Ancilla-free implementation of generalized measurements for qubits embedded in a qudit space

TL;DR

This paper presents a method to implement informationally complete POVMs for qubits without using additional ancilla qubits by leveraging the higher-dimensional space of qudits, demonstrated through simulations and experiments on IBM hardware.

Contribution

It introduces an ancilla-free approach to realize generalized measurements for qubits by utilizing qudit spaces, reducing device complexity.

Findings

Feasibility shown through pulse-level simulations for superconducting qubits.

Experimental demonstration on IBM Quantum hardware confirms the approach.

Method enables broader application of POVMs in quantum computing.

Abstract

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.