Quantum jumps of sound

arXiv:2610.10714 · quant-ph · Submitted 2026-10-07 · Read on arXiv

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Introduction to the show: ident: Quantum Radio. Generated commentary on the latest quantum physics and condensed matter papers.

Kai: Today's paper: "Quantum jumps of sound".

Mira: The gist: Discontinuous transitions between quantized energy levels in a massive, vibrating object are observed when coupling a superconducting qubit dispersively to a nanomechanical resonator,

Kai: First, who's behind it and why it matters.

Title and authors: Kai: We've talked about what the paper actually built and the specific numbers they got out of it regarding lifetime and coupling strength. Now let's look at what they are trying to achieve with this work called "Quantum jumps of sound".

Mira: The title itself points directly at the central mystery: observing sound energy in discrete packets, which is something quantum mechanics predicts but we can't see through standard position measurements.

Lev: So, the paper's summary boils down to using a superconducting qubit coupled dispersively to a nanomechanical resonator to perform repeated quantum nondemolition measurements of the phonon number.

Kai: That’s right, and they are showing that by directly measuring the mechanical energy rather than just its displacement, we can observe those quantum jumps in the mechanical energy.

Mira: They use a specific architecture: an aligned transferprint technique integrating a one-dimensional phononic crystal cavity made of lithium niobate with the qubit and the resonator.

Lev: The key result here is that this setup yields a mechanical lifetime T1 equals two point one milliseconds and a dispersive shift of two chi over two pi equals three hundred twenty eight kilohertz per phonon <ref:2610.10714#pg1,1 milliseconds and a dispersive shift of>.

Kai: Those are concrete metrics for how well the system is coupled and how long it lives before significant decay sets in.

Mira: They also explain the effective Hamiltonian they're working with: H hat eff equals omega m b dagger b plus one half (omega g e plus two chi b dagger b) sigma z.

Lev: That Hamiltonian is important because it shows why measurements of the qubit frequency are quantum nondemolition with respect to the phonon number operator, n = hat b dagger bang b.

Kai: So if we measure the qubit frequency, we’re measuring something that commutes with the number of phonons in our mechanical system.

Mira: This allows them to see those individual phonon numbers as spectrally narrow peaks separated by two chi per measurement on a spectrally narrow drive on the qubit.

Lev: So what this means is that they can resolve individual phonon numbers, which are separated by that two chi frequency offset of three hundred twenty eight kilohertz in their setup.

Kai: That's a huge number when you consider the scale of mechanical resonators we're dealing with today, and it shows the capability of this hardware.

Mira: It connects directly to their demonstration of heralding mechanical Fock states through repeated QND parity measurements, which they show gives a fidelity of P(n equals one) equals zero point eight five <ref:2610.10714#pg1>.

Lev: That fidelity is strong evidence that the method works for preparing those specific nonclassical mechanical states.

The paper's summary: Kai: Now we look at what the authors suggest to make this work even better, moving beyond just demonstrating the basic concept of "Quantum jumps of sound".

Mira: They focus on improving the AI system they used for tracking, specifically suggesting a forward-backward algorithm to get a smoother estimate of the phonon number.

Lev: That smooth estimate is crucial because it resolves those abrupt transitions from predominantly excited states to predominantly ground states, which marks that jump from n equals one to zero.

Kai: So instead of seeing just noise or an exponential decay in a classical oscillator, the AI system helps them see those distinct jumps occurring at different times along each trajectory.

Mira: They also discuss how they can use postselection to sharpen their knowledge, by performing k consecutive parity checks and then measuring the distribution.

Lev: This lets them discern the state more clearly, as shown in Figure three where consecutive excited measurements of e increase P(n equals one) <ref:2610.10714#pg1>.

Kai: So this isn't just about getting a better fidelity on a single measurement; it’s about using sequential measurements to build up confidence in the mechanical state.

Mira: This implies that the repeated QND parity checks are more powerful than they initially appeared because of how they feed information back into the distribution.

Lev: The paper also highlights that their large cooperativity, exceeding three times ten to the six, allows for much higher throughput.

Kai: They suggest this means the AI system can perform roughly one hundred seventy parity checks within a single phonon lifetime, which is a lot of measurement power.

Mira: So they are leveraging that high cooperativity to improve the overall measurement speed and efficiency of heralding these states.

The paper's improvements: Kai: So to wrap up, the paper shows a practical demonstration of observing quantum jumps in sound by coupling a superconducting qubit to a nanomechanical resonator.

Mira: The main point is that this technique allows us to directly measure energy without the back action issues associated with measuring position.

Lev: They prove they can herald single-phonon states with zero point eight five fidelity using repeated QND parity measurements and Bayesian forward propagation of the phonon number distribution.

Kai: And they show a way to track the phonon number in real time, which is important because it shows how these quantum jumps manifest in mechanical systems.

Mira: This capability has implications for sensing frequency changes at much lower drive power by preparing and nondestructively reading out nonclassical mechanical states.

Lev: And they also point out their limitation, as they state that the residual measurement back action reduces the effective phonon lifetime to T1 eff equals six hundred forty nine microseconds.

Kai: So while this method is powerful, you have to be aware that this residual back action means the effective lifetime is limited to six hundred forty nine microseconds.

Mira: It's a trade-off between measurement precision and how long the mechanical state lasts before decoherence kicks in.

Lev: The paper "Quantum jumps of sound" shows what can actually be built and measured, and it opens routes for sensing frequency changes at much lower drive power by preparing these nonclassical states nondestructively.

Kai: It’s a solid piece of experimental work showing how to bridge the gap between superconducting circuits and mechanical motion.

Mira: And it sets a clear path forward for using this resource in bosonic quantum error correction because of that high cooperativity.

Conclusion: Kai: So to wrap up, the paper "Quantum jumps of sound" shows how you can use a superconducting qubit coupled to a nanomechanical resonator to directly measure energy in discrete packets.

Mira: Exactly, it proves that by measuring the qubit frequency dispersively, you get access to those phonon numbers without disturbing them too much.

Lev: From an error-correction standpoint, this means we have a way to track mechanical states with high fidelity using repeated QND parity measurements and Bayesian forward propagation.

Kai: They showed a single-phonon state heralding fidelity of zero point eight five, which is pretty strong for preparing nonclassical mechanical states.

Mira: And they found that the large cooperativity, exceeding three times ten to the six, is exactly what you need for bosonic quantum error correction because it's an order of magnitude better than other platforms.

Lev: But we have to remember the caveat about measurement back action; it limits the effective lifetime to six hundred forty nine microseconds.

Kai: That’s the trade-off, right? You get this measurement capability, but you also have that decoherence limit imposed by how you're reading out the data.

Mira: It opens up a new route for sensing frequency changes at much lower drive power if we can prepare and nondestructively read those nonclassical mechanical states.

Lev: And the architecture itself, using an aligned transferprint technique to integrate the components, is pretty useful because it lets you stack more resonators later.

Kai: Yeah, it’s a solid piece of hardware that shows how you can bridge the gap between superconducting circuits and massive vibrating objects.

Mira: It’s definitely a practical step toward using these systems for sensing where you need very precise control over the mechanical degrees of freedom.

Lev: Next up, we're looking at some work on quasiparticle-protected qubits, which seems to be about engineering the energy landscape beyond standard Josephson junctions.

Kai: Right, moving on to those superconducting qubit papers next.

Takuma Makihara, *Erik Szakiel, *Matthew P. Maksymowych Oliver A. Hitchcock Kaveh Pezeshki Rachel G. Gruenke-Freudenstein Mihir Pendharkar Shannon P. Harvey David I. Schuster Amir H. Safavi-Naeini

Department of Applied Physics and Ginzton Laboratory, Stanford University · Department of Physics, Stanford University · SLAC National Accelerator Laboratory

quant-ph

Submitted: 2026-10-07

Updated: 2026-10-07

Comments: 12 pages, 11 figures

Journal ref: Takuma Makihara et al., Quantum jumps of sound. Science 393, 1217-1220 (2026)

DOI: 10.1126/science.aeh7535

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Importance score: 92/100

The gist: The gist: Discontinuous transitions between quantized energy levels in a massive, vibrating object are observed when coupling a superconducting qubit dispersively to a nanomechanical resonator, which

Key concepts

Quantum Nondemolition (QND) Measurement
This method allows measuring a property of a system without disturbing its state in a way that changes the observable being measured. In this experiment, coupling the resonator to the qubit enables measuring the phonon number ($\hat{n}$) while preserving its quantum state, avoiding back action that would otherwise destroy information.
Phononic Crystal Cavity
This is a one-dimensional structure made from thin-film lithium niobate designed to trap and control sound waves. The periodic patterning acts as acoustic mirrors, creating a full phononic bandgap that localizes the mechanical modes. This precise engineering maximizes the interaction between the qubit and the mechanical vibrations.
Heralding Fock States
This is the process of preparing a specific quantum state, like a single-phonon state ($n=1$), by performing sequential measurements. By applying parity checks repeatedly and analyzing qubit spectroscopy results, researchers could confirm the presence of exactly one phonon with an observed fidelity of 0.85.

Terminology

Summary

The gist: Discontinuous transitions between quantized energy levels in a massive, vibrating object are observed when coupling a superconducting qubit dispersively to a nanomechanical resonator, which requires measuring the energy directly rather than its displacement.

Experimental Setup and Device Architecture

The researchers utilize an aligned transferprint technique to integrate a one-dimensional phononic crystal cavity fabricated from thin-film lithium niobate (LN) with a superconducting qubit. The mechanical resonator is a micron-scale central rectangular block suspended by periodically patterned beams engineered to have a full phononic bandgap, acting as acoustic mirrors to localize mechanical modes. This design maximizes the overlap between the qubit and mechanics while minimizing interaction with any additional piezoelectric volume that may lead to loss. The device achieves a phonon lifetime of T1 = 2.1 ms and a dispersive shift of 2χ/2π = 328 kilohertz per phonon.

Quantum Nondemolition Measurement

Observing the quantized nature of mechanical energy requires measuring the energy directly, avoiding the back action that displacement measurements impart on the oscillator’s momentum. This is achieved by coupling the resonator to an intrinsically nonlinear system, such as a superconducting qubit. The effective Hamiltonian in the dispersive regime is given by Hˆeff = ωm ˆb†ˆb + 1/2 (ωge + 2χˆb†ˆb)ˆσz. Crucially, the phonon number operator ˆn = ˆb† ħ b commutes with Ĥeff, so measurements of the qubit frequency are QND with respect to the phonon number.

Heralding Mechanical Fock States

The researchers demonstrate heralding of mechanical Fock states through repeated QND parity measurements. After preparing the mechanical mode in a weak coherent state with ¯n ≃ 0.13, applying k consecutive parity checks and then performing qubit spectroscopy allows for the measurement of the phonon number distribution P(n). By observing six consecutive measurements of e⟩, they herald a single-phonon state with a fidelity of P(n = 1) = 0.85. This state evolution is quantitatively described by Bayesian forward propagation of the phonon number distribution.

Tracking Phonon Number in Real Time

The researchers use repeated parity checks to continuously monitor the phonon number. The forward distribution Pf(n, ti), computed from Eq. 2 using measurements up to time ti, provides an estimate of the phonon number using only past measurements. The forward-backward algorithm produces a smoother estimate by combining the forward distribution with a backward likelihood Pb(n, ti), which propagates information from future measurements back to time ti. This results in unambiguous quantum jumps between n = 1 and n = 0 occurring at different times in each trajectory.

Conclusion and Significance

The capability demonstrated here, fast repeated QND measurements of phonon number, is a consequence of their large cooperativity C = 4g 2T1T∗2, which exceeds 3 × 10 6. This combination of strong, coherent coupling and long lifetimes is precisely the resource that underlies all bosonic quantum error correction. The work brings the observation of quantum jumps to a mechanical system, where massive, vibrating objects offer a clear manifestation of the quantum nature of sound. It also opens routes to sensing frequency changes at much lower drive power by preparing and nondestructively reading out nonclassical mechanical states.

Device Parameters Summary

The device parameters are summarized in Table S1, which lists the qubit parameters ωge, T1q, T∗2, and α, as well as the dispersive shift χ. The single-shot readout performance is characterized by an average readout fidelity of F = 0.912. The effective mass meff is 0.1995 pg, yielding a zero-point fluctuation magnitude of xzpf = 3.576 fm. The effective lifetime during continuous monitoring is T1eff = 649 µs. The extracted lifetime from the jump distribution is T1 = 645 ± 29 µs. The thermal bath temperature corresponding to the mechanical mode is estimated at 36 mK. The qubit temperature measured without coherent drive is 53 mK.

Fabrication Details

The fabrication involved fabricating the mechanics and qubit separately to incorporate state-of-the-art techniques that are incompatible across material systems. The integration is achieved by using an aligned transfer print process, where the mechanical resonators are stamped onto the coupling region of the qubit. The control system uses an Operator-X (OPX) and Octave from Quantum Machines Inc. for microwave pulses. The experimental wiring involves various components such as a traveling-wave parametric amplifier (TWPA) from Lincoln Labs [43].

Measurement Backaction Analysis

The residual measurement back action reduces the effective phonon lifetime to T1eff = 649 µs. This is modeled as a per-measurement excess decay probability PD, which is approximately 0.013 per measurement. The swap probability between the e, 1⟩ and f, 0⟩ states during the Ramsey protocol is roughly 1.6%. This value is consistent with the observed demolition probability PD ≈ 0.013 reported above. The average dephasing time measured over a period of roughly 24 hours is 55 µs. This indicates that the dominant source of measurement infidelity is qubit decoherence during the Ramsey sequence rather than by readout errors.

Future Directions

A concrete next step involves a mechanical dual-rail qubit where two mechanical resonators are coupled to a shared qubit and joint parity measurements are used to detect errors. This architecture would allow phonon loss to cause a detectable erasure error. The transfer print integration technique enables this architecture because additional mechanical resonators can be stamped onto the same qubit. Furthermore, real-time tracking of mechanical degrees of freedom is important because vibrations couple to physical observables that are inaccessible to electromagnetic systems. The ability to prepare and nondestructively read out nonclassical mechanical states offers a route to sensing frequency changes at much lower drive power.

Acknowledgments and Data Availability

The authors acknowledge A. Hwang, S. Gyger, and K. Multani for helpful discussion. The material is based upon work supported by the Air Force Office of Scientific Research and the Office of Naval Research under award FA9550-23-1-0338. All data and software are available in the manuscript or are deposited at Zenodo 10.5281/zenodo.20944616. The author contributions detail who designed, fabricated, and measured the device. The competing interests section states that A.H.S.-N. and D.

Improvements for AI systems

  1. textbfFundamental Quantum State Tracking for Mechanical Systems: The Improved AI System can perform real-time tracking of mechanical degrees of freedom into the quantum domain. This is achieved by applying a forward-backward algorithm to measurement records to obtain a smooth estimate, which resolves abrupt transition[s] from predominantly e⟩ to predominantly g⟩ outcomes marks a jump from n = 1 to n = 0, analogous to tracking photon jumps in electromagnetic cavities.

  2. textbfIncreased Quantum Resource Efficiency: The Improved AI System can leverage high cooperativity for enhanced measurement throughput. Since the paper notes that Our cooperativity exceeds 3 × 106, representing an order-of-magnitude improvement over other quantum acoustic platforms, the AI system can be designed to perform roughly 170 parity checks within a single phonon lifetime.

  3. textbf Supervised Quantum State Herdalding: The Improved AI System can reliably herald single-phonon states with high fidelity. This is done by using repeated QND parity measurements and applying the Bayesian forward propagation of the phonon number distribution, resulting in a fidelity of P(n = 1) = 0.85.

  4. textbf Enhanced Noise Filtering and State Discrimination: The Improved AI System can utilize postselection to sharpen state knowledge. By performing k consecutive parity checks Π and then measuring the distribution, the system can discern the state, as shown by Fig. 3, where Consecutive excited measurements of e⟩ increase P(n = 1), allowing for the observation of quantum jumps where a classical oscillator would show only a smooth exponential decay.

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