How does one implement Hadamard gate in Pauli-based computation? 6 Pauli-based computation supposedly gives the full Clifford group For instance, the CNOT can be implemented using joint ZZ measurement and joint XX measurement and using an additional ancilla qubit To generate the Clifford group, it would be sufficient to have similar gadgets for S and H How does one achieve a hadamard gate just using
quantum memory - Qubit demands of Grovers Algorithm - Quantum . . . The ancilla shouldn't be entangled with the main register after every iteration and the same ancilla qubit should be able to be reused for every iteration, in fact the ancilla's state shouldn't change at all due to phase kickback The ancilla-aided version of the Grover oracle is implemented as a controlled gate targeting the ancilla applied depending on whether a computational basis state on
Specifying Ancilla qubits for initial_layout parameter in qiskit . . . How do I specify this ancilla qubit in my initial_layout parameter when I am trying to transpile the circuit using qiskit transpile? Or alternatively, how do I assign only 4 of these virtual qubits to 5 physical qubits using the same initial_layout parameter?
Why doesnt reading the ancilla qubit in Quantum Error Correction kill . . . The ancilla tells us about the errors, not the underlying logical state (In classical terms the ancilla in this example is a "parity check bit" - the quantum difference being we that we have to generate this bit coherently, without revealing entangling with any further information about the underlying bits )
error correction - Repetition of syndrome measurement before . . . The syndromes we use to decode the ancilla block are the multiple rounds of syndromes and 1-round of syndromes constructed by the destructive measurements apply a logical CNOT gate, and perform transversal physical destructive measurements
quantum algorithms - Ancilla intuition, when to use them, how to . . . In the above linked paper, the authors were able to greatly reduce the circuit depth required for implementing an arbitrary quantum state by introducing an ancilla register with the same size as the system register and performing controlled swaps between them This seems to be similar to a lot of width vs depth tradeoff people observe in