Concatenated Composite Pulses Compensating Simultaneous Systematic Errors

Abstract

In NMR experiments and quantum computation, many pulse (quantum gate) sequences called the composite pulses, were developed to suppress one of two dominant errors; a pulse length error and an off-resonance error. We describe, in this paper, a general prescription to design a single-qubit concatenated composite pulse (CCCP) that is robust against two types of errors simultaneously. To this end, we introduce a new property, which is satisfied by some composite pulses and is sufficient to obtain a CCCP. Then we introduce a general method to design CCCPs with shorter execution time and less number of pulses. DRAFT taneously, although they are restricted within null operation and π-rotation (NOT gate) of a nuclear spin. In order to realize a composite pulse which is robust against these two errors simultaneously and without any restriction, we designed a ConCatenated Composite Pulse (CCCP) by concatenating CORPSE and SCROFULOUS. 16) The CCCP reported previously 16) consists of 3 composite pulses, each of which consists of 3 elementary pulses. Consequently, this CCCP is made of 9 pulses in total. Although this CCCP is robust against both PLE and ORE, its execution time is considerably longer than the corresponding elementary pulse. CCCPs made of less number of elementary pulses are certainly desirable from a viewpoint of decoherence suppression.Establishing general prescription to design a CCCP and its improvement are the subjects of this paper. Some composite pulses have interesting property, which we call the residualerror-preserving (REP) property. Employing two types of composite pulses with mutually exclusive REP properties is essential to design a successful CCCP robust against both PLE and ORE. By using this method, we obtain many CCCPs systematically. Moreover, we further

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.…”

“…The time cost to make a rotation robust depends on its particular decomposition and on which composite pulse is employed [13]. To make a comparison to the sequence of Eq.…”

“…One possible strategy to make this sequence robust against amplitude errors is to replace each elementary gate by a composite pulse insensitive to such errors. Since available nontrivial composite pulses consist of at least three pulses [13], the resulting robust rotation consists of a sequence of nine elementary pulses. However, in principle, just three elementary operations are necessary to define a robust arbitrary unitary: the number of free parameters in three gates is six, whereas the zeroth and first order perturbation terms with respect to ǫ must satisfy three constraints each.…”

“…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].…”