  Methods that preserve coherence broadly impact all quantum information
processing and metrology applications. Dynamical decoupling methods accomplish
this by protecting qubits in noisy environments but are typically constrained
to the limit where the qubits themselves are non-interacting. Here we consider
the alternate regime wherein the inter-qubit couplings are of the same order as
dephasing interactions with the environment. We propose and demonstrate a
multi-pulse protocol that protects transverse spin states by suitably
Hamiltonian engineering the inter-spin coupling while simultaneously
suppressing dephasing noise on the qubits. We benchmark the method on 13C
nuclear spin qubits in diamond, dipolar coupled to each other and embedded in a
noisy electronic spin bath, and hyperpolarized via optically pumped NV centers.
We observe effective state lifetimes of 13C nuclei $T_2^{\prime}\approx$2.5s at
room temperature, an extension of over 4700-fold over the conventional
$T_2^{\ast}$ free induction decay. The spins are continuously interrogated
during the applied quantum control, resulting in 13C NMR line narrowing and an
$>$500-fold boost in SNR due to the lifetime extension. Together with
hyperpolarization spin interrogation is accelerated by $>10^{11}$ over
conventional 7T NMR. This work suggests strategies for the dynamical decoupling
of coupled qubit systems with applications in a variety of experimental
platforms.
