(a) briefly explain why we cannot find simultaneous eigenfunctions of lg, ly and lz. an electron in a hydrogen atom is in the n = 2 state. ignoring spin, write down the list of possible quantum numbers {n, l, m}. (b) for two qubits briefly explain, giving examples, the difference between a product state and an entangled state (c) consider a system of identical bosons and a system of identical fermions. briefly explain the difference in the ground state energy configurations. (d) consider two distinguishable particles in 1d which exist in single-particle (normalised) wave functions va(xı) and (x2). write down the combined two-particle wave function and show that the expectation value of the squared separation is given by: ((x1 -x2)2) = (x2)a + (x2)b - 2(x)a(x)b, where (x")a, b denotes an expectation value of r" with respect to va, b (e) the quantum logic gates x, z, h and cnot act on qubit states as follows: 1) -» |0) j0)-1), х: z 0) -> |0), |1) -» -|1) )(1/v2)(i0) - |1)) j0) (1/2)(0 00) |00), |01) -» |01), |10) - |11), 11)> |10) н: cnot where in the cnot gate above the control qubit state corresponds to the first entry in the ket, and the target qubit state corresponds to the second entry. at t = 0 a quantum computer comprising two qubits starts out in the state where both qubits are initialised in the |0) state, i. e. |v(0)) = |00). draw a circuit, carefully labelling the qubits and gates, which describes the following sequence of gates: h on qubit 1, x on qubit 1, z on qubit 2, cnot (control = qubit 1, target = qubit 2), z on qubit 1. find the final state of the two qubits.