Physicists Predict a Voltage-Free Oscillating Supercurrent in Andreev Qubits but Underestimate How Much Reading It Disturbs the Qubit
On 5 August 2026, Physical Review B published a theoretical proposal for reading out an Andreev qubit through an oscillating supercurrent that the qubit itself produces, without the ancilla qubits that many nondemolition measurement schemes use. The Letter, “Andreev qubit readout from dynamic interference supercurrent,” was written by five physicists at institutions in China and Brazil. It reports calculations and numerical simulations; the proposed readout setup has not been built.
Three of the authors are at the Beijing Institute of Technology: Xian-Peng Zhang, who is also affiliated with the Hong Kong University of Science and Technology, Chuanchang Zeng and Yugui Yao. Zhen-Biao Yang is at Fuzhou University. José Carlos Egues is at the University of São Paulo’s São Carlos Institute of Physics. Egues and Yao are the corresponding authors.
Agência FAPESP, the news service of the São Paulo Research Foundation (FAPESP), covered the work in Portuguese on 25 September and in English on 21 October, and Phys.org ran the story in October.
An Andreev qubit stores information in discrete quasiparticle states, called Andreev levels, that form where a non-superconducting region interrupts a superconductor. The device modeled in the paper is a gate-defined quantum dot in an indium arsenide nanowire, tunnel-coupled on both sides to nanowire leads made superconducting by contact with aluminum. The qubit encodes 0 as the junction’s ground state and 1 as the configuration in which the lowest Andreev level is occupied by a pair of quasiparticles, a design called an Andreev level qubit, also known as an Andreev pair qubit.
The paper calculates the supercurrent through this junction when the qubit is prepared in a superposition of its two states. According to the calculation, the current has a static part, equal to a weighted average of the currents of the two basis states, and a dynamic part that oscillates at the qubit frequency. The authors attribute the oscillation to interference between the two many-body states and describe it as an ac-like Josephson effect that occurs with no applied voltage.
In physical units, the dynamic part of the current is
$$$I^{D}(t) = 2e\omega|C_{0,1}|\sin\theta\cos\left[\omega(t-t_R) – \varphi_0 – \vartheta\right]$$$
where $$\theta$$ sets the weights of the two basis states, $$\vartheta$$ sets their relative phase, $$\omega$$ is the qubit’s angular frequency and $$t_R$$ marks the end of the microwave pulse that prepares the state. $$|C_{0,1}|$$ and $$\varphi_0$$ are the magnitude and phase of a matrix element that measures how the two states change with the superconducting phase difference across the junction. The Letter also writes the expression in units of the superconducting gap $$\Delta$$, in which currents are counted in multiples of $$2e\Delta/\hbar$$.
The proposed readout embeds the junction in a large superconducting loop and places above it the small pickup coil of a magnetometer built on a superconducting quantum interference device (SQUID). The SQUID, a highly sensitive detector of magnetic flux, would sense the flux produced by the current circulating in the loop. According to the paper, the static part of the current and the oscillation amplitude give $$\theta$$. The oscillation’s phase, measured from the end of the preparation pulse and corrected for a calibrated offset, gives $$\vartheta$$. The authors wrote that measurements can continue as the qubit evolves, without resetting it.
To test the scheme against measurement imperfections, the authors added Gaussian noise with a standard deviation of 2% of the current scale to the simulated signal and modeled the pickup coil’s back-action with a phenomenological coupling parameter. For a test state measured three, five and nine times per oscillation period, the simulated readout infidelities were 0.48%, 0.15% and 0.19%. The authors wrote that these values are within standard quantum error correction thresholds.
The authors estimated the back-action by assuming a pickup-coil current of about 0.1 microamperes against a junction supercurrent of 1 to 10 microamperes, which gives an added phase of about one thousandth of a cycle. They noted that the dynamic current vanishes at operating points where the two qubit states are degenerate, and that the scheme requires temperatures low enough for thermal energy to stay well below the qubit energy.
The work first appeared on arXiv on 25 September 2024 under the title “Non-collapsing electric readout of arbitrary Andreev qubits.” That version said the readout probed the qubit without collapsing its quantum state. The published Letter says the readout approaches the nondestructive limit arbitrarily closely; a second arXiv version posted on 26 December 2025 uses the new title.
Physical Review B received the manuscript on 28 September 2024 and a revised version on 2 March 2026, and accepted it on 8 July 2026.
“Our method doesn’t eliminate the fundamental problem of quantum measurement,” Egues said, according to Agência FAPESP. He told the agency that the parameters used in the calculations come from existing systems and that the proposed device geometry has not yet been built.
The work was funded by the National Key R&D Program of China, the Hong Kong Research Grants Council, the National Natural Science Foundation of China, Brazil’s National Council for Scientific and Technological Development and FAPESP.
My Analysis
The oscillating supercurrent that Zhang and his colleagues predict follows from standard quantum mechanics, and a measurement of it would add something real to Andreev physics. Their claim that a pickup coil can recover an arbitrary qubit state from that current while barely disturbing it depends on a simulated measurement that resolves the current finely enough to project the qubit in a single sample. The authors assign that measurement only a small back-action.
For anyone tracking qubit modalities, the paper adds a testable prediction about Andreev junctions and a detector proposal, but not a demonstrated way to read a single qubit without disturbing it.
Why a Superposition Makes the Current Oscillate
When a quantum system is in a coherent superposition of two energy states, the expectation value of any quantity that couples those states oscillates at a frequency set by their energy difference. A precessing spin does this with its transverse magnetization. A superconducting flux qubit at its symmetry point does it with its circulating current. The Letter shows that the supercurrent through a quantum-dot Josephson junction belongs to the same class: the oscillation comes from quantum interference between the two parts of a superposition.
The authors’ contribution is the size of the effect. Working within a microscopic Bogoliubov–de Gennes model of the junction, they computed the matrix element that couples the two Andreev states through the superconducting phase difference and found an oscillating current of the same order as the static one. The model treats the quasiparticles as non-interacting. In real devices the electrons interact, and a quantum dot adds a charging energy; a 2022 microwave study found signatures of those interactions in the Andreev spectrum of an InAs nanowire junction. A measured amplitude would test that simplification as well.
The idea of reading Andreev states through the current in a loop is as old as the Andreev qubit. Zazunov and colleagues’ 2003 paper, which proposed the Andreev level qubit and which the Letter cites as its first reference, placed the junction in an rf-SQUID loop and noted that the coupling between Andreev levels and the circulating supercurrent allows both manipulation and readout. A Delft group read out flux qubits through their circulating currents with an attached DC SQUID in 2003 and demonstrated a nondestructive version of that measurement in 2004.
I would describe the predicted effect as a quantum beat in the current. The “ac Josephson effect without voltage” label works as an analogy. The current swings back and forth because the relative phase between the two parts of the superposition advances at the qubit frequency, and it continues only for the coherence time.
The Simulated Readout Pairs Strong Precision With Weak Disturbance
The authors define the supercurrent as the rate of change of the expectation value of the electron number in one lead. An expectation value is the mean of the outcomes from measuring many identically prepared systems. A nuclear magnetic resonance spectrometer reads a precessing magnetization of this kind with a pickup coil, and it works because the signal comes from an enormous number of nuclei precessing together.
A detector watching one qubit in one run sees outcomes scattered around the mean by quantum projection noise. Unless the qubit is already in an eigenstate of the measured quantity, each outcome also updates the qubit’s state, a process I described in my piece on wave function collapse.
The Letter’s simulation generates each outcome as the expected current of the qubit’s present state plus Gaussian noise, a step the authors describe as an ad hoc treatment of the flux measurement’s randomness. That form is the standard description of a weak measurement record. It applies when each sample’s noise far exceeds the spread between the values the measured quantity can take, which keeps both the information gained and the disturbance small.
The Letter’s own parameters put its simulation in the opposite regime. In the qubit’s two-state space, the current has two eigenvalues, the only values a perfectly precise measurement could return. From the static currents of the two basis states and the off-diagonal term $$2e\omega|C_{0,1}|$$, computed from the values in the caption of the Letter’s Fig. 3, the two eigenvalues are about −0.27 and +0.33 in units of $$2e\Delta/\hbar$$, roughly 0.6 apart. The simulated noise per sample is 0.02 in the same units, thirty times smaller.
A detector that resolves the current that finely in one sample is making a strong measurement. Like a full measurement of a spin, which leaves it pointing up or down, it would leave the qubit close to one of the two current eigenstates. Both eigenstates are set by the junction’s parameters, so after the first sample nothing about the qubit depends on the prepared angles except which outcome occurred. The authors instead assign each sample a small back-action through a separate phenomenological parameter.
The trade between information and disturbance has a precise form. Clerk, Girvin and Stone analyzed a weak and continuous measurement of a qubit. In that setting the qubit dephases at least as fast as the detector extracts information about it. An ideal detector reaches equality, and a less efficient one dephases the qubit more for the same information.
Murch and colleagues at Berkeley watched this back-action in 2013 with weak measurements of a single transmon and a near-quantum-limited amplifier. Each run’s quantum trajectory diffused across the Bloch sphere as the measurement record came in, and confirming the trajectories took quantum state tomography over many repetitions.
Single-Copy Limits on Reading an Unknown State
Massar and Popescu answered a specific question in Physical Review Letters in 1995: given $$N$$ identical copies of an unknown pure qubit state, how close can any measurement strategy get to identifying it? Averaged over all possible input states and over measurement outcomes, the best achievable fidelity is
$$$\bar{F}_{\max} = \frac{N+1}{N+2}$$$
For a single copy, the average cannot exceed two thirds. The bound applies to averages: a strategy that always guesses one fixed state is perfect whenever the input happens to be that state, and poor on most others.
A year later, D’Ariano and Yuen proved that no measuring scheme, including any succession of measurements on the same system, can determine the state of a single quantum system. A scheme that could would also allow anyone to clone an unknown state, which Wootters and Zurek proved impossible in a paper the Letter cites in its opening paragraph. The two-thirds figure itself comes from optimizing the estimate, not from the no-cloning argument alone.
The published Letter reports infidelities of 0.15% to 0.48% for one test state, recovered by fitting both Bloch-sphere angles to the simulated current. A result for one state does not by itself violate the bound.
The authors present the method as a readout of arbitrary superposition states, though, and the 2024 preprint’s Fig. 3(b) averaged the infidelity over the whole Bloch sphere, a result the authors described as within error-correction thresholds. No single-copy procedure can bring the average infidelity below one third. The simulation reaches its numbers because each sample is as precise as a strong measurement while disturbing the qubit as little as a weak one.
The Paper’s Numbers at a 0.1 meV Gap
The published Letter gives no physical value for the gap. The 2024 preprint cites an induced gap of about 0.1 meV for these hybrid nanowires. With that value, the Letter’s operating point gives these physical numbers:
- Currents: the current scale $$2e\Delta/\hbar$$ is about 49 nA. The two basis states conduct about −4.4 nA and +7.2 nA, the oscillating component reaches about 13 nA, the largest total current is about 16 nA and the simulated noise per sample is about 1 nA. The two current eigenvalues are about 29 nA apart. A gap twice as large doubles each figure.
- Back-action example: the Letter’s back-action estimate assumes a junction current of 1 to 10 microamperes, citing a review of current-phase relations in Josephson junctions and a 1980 study of thick metallic junctions. That is roughly 60 to 600 times the largest current at the model’s own operating point. Mutual inductance and detector noise also affect the back-action, so this mismatch alone does not decide it. The authors still need one consistent set of physical scales for their signal and back-action examples.
- Frequency: at the Letter’s operating point the qubit energy is $$0.89\Delta$$, which corresponds to about 21.5 GHz and a period of about 46 picoseconds.
- Sampling: the Letter takes three to nine samples per period and quotes about 0.1 ns between samples. At 21.5 GHz the spacing would be about 5 to 15 picoseconds. A 0.1 ns spacing implies a qubit frequency of 1 to 3 GHz and a gap of roughly 5 to 15 microelectronvolts, an order of magnitude below the preprint’s figure. Under the 0.1 meV assumption the Letter’s timing and energy scales do not match, and the published text gives no gap that reconciles them.
The authors describe the detector as a SQUID magnetometer with a pickup coil. Such magnetometers are usually read through a flux-locked feedback loop, whose bandwidth with about one meter of cable to room-temperature electronics is around 20 MHz. PTB, Germany’s national metrology institute, lists commercially available electronics reaching 50 MHz and a 350 MHz demonstration with feedback electronics operated at 4 kelvin.
These are not fundamental limits on SQUID-based detection, since resonant, mixing and stroboscopic schemes can reach higher frequencies. A 21.5 GHz signal is about 60 times faster than the fastest of these feedback loops, and the authors do not specify a detection chain at that frequency, with its sensitivity, bandwidth and back-action.
Error Correction Needs Joint Parity Measurements
The authors compare their readout infidelities with quantum error correction thresholds. A fitted state’s infidelity is a different quantity from the per-operation error rates that thresholds refer to, so the comparison does not show that the scheme could support error correction below threshold. That would take an error model for the measurement, a specified code and syndrome-extraction procedure, and an account of how back-action spreads through the correction cycle.
The Letter’s introduction describes nondemolition protocols as leaving the original qubit state intact. A quantum nondemolition measurement preserves the quantity it measures, so repeating it returns the same result. It does not preserve an arbitrary superposition: a nondemolition measurement of a qubit’s energy state still destroys the coherence between 0 and 1.
Error correction depends on choosing what to measure. In the surface code, ancilla qubits measure the joint parity of several data qubits, which reveals whether an error occurred without revealing the encoded logical state, a step I cover under syndrome extraction.
Ancilla-free versions exist: in 2022, Irfan Siddiqi’s group at Berkeley ran a continuous bit-flip code with direct parity measurements and no ancilla qubits. In every version, experimenters measure several qubits jointly. The Letter’s scheme reads the current of one junction and proposes no parity measurement, so it offers no route to removing ancillas from error correction.
Researchers already read out Andreev qubits without any ancilla. The Saclay group performed single-shot readout of an Andreev level qubit in 2015 with a microwave resonator and saw quantum jumps in continuous measurements. The Yale team that demonstrated the first Andreev spin qubit in 2021 also used single-shot circuit-QED readout. Both experiments used a resonator and an amplifier chain, with no ancilla qubit.
The ancilla-assisted repetitive readout schemes the Letter cites include trapped-ion and NV-center experiments, where a co-trapped ion or a nuclear spin is used to raise readout fidelity. In the Letter’s own model the pickup coil becomes entangled with the qubit, so the coil is the meter, an auxiliary quantum system in its own right.
Changes Between the Preprint and the Letter
The preprint’s title promised a non-collapsing readout, and its text said the scheme leaves the qubit’s state intact and allows a fully nondestructive measurement. The Letter replaced the classical current meter with a SQUID whose pickup coil becomes entangled with the qubit. It added a back-action model and describes the readout as approaching the nondestructive limit.
Its abstract still says the effect enables nondestructive qubit readout, and its conclusion says the setup provides the Bloch-sphere angles nondestructively. Egues told Agência FAPESP that the method does not eliminate the basic problem of quantum measurement. In the same interview he said that tracking the current over time allows the qubit’s initial state to be reconstructed.
The headlines dropped the qualification. Agência FAPESP headlined the work as reading quantum information without destroying it, and Quantum Zeitgeist ran the same framing. Neither headline mentions back-action or that the readout only approaches the nondestructive limit, but the stronger claim starts in the Letter’s own abstract and conclusion.
Experiments That Could Test the Prediction
The predicted oscillation can be tested with ensemble methods. An experiment would prepare the same superposition with a microwave pulse and measure the loop current or flux after a controlled delay. Averaging many repetitions at each of a series of delays would trace out the oscillation.
At tens of gigahertz, experimenters would need phase-sensitive detection locked to the preparation pulse and a detector with enough bandwidth, so the experiment is demanding. Groups at Saclay, Yale and Delft have already driven Andreev transitions coherently with microwave pulses. An amplitude and phase that match the calculation would confirm the Letter’s central prediction.
A second experiment would monitor one junction’s current continuously with a weak, near-quantum-limited detector, in the style of the Berkeley trajectory work. It would show the qubit’s state diffusing under measurement at a rate set by the information extracted. Restating the readout claim in those terms, with a back-action budget tied to the detector’s noise, would give experimentalists a claim they can check.
Where Andreev Qubits Stand
The Letter models an Andreev level qubit, whose two states differ by a pair of quasiparticles. The other main kind, the Andreev spin qubit, stores information in the spin of a single trapped quasiparticle. Published coherence times for both kinds are short. The 2015 Saclay level qubit reached the microsecond range; the 2021 Yale spin qubit had a 52-nanosecond echo coherence time.
The two-qubit results so far are coupling demonstrations without benchmarked gates. A Basel group coupled two Andreev level qubits six millimeters apart through a microwave resonator, in work published in Nature Physics in 2024. The same year, Pita-Vidal and colleagues at Delft used shared supercurrent to couple two Andreev spin qubits about 25 micrometers apart, with a coupling strength of up to 178 MHz.
Single-shot readout has been demonstrated for both kinds of Andreev qubit. The open problems are coherence, gate performance and scaling. The superconductor-coated semiconductor nanowires used in the Yale, Delft and Basel devices come from the same materials family as Microsoft’s topological qubit program, which I cover in my Majorana qubits profile. Researchers searching for Majorana modes in such nanowires routinely have to rule out Andreev states, which can mimic the Majorana signature.
The Letter contains no logical-qubit resource estimate, fault-tolerant architecture or cryptanalytic benchmark. I know of no published resource estimate for breaking RSA or elliptic-curve cryptography that assumes Andreev hardware; the estimates I track assume superconducting or trapped-ion qubits, among others.
If a group measures a voltage-free oscillating supercurrent with the amplitude Zhang and his colleagues calculated, the paper will have given experimentalists a new handle on Andreev states. A readout built on that current needs a measurement model in which each sample’s precision sets the disturbance it causes.
