Subsystem pseudopure states

A critical step in experimental quantum information processing QIP is to implement control of quantum systems protected against decoherence via informational encodings, such as quantum error-correcting codes, noiseless subsystems, and decoherence-free subspaces. These encodings lead to the promise of fault-tolerant QIP, but they come at the expense of resource overheads. Part of the challenge in studying control over multiple logical qubits is that QIP testbeds have not had sufficient resources to analyze encodings beyond the simplest ones. The most relevant resources are the number of available qubits and the cost to initialize and control them. Here we demonstrate an encoding of logical information that permits control over multiple logical qubits without full initialization, an issue that is particularly challenging in liquid-state NMR. The method of subsystem pseudopure states will allow the study of decoherence control schemes on up to six logical qubits using liquid-state NMR implementations.