Quantum computers interact with the environment through decoherence, resulting in information from a computation degrading over time. This introduces errors into a computation. In Chapter 3, Quantum States, Quantum Registers, and Measurement, we discussed ways to quantify this information loss; T1 helps quantify how quickly the qubits on a given hardware experience energy loss due to environment interaction (energy loss results in a change in frequency, causing decoherence), which can cause a bit flip, and T2 helps quantify how quickly the qubits experience a phase difference due to interaction with the environment, again a cause of decoherence. The bigger T1 and T2, the more robust a quantum computation will be to errors.
IBM QX hardware and other quantum computing companies try to raise T1 and, T2 but at the present moment, and for the foreseeable future, T1 and, T2 are so low that every practical computation is likely to contain errors. These errors can come in the form of a phase difference to that expected from the ideal computation, or of a bit flip to that expected from the ideal computation. Quantum algorithms cannot run effectively without quantum error correction, to compensate for these errors. Quantum error correction functions by spreading out information from a single qubit to multiple qubits, meaning that an algorithm' without quantum error correction' will use many fewer qubits than one with quantum error correction. Since QEC is needed for practical quantum computing in the gate model of quantum computing, this means that the number of qubits needed to implement practical algorithms is much higher than the minimum number of qubits the algorithm theoretically requires.