Xue Dong, Xi Cao, Wen-Long Li, Guofeng Zhang, Zhihui Peng, Re-Bing Wu
8 min
Quantum networks rely on the transmission of "flying qubits," which are typically itinerant photons. For high-fidelity communication and distributed quantum computing, these flying qubits must be carefully shaped to match the absorption profiles of receivers. However, practical quantum devices, such as superconducting transmon qubits acting as emitters and gmon couplers, are inherently non-ideal. They suffer from anharmonicity—which causes undesired level leakage—and limited tunable coupling ranges, which complicates the generation of specific pulse shapes, such as exponentially rising wave packets.
This study applies quantum optimal control theory to address these non-idealities. The authors model the emitter as an anharmonic transmon qubit coupled to a waveguide. To overcome physical limitations, they optimize two types of controls: a coherent microwave driving field (XY control) and a tunable coupler strength. By formulating objective functionals that represent the state-preparation error and the fidelity of the generated flying-qubit shape, the authors employ a gradient-descent algorithm (specifically the L-BFGS method) to find control pulses that minimize errors.
The numerical simulations yield three significant insights. First, coherent driving fields can effectively suppress both level leakage and photon leakage during the state-preparation phase, significantly outperforming standard Gaussian or DRAG pulses. Second, while coherent control provides a basic capability for shaping flying qubits, it is insufficient on its own for complex waveforms. Finally, the authors demonstrate that when an emitter is paired with a coupler of restricted tunability, the joint optimization of both coherent driving and tunable coupling significantly enhances shaping performance, allowing for high-fidelity generation even for challenging exponentially rising pulses.
This research provides a systematic, model-based approach to improving the control of quantum signals in realistic hardware. By showing that coherent control can "compensate" for the physical limitations of hardware couplers, this work offers a pathway to increase the efficiency of quantum networks without requiring perfect hardware components. It lays the groundwork for more reliable remote quantum state transfer and entanglement distribution.
The control of flying qubits carried by itinerant photons is ubiquitous in quantum networks. Beside their logical states, the shape of flying qubits must also be tailored for high-efficiency information transmission. In this paper, we introduce quantum optimal control theory to the shaping of flying qubits. Building on the flying-qubit control model established in our previous work, we design objective functionals for the generation of shaped flying qubits under practical constraints on the emitters and couplers. Numerical simulations employing gradient-descent algorithms demonstrate that the optimized control can effectively mitigate unwanted level and photon leakage caused by these non-idealities. Notably, while coherent control offers limited shaping capacity with a fixed coupler, it can significantly enhance the shaping performance when combined with a tunable coupler that has restricted tunability. The proposed optimal control framework provides a systematic approach to achieving high-quality control of flying qubits using realistic quantum devices.
Alex: The drive manipulates the emitter’s quantum state; the authors call this coherent control. It’s normally used to prepare the emitter before release. Using it during emission can help shape the pulse, but it can also produce unwanted extra photons.
Sam: That sounds like a trade-off rather than a straightforward fix. What else makes the emitter non-ideal?
Alex: They model a transmon, a superconducting circuit used as the emitter. It has more energy levels than the desired logical pair. Driving it can populate those unwanted levels, a problem called level leakage. Meanwhile, residual coupling can release photons before preparation finishes.
Sam: So a useful optimizer must avoid unwanted emitter states and unwanted light. How do they track both without calculating every possible emitted field?
Alex: That’s the central shortcut. Their existing emission model calculates the vacuum component and the desired single-photon component. The full field state is normalized. So maximizing the appropriate desired components also leaves less probability for unwanted multiple-photon emissions, without explicitly computing all of them.
Sam: But “appropriate” matters there. Making a known photon pulse and transferring an unknown quantum state aren’t the same task.
Alex: The authors separate them. They define objectives for preparing the emitter, directly generating a chosen flying-qubit state, and transferring an unknown emitter state. For transfer, the control must preserve the distinction between an initially unexcited emitter and an initially excited one.
Sam: In practical terms, an unexcited emitter should produce no photon. An excited emitter should produce the target pulse. A good-looking pulse from either input would fail that test.
Alex: That distinction becomes important in their results. They optimize the controls using a gradient-based algorithm. The microwave pulses have bounded strength, filtered smoothness, and zero amplitude at their endpoints. Their emitter model retains five energy levels to capture leakage beyond the logical states.
Sam: Before tackling pulse shapes, does optimization actually improve preparation compared with standard controls?
Alex: In their preparation example, both optimized controls reach about 99.4 percent fidelity with the target excited state. A standard Gaussian pulse reaches about 82.5 percent. The comparison includes residual coupling, so photons can escape while the emitter is being prepared.
Sam: A Gaussian pulse isn’t designed specifically to suppress unwanted energy-level transitions. Did they include a stronger baseline?
Alex: They also test a standard correction called DRAG, designed to suppress level leakage. That reaches about 91.6 percent fidelity. It largely removes the unwanted-level population, but does not efficiently prevent premature photon emission. The optimized controls reduce both errors in this example.
Sam: That supports optimizing around the actual open connection, not just perfecting an isolated emitter. Does the same microwave control then solve shaping with a fixed connection?
Alex: Not generally in these simulations. Decaying pulses are easiest because they resemble natural spontaneous emission. Symmetric and rising pulses are harder. For unknown-state transfer, fixed coupling with optimized driving can produce nearly indistinguishable photon components from the different initial emitter states.
Sam: Which would mean the output no longer reliably reflects the input. What changes when they restore an adjustable connection, but keep its hardware limits?
Alex: They first take the ideal rising-pulse coupling schedule and clip it to the allowed range. That produces a poorly shaped photon, including early leakage because the connection cannot fully close. They then add an optimized microwave drive, and finally optimize both controls together.
Sam: Where does the drive do useful work? Is it active throughout the whole release?
Alex: Mostly where the coupler cannot follow the ideal schedule. During the interval where the desired coupling is achievable, the coupler does most of the work. The microwave drive is nearly inactive. That gives a concrete picture of complementary controls.
Sam: What’s the clearest quantitative comparison for transferring an unknown state, rather than merely fitting a pulse?
Alex: With clipped coupling and no drive, the total transfer error is about 0.34. Jointly optimizing coupling and driving lowers it to about 0.10. That’s their combined objective: preserving vacuum for the unexcited input and matching the target photon for the excited input.
Sam: Those are objective-function values, not measured failure rates from hardware. And the improvement doesn’t mean both transfer conditions become perfect.
Alex: Correct. Joint optimization improves the emitted photon shape, but it also introduces some unwanted emission from the initially unexcited emitter. The separate error budget makes that trade-off visible. My reading is that this supports the method within its model, not a claim of finished hardware performance.
Sam: What assumption would you most want a device researcher to notice before trusting these gains in the lab?
Alex: The model assumes every emitted photon enters the waveguide: 100 percent collection into that channel. The work is numerical, with a single emitter channel. Parameter uncertainty and control-line pulse distortion are discussed as directions for further control development, not demonstrated robustness tests.
Sam: Given that scope, who should read the full document, and where should they start?
Alex: Researchers designing superconducting quantum-network interfaces or emission controls. Start with the simulation section on jointly tunable coupling and coherent control, especially the conditional state-transfer error comparison. Then read the objective-function section to distinguish known-state generation from unknown-state transfer.
Sam: And what should someone outside that hardware setting carry away?
Alex: A shaped photon is not enough; it must still carry the input state correctly. The practical lesson here is that optimized microwave driving can complement an imperfect adjustable coupler, but it does not replace one.
Sam: That’s a useful distinction to keep in mind.