Initialize instruction should unroll to reset + gates

[chriseclectic]

What is the expected enhancement?

Make initialize a gate element that can be used directly in Aer simulators, and unrolled into reset + gates by the transpiler for devices and noisey simulations.

Current version

The (current) format for initialize as a QuantumCircuit method is circ.initialize(statevec, qr) to initialise a quantum register in a fixed state.

Proposed changes

• Change intialize it to accept either single-qubits or a list (or register) of qubits and to be treated as an explicit reset operation followed by gates to prepare the input state.
• On simulators and devices that support reset this would allow initialize to be placed anywhere in a circuit acting on a subset of qubits.
• To simplify the transpiler could remove unneeded reset operations.
  • If a qubit has more than 1 reset operation in a row
  • If reset is determined to be the first operation on a given qubit (Note: but for noisy simulations one might want to leave explicit reset operations at the start of a circuit to allow for reset errors)

Circuit method

The circuit method could be initialize(state, qubits), where state is a list/ndarray that is a valid statevector, and qubits can be either a full quantum register, single-qubit, or list/tuple of qubits that match the dimension of the state vector.

Qobj serialization

A suggestion for how this could be directly serialized to qobj (if the backend supports the "initialize" instruction in its basis gates) is

{"name": "initialize", "qubits": list[int], "params": complex_vector}

Example:

Consider a 2-qubit circuit, where I want to initialize both qubits into the |1> state, the following should all be equivalent:

qr = QuantumRegister(2)

# Method 1
circ1 = QuantumCircuit(qr)
circ1.initialize([0, 0, 0, 1], qr)

# Method 2
circ2 = QuantumCircuit(qr)
circ2.initialize([0, 0, 0, 1], (qr[0], qr[1]))

# Method 3
circ3 = QuantumCircuit(qr)
circ3.initialize([0, 1], qr[0])
circ3.initialize([0, 1], qr[1])


# Implementation
circ0 = QuantumCircuit(qr)
circ0.reset(qr[0])
circ0.x(qr[0])
circ0.reset(qr[1])
circ0.x(qr[1])

[ajavadia]

This is done via #1816. But I'll keep it open because the reset part is not done yet.

[1ucian0]

I think #2139 is that part that was missing in this issue. Feel free to reopen otherwise.