Add support for vectors of parameters

Some circuits need to make use of a large, fixed number of parameters. For example, variational algorithms setting rotation angles as independent parameters, to be sourced as an array from a classical optimizer. See the VariationalForm class and RYRZ algorithm in aqua as an example.

https://github.com/Qiskit/qiskit-aqua/blob/40218c2e6ea6c76791139101ac005b9a2bf7b256/qiskit/aqua/components/variational_forms/ryrz.py

With the current Parameter definition, this is possible but cumbersome. It requires the user to define, name and manage a Parameter instance for each gate they plan to vary.

It should be possible to define a parameter vector of fixed length, and access elements of that vector as individual parameters.

Possible syntax:

v = ParameterVector('v', 99)

v[10] # => Parameter(v[10])

qc = QuantumCircuit(3)
qr = qc.qregs[0]

for (t1, t2, t3) in zip(v[::3], v[1::3], v[2::3]):
  qc.cx(qr[:-1], qr[1:])
  qc.u3(t1, t2, t3, qr[0])

qc.bind_parameters({v = [...]}) 

When binding, we should verify that the supplied list matches the length of the vector and that all parameters in the vector are bound. (Partial binding within a vector is not supported.)

[dongreenberg]

Just to close this loop before I submit, the interface now looks like:

        qubits = 5
        depth = 4
        ryrz = QuantumCircuit(qubits, name='ryrz')
        theta = ParameterVector('θ0', length=len(ryrz.qubits) * 2)
        theta_iter = iter(theta)
        for q in ryrz.qubits:
            ryrz.ry(next(theta_iter), q)
            ryrz.rz(next(theta_iter), q)

        cxs = QuantumCircuit(qubits-1, name='cxs')
        for i, q in enumerate(cxs.qubits[:-1:2]):
            cxs.cx(cxs.qubits[2*i], cxs.qubits[2*i+1])

        paramvecs = [theta]
        qc = QuantumCircuit(qubits)
        for i in range(depth):
            theta_l = ParameterVector('θ{}'.format(i+1), length=len(ryrz.qubits) * 2)
            ryrz_inst = ryrz.to_instruction(parameter_map={theta: theta_l})
            paramvecs += [theta_l]
            qc.append(ryrz_inst, qargs=qc.qubits)
            qc.append(cxs, qargs=qc.qubits[1:])
            qc.append(cxs, qargs=qc.qubits[:-1])
            qc.barrier()

        print(qc.decompose().draw(line_length=1000))
        print(qc.draw(line_length=1000))
        backend = BasicAer.get_backend('qasm_simulator')
        qc_aer = transpile(qc, backend)
        print(qc_aer.draw(line_length=1000))

producing:

        ┌───────────┐┌───────────┐           ░ ┌───────────┐┌───────────┐           ░ ┌───────────┐┌───────────┐           ░ ┌───────────┐┌───────────┐           ░ 
q_0: |0>┤ Ry(θ1[0]) ├┤ Rz(θ1[1]) ├───────■───░─┤ Ry(θ2[0]) ├┤ Rz(θ2[1]) ├───────■───░─┤ Ry(θ3[0]) ├┤ Rz(θ3[1]) ├───────■───░─┤ Ry(θ4[0]) ├┤ Rz(θ4[1]) ├───────■───░─
        ├───────────┤├───────────┤     ┌─┴─┐ ░ ├───────────┤├───────────┤     ┌─┴─┐ ░ ├───────────┤├───────────┤     ┌─┴─┐ ░ ├───────────┤├───────────┤     ┌─┴─┐ ░ 
q_1: |0>┤ Ry(θ1[2]) ├┤ Rz(θ1[3]) ├──■──┤ X ├─░─┤ Ry(θ2[2]) ├┤ Rz(θ2[3]) ├──■──┤ X ├─░─┤ Ry(θ3[2]) ├┤ Rz(θ3[3]) ├──■──┤ X ├─░─┤ Ry(θ4[2]) ├┤ Rz(θ4[3]) ├──■──┤ X ├─░─
        ├───────────┤├───────────┤┌─┴─┐└───┘ ░ ├───────────┤├───────────┤┌─┴─┐└───┘ ░ ├───────────┤├───────────┤┌─┴─┐└───┘ ░ ├───────────┤├───────────┤┌─┴─┐└───┘ ░ 
q_2: |0>┤ Ry(θ1[4]) ├┤ Rz(θ1[5]) ├┤ X ├──■───░─┤ Ry(θ2[4]) ├┤ Rz(θ2[5]) ├┤ X ├──■───░─┤ Ry(θ3[4]) ├┤ Rz(θ3[5]) ├┤ X ├──■───░─┤ Ry(θ4[4]) ├┤ Rz(θ4[5]) ├┤ X ├──■───░─
        ├───────────┤├───────────┤└───┘┌─┴─┐ ░ ├───────────┤├───────────┤└───┘┌─┴─┐ ░ ├───────────┤├───────────┤└───┘┌─┴─┐ ░ ├───────────┤├───────────┤└───┘┌─┴─┐ ░ 
q_3: |0>┤ Ry(θ1[6]) ├┤ Rz(θ1[7]) ├──■──┤ X ├─░─┤ Ry(θ2[6]) ├┤ Rz(θ2[7]) ├──■──┤ X ├─░─┤ Ry(θ3[6]) ├┤ Rz(θ3[7]) ├──■──┤ X ├─░─┤ Ry(θ4[6]) ├┤ Rz(θ4[7]) ├──■──┤ X ├─░─
        ├───────────┤├───────────┤┌─┴─┐└───┘ ░ ├───────────┤├───────────┤┌─┴─┐└───┘ ░ ├───────────┤├───────────┤┌─┴─┐└───┘ ░ ├───────────┤├───────────┤┌─┴─┐└───┘ ░ 
q_4: |0>┤ Ry(θ1[8]) ├┤ Rz(θ1[9]) ├┤ X ├──────░─┤ Ry(θ2[8]) ├┤ Rz(θ2[9]) ├┤ X ├──────░─┤ Ry(θ3[8]) ├┤ Rz(θ3[9]) ├┤ X ├──────░─┤ Ry(θ4[8]) ├┤ Rz(θ4[9]) ├┤ X ├──────░─
        └───────────┘└───────────┘└───┘      ░ └───────────┘└───────────┘└───┘      ░ └───────────┘└───────────┘└───┘      ░ └───────────┘└───────────┘└───┘      ░ 
        ┌────────────────────────────────────────────────────────────────────┐        ┌──────┐ ░ ┌────────────────────────────────────────────────────────────────────┐        ┌──────┐ ░ ┌────────────────────────────────────────────────────────────────────┐        ┌──────┐ ░ ┌────────────────────────────────────────────────────────────────────┐        ┌──────┐ ░ 
q_0: |0>┤0                                                                   ├────────┤0     ├─░─┤0                                                                   ├────────┤0     ├─░─┤0                                                                   ├────────┤0     ├─░─┤0                                                                   ├────────┤0     ├─░─
        │                                                                    │┌──────┐│      │ ░ │                                                                    │┌──────┐│      │ ░ │                                                                    │┌──────┐│      │ ░ │                                                                    │┌──────┐│      │ ░ 
q_1: |0>┤1                                                                   ├┤0     ├┤1     ├─░─┤1                                                                   ├┤0     ├┤1     ├─░─┤1                                                                   ├┤0     ├┤1     ├─░─┤1                                                                   ├┤0     ├┤1     ├─░─
        │                                                                    ││      ││  cxs │ ░ │                                                                    ││      ││  cxs │ ░ │                                                                    ││      ││  cxs │ ░ │                                                                    ││      ││  cxs │ ░ 
q_2: |0>┤2 ryrz(θ1[0],θ1[1],θ1[2],θ1[3],θ1[4],θ1[5],θ1[6],θ1[7],θ1[8],θ1[9]) ├┤1     ├┤2     ├─░─┤2 ryrz(θ2[0],θ2[1],θ2[2],θ2[3],θ2[4],θ2[5],θ2[6],θ2[7],θ2[8],θ2[9]) ├┤1     ├┤2     ├─░─┤2 ryrz(θ3[0],θ3[1],θ3[2],θ3[3],θ3[4],θ3[5],θ3[6],θ3[7],θ3[8],θ3[9]) ├┤1     ├┤2     ├─░─┤2 ryrz(θ4[0],θ4[1],θ4[2],θ4[3],θ4[4],θ4[5],θ4[6],θ4[7],θ4[8],θ4[9]) ├┤1     ├┤2     ├─░─
        │                                                                    ││  cxs ││      │ ░ │                                                                    ││  cxs ││      │ ░ │                                                                    ││  cxs ││      │ ░ │                                                                    ││  cxs ││      │ ░ 
q_3: |0>┤3                                                                   ├┤2     ├┤3     ├─░─┤3                                                                   ├┤2     ├┤3     ├─░─┤3                                                                   ├┤2     ├┤3     ├─░─┤3                                                                   ├┤2     ├┤3     ├─░─
        │                                                                    ││      │└──────┘ ░ │                                                                    ││      │└──────┘ ░ │                                                                    ││      │└──────┘ ░ │                                                                    ││      │└──────┘ ░ 
q_4: |0>┤4                                                                   ├┤3     ├─────────░─┤4                                                                   ├┤3     ├─────────░─┤4                                                                   ├┤3     ├─────────░─┤4                                                                   ├┤3     ├─────────░─
        └────────────────────────────────────────────────────────────────────┘└──────┘         ░ └────────────────────────────────────────────────────────────────────┘└──────┘         ░ └────────────────────────────────────────────────────────────────────┘└──────┘         ░ └────────────────────────────────────────────────────────────────────┘└──────┘         ░ 
        ┌───────────────┐┌───────────┐           ░ ┌───────────────┐┌───────────┐           ░ ┌───────────────┐┌───────────┐           ░ ┌───────────────┐┌───────────┐           ░ 
q_0: |0>┤ U3(θ1[0],0,0) ├┤ U1(θ1[1]) ├───────■───░─┤ U3(θ2[0],0,0) ├┤ U1(θ2[1]) ├───────■───░─┤ U3(θ3[0],0,0) ├┤ U1(θ3[1]) ├───────■───░─┤ U3(θ4[0],0,0) ├┤ U1(θ4[1]) ├───────■───░─
        ├───────────────┤├───────────┤     ┌─┴─┐ ░ ├───────────────┤├───────────┤     ┌─┴─┐ ░ ├───────────────┤├───────────┤     ┌─┴─┐ ░ ├───────────────┤├───────────┤     ┌─┴─┐ ░ 
q_1: |0>┤ U3(θ1[2],0,0) ├┤ U1(θ1[3]) ├──■──┤ X ├─░─┤ U3(θ2[2],0,0) ├┤ U1(θ2[3]) ├──■──┤ X ├─░─┤ U3(θ3[2],0,0) ├┤ U1(θ3[3]) ├──■──┤ X ├─░─┤ U3(θ4[2],0,0) ├┤ U1(θ4[3]) ├──■──┤ X ├─░─
        ├───────────────┤├───────────┤┌─┴─┐└───┘ ░ ├───────────────┤├───────────┤┌─┴─┐└───┘ ░ ├───────────────┤├───────────┤┌─┴─┐└───┘ ░ ├───────────────┤├───────────┤┌─┴─┐└───┘ ░ 
q_2: |0>┤ U3(θ1[4],0,0) ├┤ U1(θ1[5]) ├┤ X ├──■───░─┤ U3(θ2[4],0,0) ├┤ U1(θ2[5]) ├┤ X ├──■───░─┤ U3(θ3[4],0,0) ├┤ U1(θ3[5]) ├┤ X ├──■───░─┤ U3(θ4[4],0,0) ├┤ U1(θ4[5]) ├┤ X ├──■───░─
        ├───────────────┤├───────────┤└───┘┌─┴─┐ ░ ├───────────────┤├───────────┤└───┘┌─┴─┐ ░ ├───────────────┤├───────────┤└───┘┌─┴─┐ ░ ├───────────────┤├───────────┤└───┘┌─┴─┐ ░ 
q_3: |0>┤ U3(θ1[6],0,0) ├┤ U1(θ1[7]) ├──■──┤ X ├─░─┤ U3(θ2[6],0,0) ├┤ U1(θ2[7]) ├──■──┤ X ├─░─┤ U3(θ3[6],0,0) ├┤ U1(θ3[7]) ├──■──┤ X ├─░─┤ U3(θ4[6],0,0) ├┤ U1(θ4[7]) ├──■──┤ X ├─░─
        ├───────────────┤├───────────┤┌─┴─┐└───┘ ░ ├───────────────┤├───────────┤┌─┴─┐└───┘ ░ ├───────────────┤├───────────┤┌─┴─┐└───┘ ░ ├───────────────┤├───────────┤┌─┴─┐└───┘ ░ 
q_4: |0>┤ U3(θ1[8],0,0) ├┤ U1(θ1[9]) ├┤ X ├──────░─┤ U3(θ2[8],0,0) ├┤ U1(θ2[9]) ├┤ X ├──────░─┤ U3(θ3[8],0,0) ├┤ U1(θ3[9]) ├┤ X ├──────░─┤ U3(θ4[8],0,0) ├┤ U1(θ4[9]) ├┤ X ├──────░─
        └───────────────┘└───────────┘└───┘      ░ └───────────────┘└───────────┘└───┘      ░ └───────────────┘└───────────┘└───┘      ░ └───────────────┘└───────────┘└───┘      ░ 

[dongreenberg]

I like the array (θ[n]) notation better, will change to that.