Nested Uhrig dynamical decoupling (NUDD) is a highly efficient quantum error suppression scheme that builds on optimized single axis UDD sequences. We prove the universality of NUDD and analyze its suppression of different error types in the setting
of generalized control pulses. We present an explicit lower bound for the decoupling order of each error type, which we relate to the sequence orders of the nested UDD layers. We find that the error suppression capabilities of NUDD are strongly dependent on the parities and relative magnitudes of all nested UDD sequence orders. This allows us to predict the optimal arrangement of sequence orders. We test and confirm our analysis using numerical simulations.
It is well known that the quantum Zeno effect can protect specific quantum states from decoherence by using projective measurements. Here we combine the theory of weak measurements with stabilizer quantum error correction and detection codes. We deri
ve rigorous performance bounds which demonstrate that the Zeno effect can be used to protect appropriately encoded arbitrary states to arbitrary accuracy, while at the same time allowing for universal quantum computation or quantum control.
We present a fault-tolerant semi-global control strategy for universal quantum computers. We show that N-dimensional array of qubits where only (N-1)-dimensional addressing resolution is available is compatible with fault-tolerant universal quantum c
omputation. What is more, we show that measurements and individual control of qubits are required only at the boundaries of the fault-tolerant computer, i.e. holographic fault-tolerant quantum computation. Our model alleviates the heavy physical conditions on current qubit candidates imposed by addressability requirements and represents an option to improve their scalability.
We introduce a scheme to perform universal quantum computation in quantum cellular automata (QCA) fashion in arbitrary subsystem dimension (not necessarily finite). The scheme is developed over a one spatial dimension $N$-element array, requiring onl
y mirror symmetric logical encoding and global pulses. A mechanism using ancillary degrees of freedom for subsystem specific measurement is also presented.
