Keeping a single qubit alive by experimental dynamic decoupling

D J Szwer (1, 2) , S C Webster (1) , a M Steane (1) , D M Lucas (1)

1 Department of Physics [Oxford]
2 Department of Physics

We demonstrate the use of dynamic decoupling techniques to extend the coherence time of a single memory qubit by nearly two orders of magnitude. By extending the Hahn spin-echo technique to correct for unknown, arbitrary polynomial variations in the qubit precession frequency, we show analytically that the required sequence of π-pulses is identical to the Uhrig dynamic decoupling (UDD) sequence. We compare UDD and CPMG sequences applied to a single 43 Ca + trapped-ion qubit and find that they afford comparable protection in our ambient noise environment. Keeping a single qubit alive by experimental dynamic decoupling 2 Dynamic decoupling (DD) is a general technique for maintaining the phase coherence of a quantum state, with particular importance for protecting the quantum information stored in the memory qubits of a quantum computer [ 1 ]. The simplest example is the Hahn spin-echo [ 2 ], a single π-pulse which protects against an arbitrary and unknown constant offset in the qubit's precession frequency [ 3, 4 ]. When the state is subject to a time-varying offset due to, for example, magnetic field noise, it can be protected by a sequence of many π-pulses. One of these, the Carr-Purcell-Meiboom-Gill (CPMG) sequence, is well known in the field of nuclear magnetic resonance [ 5 ]. More recently, other sequences have been investigated specifically for their dynamic decoupling properties, such as Periodic DD, Concatenated DD [ 6 ], random decoupling [ 7 ], composite schemes [ 8 ], and local optimisation [ 9, 10 ] ; a recent review by Yang, Wang and Liu contains further information and references [ 11 ]. In this paper, we derive a dynamic decoupling sequence in a particularly intuitive manner, as an extension to the spin-echo [ 2 ]. We prove that with n pulses, the sequence can cancel out all the dephasing that would be caused by the frequency varying as an (n − 1)th order polynomial function of time, without knowledge of the polynomial coefficients. This sequence is identical to the Uhrig Dynamic Decoupling (UDD) sequence [ 12, 13 ], which was originally derived by considering the interaction of a spin qubit with a bosonic bath. We implement the sequence on a single 43 Ca + ion, demonstrating that the coherence time of this qubit is significantly increased, and compare it with the CPMG sequence. Suppose an arbitrary qubit state is prepared at time 0, and we want to recover it at time τ. The pulse sequence is a series of (assumed ideal and instantaneous) π-pulses at times α 1 τ, α 2 τ,..., α n τ, where the α i are to be found. We have remarked that a single Hahn spin-echo will correct for a constant frequency offset. If the offset varies linearly with time, we can correct the phase error with two π-pulses at t = 1 4 and 3 4, where t = time/τ (Figure 1a). To generalise further, postulate that n pulses suffice to correct for a frequency variation δ(t) that is an (n − 1)th-order polynomial in time (Figure 1b):

Mots clés: Physical Sciences

D J Szwer, S C Webster, a M Steane, D M Lucas. Keeping a single qubit alive by experimental dynamic decoupling. Journal of Physics B: Atomic, Molecular and Optical Physics, 2011, 44 (2), pp.25501. ⟨10.1088/0953-4075/44/2/025501⟩. ⟨hal-00597871⟩