  When using single photons and photonic integrated circuits (PICs) for quantum
information processing, quantum states can be encoded using either qubits or
qudits. Qudits are more efficient in terms of requiring less photons (in
principle, only one) to encode the state, while qubits are more efficient in
terms of the number of waveguides used to reach the same dimension $d$, as
qudits need $d$ waveguides in comparison to the $2\log_2d$ waveguides used by
qubits. For dimensions large enough for useful tasks, this would indicate that
qubits are clearly the best option, as other resources scale at least
polynomially with the number of waveguides in the PIC. The comparison, however,
is not so direct. We consider the task of quantum state preparation, which is
relevant for variational quantum algorithms, for instance. For n qubits, this
task requires the circuit to have a number of Controlled-NOT (CNOT) gates that
is exponential in n. Since both implementations suffer from an exponential
resource cost, a more detailed evaluation is required. We compare the qubit and
qudit approaches in terms of the amount of electrical energy that must be
spent, on average, to program a photonic circuit to perform quantum state
preparation. We find that if a PIC with a fully reconfigurable array of
interferometers is to be used, using qubits requires more energy than using
qudits. We show, however, that a circuit with dedicated CNOT blocks has a much
smaller energy consumption, remaining viable even at large qubit numbers, where
more important bottlenecks come into play, such as the probabilistic nature of
the CNOT gates.
