Silicon quantum electronics

Zwanenburg, Floris A.; Dzurak, A. S.; Morello, Andrea; Simmons, M. Y.; Hollenberg, Lloyd C. L.; Klimeck, Gerhard; Rogge, Sven; Coppersmith, S. N.; Eriksson, M. A.

doi:10.1103/revmodphys.85.961

Cited by 1,114 publications

(1,214 citation statements)

References 477 publications

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“…34,35,50,53,54,[56][57][58][59][60][61][62][63][64][65][66][67] Our work completes these findings by a global, quantitative understanding of two-electron lateral silicon double quantum dots. We investigate the spin-orbit and hyperfine-induced relaxation rate as a function of interdot coupling, detuning, and the magnitude and orientation of the external magnetic field for zero and finite temperatures, and for natural and isotopically purified silicon.…”

Section: Introductionsupporting

confidence: 71%

Theory of spin relaxation in two-electron laterally coupled Si/SiGe quantum dots

2012

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Highly accurate numerical results of phonon-induced two-electron spin relaxation in silicon double quantum dots are presented. The relaxation, enabled by spin-orbit coupling and the nuclei of 29 Si (natural or purified abundance), is investigated for experimentally relevant parameters, the interdot coupling, the magnetic field magnitude and orientation, and the detuning. We calculate relaxation rates for zero and finite temperatures (100 mK), concluding that our findings for zero temperature remain qualitatively valid also for 100 mK. We confirm the same anisotropic switch of the axis of prolonged spin lifetime with varying detuning as recently predicted in GaAs. Conditions for possibly hyperfine-dominated relaxation are much more stringent in Si than in GaAs. For experimentally relevant regimes, the spin-orbit coupling, although weak, is the dominant contribution, yielding anisotropic relaxation rates of at least two orders of magnitude lower than in GaAs.

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Section: Introductionsupporting

confidence: 71%

Theory of spin relaxation in two-electron laterally coupled Si/SiGe quantum dots

2012

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“…Among the many different approaches to qubit fabrication, donors in silicon represent a promising path for encoding and manipulating qubits of information [15]. As originally proposed by Kane, the idea is to encode quantum information into the nuclear spin state of a dopant atom like phosphorous ( 31 P) that is shallowly embedded in a silicon lattice composed of 28 Si [16].…”

Section: Silicon Donor Qubit Modelsmentioning

confidence: 99%

A computational workflow for designing silicon donor qubits

et al. 2016

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Developing devices that can reliably and accurately demonstrate the principles of superposition and entanglement is an on-going challenge for the quantum computing community. Modeling and simulation offer attractive means of testing early device designs and establishing expectations for operational performance. However, the complex integrated material systems required by quantum device designs are not captured by any single existing computational modeling method. We examine the development and analysis of a multi-staged computational workflow that can be used to design and characterize silicon donor qubit systems with modeling and simulation. Our approach integrates quantum chemistry calculations with electrostatic field solvers to perform detailed simulations of a phosphorus dopant in silicon. We show how atomistic details can be synthesized into an operational model for the logical gates that define quantum computation in this particular technology. The resulting computational workflow realizes a design tool for silicon donor qubits that can help verify and validate current and nearterm experimental devices.

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“…On the experimental side, the effects of the valleys can be bound up with spin and orbital effects, thus making effective classical and coherent control of the devices more challenging. We propose a simple experimental method (lateral gate voltages) to both analyze and to control these confounding experimental effects when they arise from the complex phase.Quantum coherent manipulation of electrons in Si has been a very active field of study recently [1][2]. The advantages of Si include low spin-orbit coupling and the ability to isotopically enrich 28 Si, both of which will tend to reduce the decoherence of spin qubits.…”

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Valley Phase and Voltage Control of Coherent Manipulation in Si Quantum Dots

2017

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With any roughness at the interface of an indirect-bandgap semiconducting dot, the phase of the valley-orbit coupling can take on a random value. This random value, in double quantum dots, causes a large change in the exchange splitting. We demonstrate a simple analytical method to calculate the phase, and thus the exchange splitting and singlet-triplet qubit frequency, for an arbitrary interface. We then show that, with lateral control of the position of a quantum dot using a gate voltage, the valley-orbit phase can be controlled over a wide range, so that variations in the exchange splitting can be controlled for individual devices. Finally, we suggest experiments to measure the valley phase and the concomitant gate voltage control.The physics of valleys in Si is complicated, both theoretically and experimentally. On the theory side, calculations of the effects of valleys, especially with rough interfaces, often requires very large atomistic simulations; those simulations can sometimes make it more difficult to achieve a simple, intuitive understanding of the underlying physics. In this paper, we present a very simple and intuitively-appealing framework to understand and calculate the effect of the phase of the complex valley-orbit coupling in devices with rough interfaces. On the experimental side, the effects of the valleys can be bound up with spin and orbital effects, thus making effective classical and coherent control of the devices more challenging. We propose a simple experimental method (lateral gate voltages) to both analyze and to control these confounding experimental effects when they arise from the complex phase.Quantum coherent manipulation of electrons in Si has been a very active field of study recently [1][2]. The advantages of Si include low spin-orbit coupling and the ability to isotopically enrich 28 Si, both of which will tend to reduce the decoherence of spin qubits. In addition, the integration with CMOS classical circuitry holds the potential for monolithically integrating qubits with control circuits . The experimental work most relevant for our study is Shi et al [10], which showed experimentally a shift in the single-triplet splitting J for two electrons on a single dot, where J is dominated by the energy difference between single-particle ground and excited valley-orbit states in Si/SiGe. In particular, they measured J as a function of lateral shift using gate voltages; they showed about a 20 % shift, and interpreted it as coming from the change in single-particle valley-orbit energies arising from a rough interface (they solved this for the toy model of a single atomic step).In the vicinity of an interface, the lowest energy valleys are typically perpendicular to the interface, and are split by the valley-orbit coupling, which is defined aswhere|z , |z are the bare valley states centered at k z = ±k 0 = ±(0.85)2π/a 0 , V is the interfacial potential energy, F is the applied electric field, and a 0 is lattice constant; this leads to eigenstates which are symmetric superpositions of...

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Silicon quantum electronics

Cited by 1,114 publications

References 477 publications

Theory of spin relaxation in two-electron laterally coupled Si/SiGe quantum dots

Theory of spin relaxation in two-electron laterally coupled Si/SiGe quantum dots

A computational workflow for designing silicon donor qubits

Valley Phase and Voltage Control of Coherent Manipulation in Si Quantum Dots

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