Methods for Measuring Quantum States in Physics

Today, Anthony Chen and I are posting a theory paper tackling a problem that I have been contemplating for a long time. Conventional wisdom suggests that quantum states are very fragile, like Schrodinger’s cat — if you look at the state, you destroy it. This poses a huge problem in using quantum computers for quantum simulation. Suppose you spend 3 hours meticulously preparing the ground state of some material or molecule on my quantum computer. If you measure the state, you get a few bits of information, but you destroy the state. In order to accurately predict physical phenomena, you may need to measure millions of times. In this paper, we show how to measure a ground state without causing any disturbance to the state. We call it “catalytic tomography”, since the quantum state is used but not consumed. How is this possible? The key is to use the parent Hamiltonian, and to apply energy filtering. As a consequence, ground states are not fragile like Schrodinger’s cats, but are robust like a classical memory, and readable like a book! Link to paper ➡️ https://lnkd.in/eBxydfwh

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.

Quantum state tomography, the process of reconstructing an unknown quantum state, traditionally suffers from computational demands that grow exponentially with system size, a significant barrier to progress in quantum technologies. S. M. Yousuf Iqbal Tomal and Abdullah Al Shafin, both from BRAC University, now present a new approach, geometric latent space tomography, which overcomes this limitation while crucially preserving the underlying geometric structure of quantum states. Their method combines classical neural networks with quantum circuit decoders, trained to ensure that distances within the network’s ‘latent space’ accurately reflect the true distances between quantum states, measured by the Bures distance. This innovative technique achieves high-fidelity reconstruction of quantum states and reveals an intrinsic, lower-dimensional structure within the complex space of quantum possibilities, offering substantial computational advantages and enabling direct state discrimination and improved error mitigation for quantum devices. https://lnkd.in/eSpH3YhD