Spin quantum computation in silicon nanostructures

Abstract Proposed silicon-based quantum-computer architectures have attracted attention because of their promise for scalability and their potential for synergetically utilizing the available resources associated with the existing Si technology infrastructure. Electronic and nuclear spins of shallow donors (e.g. phosphorus) in Si are ideal candidates for qubits in such proposals because of their long spin coherence times due to their limited interactions with their environments. For these spin qubits, shallow donor exchange gates are frequently invoked to perform two-qubit operations. We discuss in this review a particularly important spin decoherence channel, and bandstructure effects on the exchange gate control. Specifically, we review our work on donor electron spin spectral diffusion due to background nuclear spin flip–flops, and how isotopic purification of silicon can significantly enhance the electron spin dephasing time. We then review our calculation of donor electron exchange coupling in the presence of degenerate silicon conduction band valleys. We show that valley interference leads to orders of magnitude variations in electron exchange coupling when donor configurations are changed on an atomic scale. These studies illustrate the substantial potential that donor electron/nuclear spins in silicon have as candidates for qubits and simultaneously the considerable challenges they pose. In particular, our work on spin decoherence through spectral diffusion points to the possible importance of isotopic purification in the fabrication of scalable solid state quantum computer architectures. We also provide a critical comparison between the two main proposed spin-based solid state quantum computer architectures, namely, shallow donor bound states in Si and localized quantum dot states in GaAs.

[1]  L. Vandersypen,et al.  Single-shot read-out of an individual electron spin in a quantum dot , 2004, Nature.

[2]  S. Das Sarma,et al.  Electron spin coherence in semiconductors: Considerations for a spin-based solid-state quantum computer architecture , 2002, cond-mat/0203101.

[3]  A. Khaetskii,et al.  Electron spin decoherence in quantum dots due to interaction with nuclei. , 2002, Physical review letters.

[4]  S. A. Lyon,et al.  Electron spin relaxation times of phosphorus donors in silicon , 2003 .

[5]  Xuedong Hu,et al.  Exchange in silicon-based quantum computer architecture. , 2002, Physical review letters.

[6]  K. Andres,et al.  Low-temperature magnetic susceptibility of Si: P in the nonmetallic region , 1981 .

[7]  Robert Joynt,et al.  Decoherence of electron spin qubits in Si-based quantum computers , 2002 .

[8]  Walter Kohn,et al.  Shallow Impurity States in Silicon and Germanium , 1957 .

[9]  Peter W. Shor,et al.  Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer , 1995, SIAM Rev..

[10]  S. Tarucha,et al.  Nuclear-spin-induced oscillatory current in spin-blockaded quantum dots. , 2003, Physical review letters.

[11]  One- and two-dimensional N -qubit systems in capacitively coupled quantum dots , 2000, quant-ph/0009030.

[12]  S. Pantelides.  The electronic structure of impurities and other point defects in semiconductors , 1978 .

[13]  S. Sarma,et al.  Theory of nuclear-induced spectral diffusion: Spin decoherence of phosphorus donors in Si and GaAs quantum dots , 2002, cond-mat/0211567.

[14]  M. Y. Simmons,et al.  Towards the fabrication of phosphorus qubits for a silicon quantum computer , 2001 .

[15]  H. Carr,et al.  The Principles of Nuclear Magnetism , 1961 .

[16]  P. H. Citrin,et al.  Atomic-scale imaging of individual dopant atoms and clusters in highly n-type bulk Si , 2002, Nature.

[17]  D. D. Awschalom,et al.  Quantum information processing using quantum dot spins and cavity QED , 1999 .

[18]  Eli Yablonovitch,et al.  Electron-spin-resonance transistors for quantum computing in silicon-germanium heterostructures , 1999, quant-ph/9905096.

[19]  Electron-spin phase relaxation of phosphorus donors in nuclear-spin-enriched silicon , 2004, cond-mat/0402152.

[20]  C. Slichter.  Principles of magnetic resonance , 1963 .

[21]  D. DiVincenzo,et al.  Coupled quantum dots as quantum gates , 1998, cond-mat/9808026.

[22]  V. L. Korenev,et al.  Electron and nuclear spin interactions in the optical spectra of single GaAs quantum dots. , 2001, Physical review letters.

[23]  B. E. Kane,et al.  Hydrogenic spin quantum computing in silicon: a digital approach. , 2002, Physical review letters.

[24]  C. Herring,et al.  Asymptotic Exchange Coupling of Two Hydrogen Atoms , 1964 .

[25]  S. Das Sarma,et al.  Overview of spin‐based quantum dot quantum computation , 2002, cond-mat/0211358.

[26]  Philip W. Anderson,et al.  Spectral Diffusion Decay in Spin Resonance Experiments , 1962 .

[27]  V. Privman,et al.  QUANTUM COMPUTATION IN QUANTUM-HALL SYSTEMS , 1997, quant-ph/9707017.

[28]  Steane,et al.  Error Correcting Codes in Quantum Theory. , 1996, Physical review letters.

[29]  Lov K. Grover,et al.  Quantum computation , 1999, Proceedings Twelfth International Conference on VLSI Design. (Cat. No.PR00013).

[30]  S. Sarma,et al.  Disentangling the exchange coupling of entangled donors in the Si quantum computer architecture. , 2002, Physical review letters.

[31]  Jeffrey Bokor,et al.  Solid state quantum computer development in silicon with single ion implantation , 2003 .

[32]  Electron exchange coupling for single-donor solid-state spin qubits , 2003, cond-mat/0309417.

[33]  Shor,et al.  Scheme for reducing decoherence in quantum computer memory. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[34]  M Y Simmons,et al.  Atomically precise placement of single dopants in si. , 2003, Physical review letters.

[35]  R. Jozsa,et al.  Quantum Computation and Shor's Factoring Algorithm , 1996 .

[36]  E. A. Gere,et al.  Electron Spin Resonance Experiments on Donors in Silicon. II. Electron Spin Relaxation Effects , 1959 .

[37]  S. Sarma,et al.  Spintronics: Fundamentals and applications , 2004, cond-mat/0405528.

[38]  K. Nassau,et al.  Spectral Diffusion in Electron Resonance Lines , 1961 .

[39]  S. Sarma,et al.  Spin electronics and spin computation , 2001, cond-mat/0105247.

[40]  Michel Devoret,et al.  Single Charge Tunneling , 1992 .

[41]  Xuedong Hu,et al.  Strain effects on silicon donor exchange: Quantum computer architecture considerations , 2002 .

[42]  David P. DiVincenzo,et al.  Quantum information and computation , 2000, Nature.

[43]  J. P. Gordon,et al.  Microwave Spin Echoes from Donor Electrons in Silicon , 1958 .

[44]  A self-aligned fabrication process for silicon quantum computer devices , 2002, cond-mat/0208374.

[45]  Optical pumping of quantum-dot nuclear spins. , 2003, Physical review letters.

[46]  K. Birgitta Whaley,et al.  Qubit coherence control in a nuclear spin bath , 2005 .

[47]  B. E. Kane.  A silicon-based nuclear spin quantum computer , 1998, Nature.

[48]  John C. Slater,et al.  Quantum Theory of Molecules and Solids , 1951 .

[49]  E. Hahn,et al.  Transient Nuclear Induction and Double Nuclear Resonance in Solids , 1956 .

[50]  Akira Hirai,et al.  Electron Spin Echo Decay Behaviours of Phosphorus Doped Silicon , 1972 .

[51]  John Bardeen,et al.  Nuclear Polarization and Impurity-State Spin Relaxation Processes in Silicon , 1957 .

[52]  Mark A. Eriksson,et al.  Practical design and simulation of silicon-based quantum-dot qubits , 2003 .

[53]  I. Chuang,et al.  Quantum Computation and Quantum Information: Bibliography , 2010 .

[54]  Decoherence and dephasing in spin-based solid state quantum computers , 2001, cond-mat/0108339.

[55]  Xuedong Hu,et al.  Hilbert-space structure of a solid-state quantum computer: Two-electron states of a double-quantum-dot artificial molecule , 2000 .

[56]  D. DiVincenzo,et al.  Quantum computation with quantum dots , 1997, cond-mat/9701055.

[57]  Y. Yafet.  g Factors and Spin-Lattice Relaxation of Conduction Electrons , 1963 .