Methods for Measuring Quantum States in Physics

20 years ago, at Yale University, we first read out the #quantum state of a superconducting #qubit by measuring the state-dependent frequency shift which a qubit exerts on a microwave frequency #resonator. This dispersive readout mechanism is enabled by the strong, but non-resonant coupling of the qubit to the resonator provided by circuit quantum electrodynamics, or short circuit QED. Today this technique is widely and almost exclusively used to read out superconducting qubits, e.g. in the #quantum computing industry by Google, IBM, Amazon Web Services (AWS), by startups such as Rigetti Computing, IQM Quantum Computers or Alice & Bob, and in academic labs. Through successive refinements this approach continues to provide faster and higher fidelity readout every year. Check out the short discussion below for some references.

Ever wondered what role resonators play in superconducting qubits? Resonators are typically used as readout components in quantum computing, serving as intermediaries between the quantum and classical worlds. A resonator is a circuit element that stores energy at a specific frequency. When paired with a qubit, it forms a hybridised system, enabling dispersive readout—the most common method for measuring qubit states. In the dispersive regime, the qubit and resonator are coupled but operate at different frequencies. Instead of exchanging energy, the qubit slightly shifts the resonator’s frequency depending on whether it is in the |0⟩ or |1⟩ state. By sending a microwave tone through the resonator, we can measure this shift and infer the qubit’s state—without directly disturbing it. However, achieving high-fidelity readout is far from straightforward. The process must be fast enough to support high-throughput quantum operations while minimising errors and avoiding back-action that could disturb the qubit. This balance requires careful tuning of the coupling between the qubit, resonator, and feedline. Too much coupling risks qubit decoherence, while too little slows down the readout. To address this, we can use hardware tricks like Purcell filters, which protect qubit coherence while enabling fast and efficient readout. However, hardware is only part of the equation. On the software side, optimising the microwave pulses used for readout is critical for improving fidelity and speed. One particularly exciting approach is reinforcement learning, which can autonomously explore the qubit-resonator landscape and design novel readout waveforms. If you’re curious, Yvonne Y. Gao's recent paper on this topic (arXiv:2412.04053) is a great place to dive deeper.

In a recent paper published in Physical Review Research, we reported a scheme for tomography of quantum simulators which can be described by a Bose-Hubbard Hamiltonian while having measurement access to only some sites on the boundary of the lattice. We present an algorithm that uses the experimentally routine transmission and two-photon correlation functions, measured at the boundary, to extract the Hamiltonian parameters at the standard quantum limit. Furthermore, by building on quantum enhanced spectroscopy protocols that, we show that with the additional ability to switch on and off the on-site repulsion in the simulator, we can sense the Hamiltonian parameters beyond the standard quantum limit.