We theoretically consider possible errors in solid-state quantum computation due to the interplay of the complex solid-state environment and gate imperfections. In particular, we study two examples of gate operations in the opposite ends of the gate speed spectrum, an adiabatic gate operation in electron-spin-based quantum dot quantum computation and a sudden gate operation in Cooper-pair-box superconducting quantum computation. We evaluate quantitatively the nonadiabatic operation of a two-qubit gate in a two-electron double quantum dot. We also analyze the nonsudden pulse gate in a Cooper-pair-box-based quantum-computer model. In both cases our numerical results show strong influences of the higher excited states of the system on the gate operation, clearly demonstrating the importance of a detailed understanding of the relevant Hilbert-space structure on the quantum-computer operations.
High-fidelity quantum gates are a cornerstone of any quantum computing and communications architecture. Realizing such control in the presence of realistic errors at the level required for beyond-threshold quantum error correction is a long-standing challenge for all quantum hardware platforms. Here we theoretically develop and experimentally demonstrate error-protected quantum gates in a solid-state quantum network node. Our work combines room-temperature randomized benchmarking with a new class of composite pulses that are simultaneously robust to frequency and amplitude, affecting random and systematic errors. We introduce Power-Unaffected, Doubly-Detuning-Insensitive Gates (PUDDINGs) -- a theoretical framework for constructing conditional gates with immunity to both amplitude and frequency errors. For single-qubit and two-qubit CNOT gate demonstrations in a solid-state nitrogen-vacancy (NV) center in diamond, we systematically measure an improvement in the error per gate up to a factor of 9. By projecting the application of PUDDING to cryogenic temperatures we show a record two-qubit error per gate of
1.2×10−5, corresponding to a fidelity of
99.9988%, far below the thresholds required by surface and color code error correction. These results present viable building blocks for a new class of fault-tolerant quantum networks and represent the first experimental realization of error-protected conditional gates in solid-state systems.
In this paper we investigate the effect of dephasing on proposed quantum gates for the solid-state Kane quantum computing architecture. Using a simple model of the decoherence, we find that the typical error in a controlled-NOT gate is $8.3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$. We also compute the fidelities of
Z,
X, swap, and controlled
Z operations under a variety of dephasing rates. We show that these numerical results are comparable with the error threshold required for fault tolerant quantum computation.