⚛️ quantum physics

Gradient-free pulse optimization for adiabatic control in open few-body quantum systems

This paper presents a robust, gradient-free pulse optimization method for adiabatic control in open few-body quantum systems that outperforms ensemble optimization and is successfully validated on real IBM Quantum hardware through applications to both atomic and superconducting qubits.

Original authors: Daniel Turyansky, Yehonatan Zolti, Yuval Cohen, Adi Pick

Published 2026-02-06

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Daniel Turyansky, Yehonatan Zolti, Yuval Cohen, Adi Pick

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are trying to guide a very delicate, high-speed car (a quantum system) from a starting point to a destination. The goal is to get there as fast as possible without the car ever leaving the smooth, safe lane (the "ground state"). If the car swerves even slightly, it crashes or loses its cargo (this is called "leakage" or "error").

This paper presents a new, smarter way to steer that car. Instead of just guessing how to turn the wheel, the authors created a "GPS navigation system" that constantly checks if the car is staying in the safe lane and adjusts the steering instantly to keep it there.

Here is a breakdown of their method and findings using simple analogies:

1. The Problem: The "Slow and Steady" Trap

In quantum physics, there is a rule called the "adiabatic theorem." It says that if you want to move a system from one state to another without making mistakes, you must do it very slowly.

The Analogy: Imagine walking across a tightrope. If you move slowly, you have time to balance. If you run, you might fall.
The Issue: In the real world, we don't have time to move slowly. We need to get to the destination quickly. But if we speed up, the system gets "jittery" and falls off the tightrope (this is called a "diabatic error").

2. The Solution: A "Smart Steering Wheel"

The authors developed a method to find the perfect steering instructions (control pulses) that allow the system to move fast but still stay perfectly balanced on the tightrope.

They didn't just look at the finish line; they looked at the entire journey.

Traditional Method: Most old methods only checked: "Did we arrive at the destination correctly?" If the car crashed halfway but somehow landed on its feet at the end, the old method might say, "Good job!"
Their New Method: They check: "Was the car staying on the tightrope the whole time?" They use a special "cost function" (a scoring system) that penalizes the car for even a tiny wobble during the trip, not just at the end.

3. How They Did It: The "Trial and Error" Coach

To find these perfect steering instructions, they didn't use complex math that requires knowing every single detail of the car's engine (which is often impossible in complex quantum systems). Instead, they used a "gradient-free" approach.

The Analogy: Imagine a coach trying to teach a runner the perfect stride. Instead of analyzing the runner's muscle fibers, the coach tries thousands of random stride patterns.
1. They try a pattern.
2. They see how well the runner stayed on the track.
3. They keep the patterns that worked best and tweak them slightly.
4. They repeat this until they find the perfect stride.
The Tool: They used a computer algorithm called CMA-ES (a type of evolutionary algorithm) to do this "trial and error" very efficiently. They also tested different "languages" to describe the steering (like using sine waves or special math curves called Chebyshev polynomials) to see which one worked best.

4. The Proof: Three Different Races

To prove their method works, they tested it on three different "races" involving different types of quantum cars:

Race 1: The Simple Two-Lane Road (Atomic Qubits)
They tested a basic system where a particle moves from state A to state B.
- Result: Their "smart steering" kept the particle on the path even when the road got bumpy (noise or fluctuations in the signal). When they tested this on a real quantum computer in the cloud (IBM Quantum), it worked just as well as the simulations predicted.
Race 2: The Multi-Lane Highway (Superconducting Qubits)
They tested a more complex system involving two qubits connected by a waveguide (like a microwave pipe).
- Result: Their method was much faster to calculate than older methods. While older methods took an hour to find a good path, their method took only minutes, and the resulting path was just as robust against errors.
Race 3: The Maze (Rydberg Atoms & Graph Problems)
They used the method to solve a math puzzle called the "Maximum Independent Set" (finding the largest group of items that don't touch each other) using a grid of atoms.
- Result: As the puzzle got bigger (more atoms), their method still found the solution with high accuracy, outperforming standard "constant speed" or "simple curve" approaches.

5. The Bottom Line

The paper claims that by focusing on keeping the system on its "instantaneous ground state" (the safe lane) throughout the entire journey, rather than just checking the finish line, they can:

Speed up quantum processes significantly.
Make them robust against real-world noise (like signal fluctuations).
Do this efficiently without needing to know every tiny detail of the quantum system's internal mechanics.

They successfully demonstrated this on both computer simulations and real hardware, showing that their "smart steering" is a practical tool for the future of quantum computing.

Technical Summary: Gradient-free Pulse Optimization for Adiabatic Control in Open Few-Body Quantum Systems

Problem Statement
Adiabatic control protocols, including Adiabatic Population Transfer (APT) and Adiabatic Quantum Computation (AQC), are inherently robust to control fluctuations but are limited in speed by the requirement that the system must evolve slowly relative to its spectral gap. Accelerating these protocols without sacrificing fidelity or robustness is a significant challenge. While Quantum Optimal Control (QOC) has successfully enhanced gate-based algorithms, applying it to adiabatic protocols requires minimizing "diabatic errors" (leakage from the instantaneous ground state). Existing acceleration techniques, such as Shortcuts to Adiabaticity (STA), often require full knowledge of eigenstates and their derivatives, which is generally unavailable in large-scale systems required for AQC. Furthermore, traditional ensemble optimization methods, while robust, are computationally inefficient.

Methodology
The authors propose a robust, gradient-free pulse optimization method designed to keep an evolving open quantum system close to its instantaneous ground state. The approach integrates advanced optimization tools with specialized cost functions tailored for adiabatic control.

System Model: The dynamics of the open quantum system are modeled using the Markovian Lindblad master equation, accounting for population relaxation and dephasing.
Cost Functions: The optimization minimizes a composite cost function $C = C_i + \eta C_0$ $C = C_{i} + η C_{0}$ , balancing infidelity and power constraints. The authors define three specific infidelity metrics:
- $C_1$ : The "diabatic error" at the end of the protocol (final state deviation). Minimizing this yields "traditional QOC."
- $C_2$ : The accumulated diabatic error along the entire propagation path. Minimizing this yields "adiabatic QOC."
- $C_3$ : The average diabatic error over an ensemble of systems with shifted or scaled controls, used for ensemble optimization.
  The study demonstrates that minimizing a weighted sum of $C_1$ and $C_2$ enhances robustness.
Pulse Representation: Control pulses are constructed as a sum of a known adiabatic reference pulse and a correction term. The correction is expanded using a finite sum of basis elements (Gaussians, sine functions, or Chebyshev polynomials) with tunable weights. The squared sine envelope ensures smoothness at the protocol boundaries.
Optimization Algorithm: The authors employ the Covariance Matrix Adaptation Evolution Strategy (CMA-ES), a gradient-free evolutionary algorithm. This method draws random samples of expansion coefficients from a normal distribution, evaluates the cost function via simulation (using QuTiP), and iteratively updates the distribution to minimize the cost. This approach is chosen for its ability to handle multi-objective cost functions effectively.

Key Results
The method was validated through three numerical examples involving atomic and superconducting qubits, and verified on real quantum hardware:

Two-Level System (RAP): In Rapid Adiabatic Passage (RAP) for a qubit, the "adiabatic QOC" pulse (minimizing $C_1 + C_2$ ) successfully tracked the instantaneous ground state on the Bloch sphere, unlike traditional QOC or unoptimized pulses. Robustness tests against Rabi frequency and detuning fluctuations showed that adiabatic QOC maintained high fidelity over a significantly wider parameter range. These results were replicated on the IBM Quantum cloud (Brisbane processor) using a digitized, Trotterized version of the pulses.
Multilevel System (STIRAP): The method was applied to a superconducting qubit system coupled via a multimode waveguide (a generalized STIRAP scheme). Compared to Super-Adiabatic Transitionless Driving (SATD), the adiabatic QOC pulses demonstrated improved robustness to intensity fluctuations. The authors noted that while ensemble optimization ( $C_3$ ) produced robust results, the adiabatic QOC approach was substantially more efficient (minutes vs. hours).
Few-Body System (AQC for MIS): The algorithm was used to accelerate an AQC protocol for finding the Maximum Independent Set (MIS) of a graph using Rydberg atoms. Using ring graphs with up to 14 atoms, the adiabatic QOC pulses achieved higher fidelity than constant or squared-sine pulses. The study highlighted that for larger Hilbert spaces, the weight of the accumulated error term ( $C_2$ ) should be reduced to improve convergence.

Significance and Claims
The paper claims to present a general, efficient, and robust method for accelerating adiabatic protocols in open few-body quantum systems without requiring full knowledge of the system's eigenstates. By combining gradient-free optimization with a cost function that penalizes deviations from the instantaneous ground state throughout the evolution (rather than just at the end), the method achieves high-fidelity control that is resilient to intensity and frequency fluctuations.

The authors emphasize that their approach outperforms ensemble optimization in terms of computational efficiency while maintaining comparable robustness. The successful implementation on IBM Quantum hardware validates the practical applicability of the digitized pulses. The work suggests that adherence to the instantaneous ground state is a viable strategy for improving AQC, even when the full state is not known, potentially by utilizing approximate ground states or knowledge from early protocol stages. Future directions identified include optimizing the division between classical optimization resources and quantum evolution resources.