  Informationally complete (IC) positive operator-valued measures (POVMs) are
generalized quantum measurements that offer advantages over the standard
computational basis readout of qubits. For instance, IC-POVMs enable efficient
extraction of operator expectation values, a crucial step in many quantum
algorithms. POVM measurements are typically implemented by coupling one
additional ancilla qubit to each logical qubit, thus imposing high demands on
the device size and connectivity. Here, we show how to implement a general
class of IC-POVMs without ancilla qubits. We exploit the higher-dimensional
Hilbert space of a qudit in which qubits are often encoded. POVMs can then be
realized by coupling each qubit to two of the available qudit states, followed
by a projective measurement. We develop the required control pulse sequences
and numerically establish their feasibility for superconducting transmon qubits
through pulse-level simulations. Finally, we present an experimental
demonstration of a qudit-space POVM measurement on IBM Quantum hardware. This
paves the way to making POVM measurements broadly available to quantum
computing applications.
