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In order to achieve fault-tolerant quantum computation, we need to repeat thefollowing sequence of four steps: First, perform 1 or 2 qubit quantum gates (inparallel if possible). Second, do a syndrome measurement on a subset of thequbits. Third, perform a fast classical computation to establish which errorshave occurred (if any). Fourth, depending on the errors, we apply a correctionstep. Then the procedure repeats with the next sequence of gates. In order forthese four steps to succeed, we need the error rate of the gates to be below acertain threshold. Unfortunately, the error rates of current quantum hardwareare still too high. On the other hand, current quantum hardware platforms aredesigned with these four steps in mind. In this work we make use of thisfour-step scheme not to carry out fault-tolerant computations, but to enhanceshort, constant-depth, quantum circuits that perform 1 qubit gates andnearest-neighbor 2 qubit gates. To explore how this can be useful, we study acomputational model which we call Local Alternating Quantum ClassicalComputations (LAQCC). In this model, qubits are placed in a grid allowingnearest neighbor interactions; the quantum circuits are of constant depth withintermediate measurements; a classical controller can perform log-depthcomputations on these intermediate measurement outcomes to control futurequantum operations. This model fits naturally between quantum algorithms in theNISQ era and full fledged fault-tolerant quantum computation. We show thatLAQCC circuits can create long-ranged interactions, which constant-depthquantum circuits cannot achieve, and use it to construct a range of usefulmulti-qubit gates. With these gates, we create three new state preparationprotocols for a uniform superposition over an arbitrary number of states,W-states and Dicke states.

State preparation by shallow circuits using feed forward