limits.…”

Section: Introductionmentioning

confidence: 99%

Physical Limits of Computation

Guba¹,

Nánai²,

George³

2017

JQIS

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“…We further note that although logical reversibility can break the Landauer's limit, it does not warrant the full elimination of energy dissipation. Energy dissipation in a reversible computer shall remain finite due to the inevitable physicalirreversibility of electronic devices and circuits [72,73]. Finally, we remark that it remains a technological challenge to fabricate the proposed valleytronic devices at current stage.…”

Section: Class-1 Logics In Which Thementioning

confidence: 99%

Valleytronics in merging Dirac cones: All-electric-controlled valley filter, valve, and universal reversible logic gate

et al. 2017

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Despite much anticipation of valleytronics as a candidate to replace the aging complementary metal-oxidesemiconductor (CMOS) based information processing, its progress is severely hindered by the lack of practical ways to manipulate valley polarization all electrically in an electrostatic setting. Here, we propose a class of all-electric-controlled valley filter, valve, and logic gate based on the valley-contrasting transport in a merging Dirac cones system. The central mechanism of these devices lies on the pseudospin-assisted quantum tunneling which effectively quenches the transport of one valley when its pseudospin configuration mismatches that of a gate-controlled scattering region. The valley polarization can be abruptly switched into different states and remains stable over semi-infinite gate-voltage windows. Colossal tunneling valleypseudomagnetoresistance ratio of over 10000% can be achieved in a valley-valve setup. We further propose a valleytronic-based logic gate capable of covering all 16 types of two-input Boolean logics. Remarkably, the valley degree of freedom can be harnessed to resurrect logical reversibility in two-input universal Boolean gate. The (2+1) polarization states (two distinct valleys plus a null polarization) reestablish one-to-one inputto-output mapping, a crucial requirement for logical reversibility, and significantly reduce the complexity of reversible circuits. Our results suggest that the synergy of valleytronics and digital logics may provide new paradigms for valleytronic-based information processing and reversible computing. Despite much anticipation of valleytronics as a candidate to replace the aging complementary metal-oxidesemiconductor (CMOS) based information processing, its progress is severely hindered by the lack of practical ways to manipulate valley polarization all electrically in an electrostatic setting. Here, we propose a class of all-electric-controlled valley filter, valve, and logic gate based on the valley-contrasting transport in a merging Dirac cones system. The central mechanism of these devices lies on the pseudospin-assisted quantum tunneling which effectively quenches the transport of one valley when its pseudospin configuration mismatches that of a gate-controlled scattering region. The valley polarization can be abruptly switched into different states and remains stable over semi-infinite gate-voltage windows. Colossal tunneling valley-pseudomagnetoresistance ratio of over 10 000% can be achieved in a valley-valve setup. We further propose a valleytronic-based logic gate capable of covering all 16 types of two-input Boolean logics. Remarkably, the valley degree of freedom can be harnessed to resurrect logical reversibility in two-input universal Boolean gate. The (2 + 1) polarization states (two distinct valleys plus a null polarization) reestablish one-to-one input-to-output mapping, a crucial requirement for logical reversibility, and significantly reduce the complexity of reversible circuits. Our results suggest that the synergy of va...

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Limits on fundamental limits to computation

Cited by 362 publications

References 98 publications

Fast quantum computation at arbitrarily low energy

Fast quantum computation at arbitrarily low energy

Physical Limits of Computation

Valleytronics in merging Dirac cones: All-electric-controlled valley filter, valve, and universal reversible logic gate

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