Error corrected variational algorithms

An apparatus comprising:

• quantum hardware comprising:
• a quantum system;
• one or more control devices configured to generate and apply quantum circuits to the quantum system;
• and
• one or more classical processors;
• wherein the apparatus is configured to perform operations for approximating a target quantum state, the operations comprising:
• receiving data representing the target quantum state of a quantum system, wherein the target quantum state is defined as a result of applying a specific quantum circuit to an initial quantum state of the quantum system;
• determining an approximate quantum circuit that approximates the specific quantum circuit by adaptively adjusting a number of T gates available to the specific quantum circuit;
• and
• applying the determined approximate quantum circuit to the initial quantum state to obtain an approximation of the target quantum state.