When trying to solve a problem using quantum information processing, an important issue is to determine what physical resources are available and how much of each resource is needed for the solution. As mentioned before, in classical information, the primary resources are bits and operations. The number of bits used by an algorithm is called its ``space'' requirement. The number of operations used is called its ``time'' requirement. If parallel computation is available, one can distinguish between the total number of operations (``work'') and the number of parallel steps (``time'').
When quantum information processing is used, the classical resources are still relevant for running the computer that controls the quantum system and performs any pre- and post-processing tasks. The main quantum resources are analogous to the classical ones: ``quantum space'' is the number of qubits needed, and ``quantum time'' the number of quantum gates. Because it turns out that reset operations have a thermodynamic cost, one can count irreversible quantum operations separately. This accounting of the resource requirements of algorithms and of the minimum resources needed to solve problems forms the foundations of quantum complexity theory.
As a simple example of resource accounting, consider the algorithm for
the parity problem. No classical computation is required to decide
which quantum gates to apply, or to determine the answer from the
measurement. The quantum network consists of a total of 11 quantum
gates (including the 
's and 
's operations) and
one oracle call (the application of the black box). In the case of
oracle problems, one usually counts the number of oracle calls first,
as we have done in discussing the algorithm. The network is readily
parallelized to reduce the time resource to 6 steps.