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arXiv:0811.3865 · Physical Review B

Quantum computation with doped silicon cavities

Miguel Abanto, L. Davidovich, Belita Koiller, R. L. de Matos Filho

Published Feb 18, 2010• 12 citations
arXivHTMLPDF

Abstract

We propose an architecture for quantum computing involving substitutional donors in photonic-crystal silicon cavities and the optical initialization, manipulation, and detection processes already demonstrated in ion traps and other atomic systems. Our scheme leads to easily achievable requirements on the positioning of the donors and considerably simplifies the implementation of the building blocks required for the operation of silicon-based quantum computing devices, including realization of one- and two-qubit gates, initialization, and readout of the qubits. Detailed consideration of the processes involved, using state-of-the-art values for the relevant parameters, indicates that this architecture leads to errors per gate compatible with fault-tolerant quantum computation and should be useful for quantum simulations and quantum optics applications.

DOI
10.1103/physrevb.81.085325

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Quantum Computation With Electron Spins of Phosphorous Donors in Silicon

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•Oct 1, 2005•0 citations

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Universal quantum computing holds the promise to fundamentally change today’s information-based society, yet a hardware platform that will provide a clear path to fault-tolerant quantum computing remains elusive. One recently proposed platform involves the use of circuit-bound photons to build cluster states and perform one-way measurement-based quantum computations on arrays of long-coherence-time solid-state spin qubits. Herein, we discuss the challenges that are faced during any practical implementation of this architecture by itemizing the key physical building blocks and the constraints imposed on the spin qubits and the photonic circuit components by the requirements of fault-tolerant performance. These considerations point to silicon as a leading candidate to host such a platform, and a roadmap for developing a silicon photonic circuit-based platform for measurement-based, fault-tolerant universal quantum computing is offered.

APL Photonics•Jul 1, 2021•50 citations
We propose an architecture for quantum computing involving substitutional donors in photonic-crystal silicon cavities and the optical initialization, manipulation, and detection processes already demonstrated in ion traps and other atomic systems. Our scheme leads to easily achievable requirements on the positioning of the donors and considerably simplifies the implementation of the building blocks required for the operation of silicon-based quantum computing devices, including realization of one- and two-qubit gates, initialization, and readout of the qubits. Detailed consideration of the processes involved, using state-of-the-art values for the relevant parameters, indicates that this architecture leads to errors per gate compatible with fault-tolerant quantum computation and should be useful for quantum simulations and quantum optics applications.
Abstract A comprehensive circuit architecture and a protocol for realizing 3D cluster states through photonic‐measurement‐based donor‐spin‐qubit entanglement and readout are described. The basic building blocks and protocol are chosen to be compatible with a fully integrated photonic circuit implementation, using Se+ as the photonically coupled matter qubit. The basic operational building blocks of this universal quantum computing machine are local measurements and unitaries, plus an entangling measurement of non‐local Pauli operators. By analyzing several sources of error, a theoretical fault‐tolerant threshold value is estimated on the order of 1%. Considering the literature where required components have already been realized in integrated silicon circuits, albeit not all on the same chip, this suggests the threshold is within reach.
An architecture for a quantum computer is presented in which spins associated with donors in silicon function as qubits. Quantum operations on the spins are performed using a combination of voltages applied to gates adjacent to the spins and radio frequency magnetic fields applied resonant with spin transitions. Initialization and measurement of electron spins is made by electrostatic probing of a two electron system, whose orbital configuration must depend on the spin states of the electrons because of the Pauli Principle. Specific devices will be discussed which perform all the necessary operations for quantum computing, with an emphasis placed on a qualitative presentation of the principles underlying their operation. The likely impediments to achieving large-scale quantum computation using this architecture will be addressed: the computer must operate at extremely low temperature, must be fabricated from devices built with near atomic precision, and will require extremely accurate gating operations in order to perform quantum logic. Refinements to the computer architecture will be presented which could remedy each of these deficiencies. I will conclude by discussing a possible specific realization of the computer using Si/SixGe1–x heterostructures into which donors are deposited using a low energy focused ion beam.
The discovery of efficient quantum algorithms a decade ago has shown that a quantum computer encoding and processing information quantum mechanically, can solve important problems intractable with conventional computers. The invention of quantum error correction principle, makes quantum computation possibly fault-tolerant against the decoherence of information carriers. Thereafter, intensive research activities have been made toward the implementation of quantum computation with various realistic quantum systems. Among them, the most attractive implementation proposals are using silicon-based materials, which have the advantage of borrowing the existing ingenuity and resources accumulated during the development of modern microelectronics. In this dissertation we investigate several theoretical aspects of a silicon- based quantum computer in which qubits are represented by the spins of electrons bound to phosphorous donors in silicon. Encoding each qubit in terms of three neighboring donor electron spins, we can realize universal quantum gate operations with only the Heisenberg exchange coupling J S1 •S2 between neighboring donors. Therefore, studying the exchange coupling for a phosphorous donor pair in silicon is of central importance for providing the experimentalists with qualitative insights and quantitative guidance for building such a silicon quantum computer. After giving some general considerations on the quantum computer architecture, we develop the necessary theoretical tools. A multi-valley effective mass equation is derived and discussed, to handle impurities in a multi-valley semiconductor. Then we apply it to solve a single Si:P donor embedded in our quantum computer architecture. We show that the width of the silicon quantum well can significantly influence the energy splitting and charge distributions of the ground state. Oscillation of level splitting is observed as the quantum well width or donor position is varied at atomic scale. Elementary gate operations for 3-donor-spin qubits involve a neighboring pair of donors at each step. The exchange coupling in Heisenberg model hamiltonian, defined as the energy splitting of the lowest singlet and triplet states, has to be calculated from the realistic two-donor hamiltonian. We discuss several popular methods to solve the two-donor problem and develop an appropriate extended Hartree-Fock method that can give reliable results for a well-separated donor pair subject to tunable coupling. This method is first applied to a Si:P donor pair in the framework of hydrogenic effective mass theory, to study how to tune the exchange coupling with simple gate potentials. A followed study shows that under a parallel electric field the singlet and triplet states exhibit very different polarization behaviors. This difference can be exploited to measure the state of an electron spin. We also show that, a perpendicular electric field cannot tune the exchange coupling efficiently. Then we apply the realistic multi-valley effective mass equation, coupled with a realistic modeling of the potential generated by gate electrodes, to a pair of phosphorous donors in silicon quantum well. By varying the gate electrode voltages, the exchange coupling can be tuned with exponential efficiency in a wide range. We find that, for best performance, we need to set the quantum well width to be around 10 nm, and the donor separation to be around 10 a∗ b---- 24nm in the doping plane. We analyze in detail an adiabatic half-swap operation between neighboring donor spins. The gate operation time is estimated to be 0.2 ns, which satisfies the constraints put by the donor spin decoherence time and by the validity of adiabatic approximation. The interference between different valley components could lead to oscillations of exchange coupling as donor positions are shifted by occasion. We find the exchange oscillation persists even with only two relevant valleys for donors in a strongly-strained silicon quantum well. It is also shown that the oscillation induced by changing donor separation at atomic scale is strongly suppressed as donors approach each other. Finally, we study the entanglement issue in quantum computing context. We analyze the low-energy Hilbert space for a pair of qubits encoded by localized electron spins and suggest a suitable measure to describe the entanglement between qubits involving indistinguishable electrons and in the presence of leakage errors. The dynamics of inter-qubit entanglement during a gate operation is also studied.
Universal quantum computing holds the promise to fundamentally change today’s information-based society, yet a hardware platform that will provide a clear path to fault-tolerant quantum computing remains elusive. One recently proposed platform involves the use of circuit-bound photons to build cluster states and perform one-way measurement-based quantum computations on arrays of long-coherence-time solid-state spin qubits. Herein, we discuss the challenges that are faced during any practical implementation of this architecture by itemizing the key physical building blocks and the constraints imposed on the spin qubits and the photonic circuit components by the requirements of fault-tolerant performance. These considerations point to silicon as a leading candidate to host such a platform, and a roadmap for developing a silicon photonic circuit-based platform for measurement-based, fault-tolerant universal quantum computing is offered.