[Circuit renderer] Compact rendering of classically controlled gate

[Dima Fedoriaka (fedimser)]

• Object model changes (circuit.rs/circuit.ts):
  • Added ControlRegister to represent a register (classical or quantum) that is used to as control to a gate.
  • ControlRegister is Register plus boolean inverted.
  • Unitary.controls now is a vector of ControlRegister and can contain both classical and quantum registers.
  • ControlRegister extends Register in typescript rathe than wrapping it - this is done for backwards compatibility. Even though we changed type of controls, JSON looks exactly the same and old .qsc files will be correctly parsed.
  • To support this "flattened" serialization, I had to implement custom JSON serializer for ControlRegister.
  • Currenlty only classical controls can be inverted, but this model supports writing JSON representing quantum antic-control, and I checked that it would be rendered correctly.
• Q#-to-circuit changes:
  • If there is a then/else branch with condition "resullt==One" or "result==Zero" and all gates inside have single target, instead of generating a group, emit gates without grouping them, but with added classical control.
  • Note that we allow quantum controls on these gates, so you can have gate in circuit with classical and quantum control (see Example 2 below).
• Rendering changes:
  • Render controls of classically-controlled Unitary the same way as we would render quantum controls.
  • Render inverted controls with a hollow control dot (done with CSS).
• Added circuit-to-Q# conversion for classically controlled gate (and a test).
• Circuit-to-string rendering for classically controlled gate works without any changes, but updated Python tests to demonstrate new it.

Example 1 - teleportation

Before:

After:

Example 2

operation Tmp1() : Unit {
    use q = Qubit[4];
    H(q[0]);
    let m0 = M(q[0]);
    if (m0 == One) {
        X(q[1]);
        X(q[0]);
    } else {
        X(q[2]);
        Z(q[2]);
        CZ(q[3], q[2]);
        CNOT(q[2], q[3]);
    }
    let m1 = M(q[1]);
    if (m0 == Zero) {
        Rx(0.5, q[3]);
    } else {
        Ry(0.5, q[3]);
        if (m1==Zero) {
            X(q[1]);
        }
    }
}

Example 3 - negative cases (complex condition, 2-qubit gate).

operation Tmp2() : Unit {
    use q = Qubit[4];
    
    H(q[0]);
    H(q[1]);
    let m0 = M(q[0]);
    let m1 = M(q[1]);

    if (m0 == One and m1 == One) {
        X(q[1]);
    }
    if (m0 == Zero) {
        Rxx(0.5, q[2], q[3]);
    }
}