Designing robust unitary gates: Application to concatenated composite pulses

Abstract

We propose a simple formalism to design unitary gates robust against given systematic errors. This formalism generalizes our previous observation [Y. Kondo and M. Bando, J. Phys. Soc. Jpn. 80, 054002 (2011)] that vanishing dynamical phase in some composite gates is essential to suppress pulse-length errors. By employing our formalism, we derive a new composite unitary gate which can be seen as a concatenation of two known composite unitary operations. The obtained unitary gate has high fidelity over a wider range of error strengths compared to existing composite gates.

Progress in Compensating Pulse Sequences for Quantum Computation

“…Formally U I (v(t) − u(t)) may be studied using a Magnus expansion, however this method is usually impeded by the complexity of the Magnus series. The determination of sequences which compensate simultaneous errors is currently an unresolved problem, although some progress has been made by considering concatenated pulse sequences [31]. As an example relevant to an NMR quantum computer, we now study error models where two systematic errors occur simultaneously and show that these errors can be compensated by concatenation of pulse sequences.…”

“…Quite generally, when a fully compensating pulse sequence is transformed into the interaction frame the resulting propagator must approximate the identity operation [31]. The techniques for constructing compensating pulse sequences discussed in the present article rely on performing a series expansion by powers of for the interaction frame propagator U I ( δu(t); τ, 0), then choosing a set of controls which remove the leading terms of the distortion, and finally transforming back out of the interaction frame.…”

Construction of arbitrary robust one-qubit operations using planar geometry

“…Once a composite pulse robust against amplitude errors has been designed, simultaneous robustness to amplitude and off-resonance errors can be achieved if each of the elementary gates is replaced by a CORPSE pulse [11,13,17]. This procedure is called nesting.…”

“…Controlled-NOT and SWAP gates robust against coupling strength error were designed for Ising-type interactions [12]. Furthermore, propagators with simultaneous robustness to two types of systematic errors have been obtained [11,[13][14][15][16][17][18].…”

“…In recent works [11][12][13][14][15][16][17][18], several composite pulses were proposed and their properties investigated. For example, it was shown that any sequence robust against amplitude errors is a geometric quantum gate using AharonovAnandan phase [19,20].…”