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Qubit Transport and Fault-tolerant Architectures

Lloyd C. L. Hollenberg, Andrew D. Greentree, Cameron J. Wellard, Austin G. Fowler, Jared H. Cole

Published Jan 1, 2006• 0 citations
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Abstract

We review a new adiabatic scheme - coherent spin transport by adiabatic passage (CSTAP) - for physical qubit transport particularly suited to atomic and solid-state systems. Several applications immediately follow, including a 2D Si:P donor electron spin architecture for quantum computing, and protocols for generating entangled states across non-local qubits.

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arXiv:0903.1142•Physical Review B•Jul 7, 2009•30 citations
We review a new adiabatic scheme - coherent spin transport by adiabatic passage (CSTAP) - for physical qubit transport particularly suited to atomic and solid-state systems. Several applications immediately follow, including a 2D Si:P donor electron spin architecture for quantum computing, and protocols for generating entangled states across non-local qubits.
Solid state quantum computer architectures are often touted as inherently scalable on the basis of proven classical architecture miniaturisation - i.e. through sheer ease of component replication. However, this weak scaling argument misses the vast complexity of the implementation of fault-tolerant quantum protocols required to protect quantum information processing against errors. In a successful design of strongly scalable quantum computer architecture, highly non-trivial requirements such as qubit transport, logic gates for physically separated qubits, fast read-out and resources for classical processing and error correction must be incorporated. We review a new adiabatic scheme coherent (spin) transport by adiabatic passage (CTAP) for physical qubit transport particularly suited to atomic and solid-state systems. The tunnelling rates, transfer times and the effects of decoherence are calculated for CTAP using phosphorous donors in silicon. Using CTAP qubit transport we have proposed a bi-linear donor electron spin architecture with potential for scale-up to fault-tolerant operation. This architecture allows for the distribution of interaction, storage and readout regions and incorporates non-nearest-neighbour interactions between qubits. The transport rails which provide these non-local interactions, also provide alternative pathways to avoid non-functioning regions. The key questions under investigation are whether one can: perform fault-tolerant quantum computation on such an architecture, and determine quantitative estimates of the fault-tolerant threshold.
Qubit transport has been identified as vital in improving quantum error correction thresholds in scalable quantum computer architectures. Introducing practical transport in the solid-state is problematic, but in phosphorus in silicon implementations we have shown an interesting adiabatic protocol for qubit transfer, coherent tunneling adiabatic passage (CTAP). Here we review the role of CTAP as a quantum wire, highlighting the protocol and the temporal scaling as the length of the transport chain is increased. We also highlight an extension of CTAP to generate spatial superposition states which demonstrates some of the flexibility of quantum electronic structures over quantum optical systems.
We introduce an adiabatic transfer protocol for spin states in large quantum dot arrays that is based on time-dependent modulation of the Heisenberg exchange interaction in the presence of a magnetic field gradient. We refer to this protocol as spin-CTAP (coherent transport by adiabatic passage) in analogy to a related protocol developed for charge-state transfer in quantum dot arrays. The insensitivity of this adiabatic protocol to pulse imperfections has potential advantages for reading out extended spin qubit arrays. When the static exchange interaction varies across the array, a quantum-controlled version of spin-CTAP is possible, where the transfer process is conditional on the spin states in the middle of the array. This conditional operation can be used to generate NNN-qubit entangled GHZ states. Using a realistic noise model, we analyze the robustness of the spin-CTAP operations and find that high-fidelity (>95>95%>95) spin eigenstate transfer and GHZ state preparation is feasible in current devices.
A solid-state analog of stimulated Raman adiabatic passage can be implemented in a triple-well solid-state system to coherently transport an electron across the wells with exponentially suppressed occupation in the central well at any point of time. Termed coherent-tunneling adiabatic passage (CTAP), this method provides a robust way to transfer quantum information encoded in the electronic spin across a chain of quantum dots or donors. Using large-scale atomistic tight-binding simulations involving over $3.5\ifmmode\times\else\texttimes\fi{}{10}^{6}$ atoms, we verify the existence of a CTAP pathway in a realistic solid-state system: gated triple donors in silicon. Realistic gate profiles from commercial tools were combined with tight-binding methods to simulate gate control of the donor to donor tunnel barriers in the presence of crosstalk. As CTAP is an adiabatic protocol, it can be analyzed by solving the time-independent problem at various stages of the pulse justifying the use of time-independent tight-binding methods to this problem. This work also involves the first atomistic treatment to translate the three-state-based quantum-optics type of modeling into a solid-state description beyond the ideal localization assumption. Our results show that a three-donor CTAP transfer, with interdonor spacing of 15 nm can occur on time scales greater than 23 ps, well within experimentally accessible regimes. The method not only provides a tool to guide future CTAP experiments but also illuminates the possibility of system engineering to enhance control and transfer times.