⚛️ quantum physics

Utility of NISQ devices: optimizing experimental parameters for the fabrication of Au atomic junction using gate-based quantum computers

This study demonstrates that gate-based NISQ devices outperform D-Wave quantum annealers in autonomously optimizing experimental parameters for fabricating Au atomic junctions via feedback-controlled electromigration, achieving lower residual energies and higher-quality solutions for large-scale combinatorial problems.

Original authors: Takumi Kanezashi, Daisuke Tsukayama, Jun-ichi Shirakashi, Tetsuo Shibuya, Hiroshi Imai

Published 2026-04-15

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CC BY 4.0

Original authors: Takumi Kanezashi, Daisuke Tsukayama, Jun-ichi Shirakashi, Tetsuo Shibuya, Hiroshi Imai

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

The Big Picture: Tuning a Radio with a Quantum Radio

Imagine you are trying to build a tiny, microscopic bridge made of a single gold atom. This isn't just a bridge for cars; it's a bridge for electrons. Scientists call this an atomic junction.

To build it, they use a process called Electromigration. Think of this like a strong wind (electric current) blowing through a narrow canyon (a gold wire). The wind pushes the rocks (gold atoms) around. If the wind is too strong, the canyon collapses. If it's too weak, the rocks don't move.

The goal is to blow just the right amount of wind to move the rocks one by one, creating a perfect, tiny gap. To do this, scientists have to constantly adjust the "wind speed" (voltage) based on how the rocks are moving. This is called Feedback-Controlled Electromigration (FCE).

The Problem: Too Many Knobs to Turn

The tricky part is that there are dozens of "knobs" to turn (like voltage levels, step sizes, and timing). Finding the perfect sequence of knob-turns to build the bridge is like trying to solve a massive, 3D puzzle while blindfolded.

In the past, scientists used:

Human guesswork: Slow and prone to error.
Machine Learning: Getting better, but still heavy on computing power.
Quantum Annealers (D-Wave): A special type of quantum computer that acts like a "heat-seeking missile" for solutions. It works well, but it's like trying to fit a square peg in a round hole; it requires a lot of extra "helper" bits to work, which introduces noise and errors.

The New Solution: The Gate-Based Quantum Computer

This paper asks: Can we use a different kind of quantum computer (called a Gate-based NISQ device) to solve this puzzle faster and better?

Think of the Gate-based computer (like the IBM machines used here) as a highly skilled, albeit slightly tired, orchestra conductor. It doesn't just "heat-seek" a solution; it actively conducts a symphony of calculations to find the best path.

How they did it:

The Database: They ran thousands of experiments to create a "recipe book" of what happens when you turn the knobs different ways.
The Puzzle: They turned the problem of "which knob to turn next" into a math problem called a Combinatorial Optimization Problem.
- Analogy: Imagine you are a tour guide planning a trip to 10 cities. You want to visit them in an order that minimizes travel time. This is the famous "Traveling Salesman Problem." Here, the "cities" are the voltage settings, and the "travel time" is how well the gold atoms move.
The Algorithm: They used a method called VQE (Variational Quantum Eigensolver).
- Analogy: Imagine you are trying to find the deepest point in a foggy valley. You send out a drone (the quantum computer) that bounces around, measuring the ground. A computer on the ground (the classical optimizer) tells the drone, "Go left, you're getting closer to the bottom." They repeat this until the drone finds the absolute lowest point (the best solution).

The Results: The New Kid on the Block Wins

The researchers compared their new Gate-based quantum computers (IBM's "Eagle" processors) against the old Quantum Annealers (D-Wave) and standard supercomputers.

Here is what they found:

The "Helper" Problem: The old Quantum Annealers needed a huge team of "helpers" (physical qubits) to represent just one piece of the puzzle. It was like needing 5 people to carry one suitcase. This caused a lot of noise and mistakes.
The Efficiency Win: The Gate-based computers were much more efficient. They needed exactly one person per suitcase. Because they didn't need as many helpers, they made fewer mistakes.
The Outcome: For small puzzles, everyone did okay. But as the puzzles got bigger (more complex), the Gate-based quantum computers found better, more accurate solutions than the Annealers. They found "lower residual energy," which is just a fancy way of saying they found a solution closer to the perfect answer.

Why This Matters

This paper is a big deal because it proves that current, imperfect quantum computers (NISQ) are already good enough to solve real-world, messy scientific problems.

Before: We thought we needed perfect, error-free quantum computers to do useful work.
Now: We know that even with the current "noisy" hardware, we can use these machines to optimize complex experiments, like building atomic-scale electronics.

The Takeaway

Imagine you are trying to navigate a maze.

Classical computers are like a person walking every single path until they find the exit.
Old Quantum Annealers are like a heat-seeking missile that flies toward the exit but sometimes crashes into walls because it needs too much fuel.
New Gate-Based Quantum Computers are like a smart drone that learns the map as it flies. Even though the drone is a bit shaky (noisy), it figured out the maze faster and more accurately than the missile.

This study shows that we are ready to use these "shaky drones" to build the next generation of microscopic technology, from super-fast computers to ultra-sensitive sensors.

1. Problem Statement

The fabrication of Gold (Au) atomic junctions via Feedback-Controlled Electromigration (FCE) requires the precise regulation of atomic migration. This process depends on the careful optimization and scheduling of multiple experimental parameters, specifically:

Feedback Voltage ( $V_{FB}$ )
Threshold Differential Conductance ( $G_{TH}$ )
Voltage Step Size ( $V_{STEP}$ )

Manually fine-tuning these parameters is inefficient and challenging. While previous studies utilized machine learning, Ising computing, and Quantum Annealing (QA) (specifically D-Wave systems) to automate this scheduling, these methods face limitations. QA systems often require "minor embedding," where logical qubits are mapped to chains of physical qubits, significantly increasing hardware resource requirements and susceptibility to noise (chain breaks) as problem size grows.

The core problem addressed is whether gate-based Noisy Intermediate-Scale Quantum (NISQ) devices can autonomously optimize these FCE parameters more effectively than current QA systems, particularly for larger-scale combinatorial optimization problems.

2. Methodology

A. Problem Formulation

The authors formulated the scheduling of $V_{FB}$ parameters as a combinatorial optimization problem similar to the Traveling Salesman Problem (TSP), but with relaxed constraints (repetition of parameters is allowed).

Objective: Maximize a "Score" ( $S_{max}$ ) representing the stability of normalized conductance ( $G/G_0$ ) and the smoothness of atomic migration.
Cost Function: The problem is mapped to a Hamiltonian $H$ $H$ to be minimized:
$E(x) = A \sum_n \left( \sum_i x_{n,i} - 1 \right)^2 - B \sum_n \sum_i \sum_j W_{ij} x_{n,i} x_{n+1,j}$
Where:
- $x_{n,i}$ is a binary variable indicating if voltage level $i$ is selected at step $n$ .
- $W_{ij}$ represents the interaction coefficient (transition score) between voltage levels derived from experimental data.
- The first term enforces a one-hot encoding constraint (one voltage per step).
- The second term maximizes the transition score.

B. Quantum Algorithm

The study employed Variational Quantum Algorithms (VQAs), specifically the Variational Quantum Eigensolver (VQE), to find the ground state of the cost function.

Ansatz: A hardware-efficient Ansatz using only $R_Y$ gates was selected. This choice minimizes circuit depth and optimization parameters, mitigating errors associated with limited coherence times and gate fidelities on NISQ devices.
Optimization Loop: A classical optimizer (NFT) iteratively updates parameters $\theta$ to minimize the expectation value $\langle \psi(\theta) | H | \psi(\theta) \rangle$ .

C. Experimental Setup

Data Source: A database of 50 FCE experimental datasets was used to calculate interaction coefficients ( $W_{ij}$ ).
Hardware:
- Gate-based NISQ: IBM Eagle processors (ibm_nazca and ibm_brussels, 127 qubits).
- Quantum Annealing (QA): D-Wave 2000Q, D-Wave Advantage, and D-Wave Advantage2.
- Classical Baseline: Simulated Annealing (SA) and a noiseless quantum simulator (aer_simulator_matrix_product_state).
Scope: Problems ranging from $N=2$ to $N=10$ orders (scheduling steps), corresponding to 18 to 90 logical qubits.

3. Key Contributions

First Application of Gate-Based NISQ to FCE: The study demonstrates the feasibility of using gate-based quantum computers to autonomously schedule experimental parameters for atomic junction fabrication.
Superiority over QA for Large-Scale Problems: The paper provides empirical evidence that gate-based NISQ devices outperform D-Wave QA systems for larger problem sizes ( $N \geq 5$ ), despite the presence of noise.
Hardware-Efficient Ansatz Validation: It validates that a simple $R_Y$ -only Ansatz is sufficient for NISQ devices to solve complex real-world optimization problems, reducing the overhead of error correction and circuit depth.
Resource Efficiency Analysis: The study highlights that gate-based devices require a 1:1 ratio of logical to physical qubits, whereas QA systems require 2.3x to 9.4x more physical qubits due to minor embedding, making gate-based approaches more scalable for this specific problem type.

4. Results

Residual Energy ( $E_{res}$ ):
- Residual energy (the difference between the found solution energy and the optimal Simulated Annealing energy) was measured.
- Gate-based devices (ibm_brussels, ibm_nazca) achieved lower residual energies than all D-Wave QA backends for $N \geq 5$ .
- ibm_brussels performed exceptionally well, achieving residual energies comparable to the noiseless simulator for $N \leq 4$ (36 qubits), attributed to lower readout errors and circuit optimization.
Solution Quality ( $S_{max}$ ):
- The quality of the generated schedules was evaluated using the $S_{max}$ metric.
- For $N \leq 4$ , gate-based devices matched the performance of QA and SA.
- For $N \geq 5$ , gate-based devices produced schedules with higher $S_{max}$ values than QA systems.
- The schedules generated by NISQ devices closely resembled the optimal "20% and 60% repetitive" patterns known to provide high atomic controllability, confirming their practical utility.
Scalability: As problem size increased, QA performance degraded significantly due to chain breaks in minor embedding. Gate-based devices maintained high solution quality because they did not require embedding chains.

5. Significance and Conclusion

This study marks a critical advancement in the practical application of quantum computing to nanofabrication. It demonstrates that gate-based NISQ devices are not only viable but potentially superior to quantum annealers for specific combinatorial optimization tasks involving real-world experimental data.

Practical Impact: The ability to autonomously optimize FCE parameters using NISQ devices enables more reliable and precise fabrication of single-electron transistors, single-molecule transistors, and superconducting qubits.
Technological Insight: The results challenge the assumption that QA is the default choice for optimization; for problems where minor embedding is costly, gate-based approaches with efficient ansatzes offer a more robust path forward on current hardware.
Future Directions: The authors suggest that further improvements can be achieved through readout error mitigation techniques (e.g., mthree) and advanced algorithms like CVaR-VQE, which could further reduce residual energy and stabilize solutions for even larger problem scales.

In summary, the paper proves that current NISQ hardware can effectively solve complex, real-world combinatorial optimization problems in nanotechnology, outperforming established quantum annealing solutions in terms of solution quality and resource efficiency for larger problem instances.