A General Framework for Gradient-Based Optimization of Superconducting Quantum Circuits using Qubit Discovery as a Case Study

arXiv:2408.12704 · quant-ph, cond-mat.mes-hall, physics.app-ph · Submitted 2024-08-22 · 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: I'm Kai, and with me are Mira and Lev, guest researcher.

Mira: Today's paper: "A General Framework for Gradient-Based Optimization of Superconducting Quantum Circuits using Qubit Discovery as a Case Study".

Kai: Automating Hamiltonian design through gradient-based optimization can dramatically accelerate the process,

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

Title and authors: Kai: So we've got this paper here titled "A General Framework for Gradient-Based Optimization of Superconducting Quantum Circuits using Qubit Discovery as a Case Study." It looks like the authors are tackling the core difficulty in designing these circuits automatically by creating a general framework that uses gradient-based optimization.

Mira: That sounds ambitious, Kai. The title suggests they're not just looking at one specific circuit design, but trying to build a method that works for any superconducting circuit using qubit discovery as an application example. I wonder what the actual mechanism behind this general approach is, Mira muses.

Lev: From my side, the implication is that if this framework actually works reliably across different circuit types, it could significantly speed up how we explore the design space for qubits that meet specific criteria for quantum error correction.

Kai: Exactly! The paper suggests they are addressing the challenge of calculating gradients of eigenvalues and eigenvectors for large, sparse Hamiltonians relative to system properties, which is a major hurdle when you try to automate this.

Mira: I see what they're proposing: integrating automatic differentiation into existing software like SQcircuit to compute those gradients efficiently without having to manually calculate them every time.

Lev: That's the key, because if we could reliably get gradients for the eigenfrequencies and eigenvectors, it would give us a direct way to tell the optimization algorithm which direction in the parameter space leads toward better performance metrics on real hardware.

Kai: Right, so they are using automatic differentiation to compute gradients for loss functions that measure how far a simulated circuit property is from an ideal target.

Mira: And they tackle the problem of calculating those derivatives by introducing a custom node that uses perturbation theory to approximate the derivatives of the eigenfrequency and eigenvector.

Lev: Perturbation theory is a way to get an approximation when direct calculation is too computationally expensive, but I have to ask if that approximation holds up well enough for real-world hardware characterization where precision matters.

Kai: The paper mentions they calculate the gradient of the eigenfrequency using an expression like ∂f i/∂x = ⟨f i∂Hˆ/∂x f i⟩, and similarly for the eigenvector.

Mira: And then they use these gradients with the chain rule to compute dL/dx, even though the charge and flux operators themselves don't depend on those circuit element parameters.

Lev: That part about using automatic differentiation via a PyTorch computational graph is interesting because it shows how you can leverage modern ML tools for something that is fundamentally quantum mechanical in nature.

Title and authors: Kai: So they apply this entire framework to qubit discovery, which they frame as a search problem to maximize metrics like the number of gates (N) while keeping physical constraints in mind.

Mira: The optimization setup involves converting that search problem into a dual optimization problem, minimizing Lobj plus Lconst where Lobj is the primary objective and Lconst penalizes constraint violations using hinge loss functions.

Lev: That dual formulation is important because it handles those hard physical limits—like fabrication constraints or flux sensitivity bounds—without completely throwing off the optimization process.

Kai: The optimization loop itself uses the BFGS algorithm with random restarts, which they've sped up by incorporating automatic truncation number assignment and diagonalization convergence tests to keep things reliable.

Mira: It seems like a comprehensive approach that tries to manage both the complexity of high-dimensional quantum calculations and the requirements of a robust optimization search.

Lev: I just wonder how computationally intensive those truncation assignments are during the search phase; if it slows down the process too much, it defeats the purpose of automating design acceleration.

Kai: Well, moving on to what they actually found, this paper presents several key performance metrics that are evaluated for candidate qubits based on their decoherence time T, single-qubit gate speed G, and number of single-qubit gates N.

Mira: And they also look at flux sensitivity Sφ and charge sensitivity Sn, which are crucial because those metrics directly relate to how well the circuit interacts with the external environment.

Lev: When I think about running this on real hardware, I'm thinking about whether we can actually measure those decoherence times and gate speeds accurately enough to feed into this optimization loop effectively.

Kai: The results show that their optimization pipeline successfully identifies optimized designs, specifically noting that the fluxonium qubit exhibited the best overall properties for the objective function they were optimizing.

Mira: That's a tangible result because it shows that this automated framework can lead to designs with improved performance metrics compared to what was already known in existing literature on superconducting qubits.

Lev: If they can consistently find better designs than existing literature, it suggests this method might be useful for finding novel qubit architectures that are inherently more robust against the noise we deal with every day.

Kai: The practical implementation details also include using automatic truncation number assignment to minimize the total Hilbert space dimension K while maximizing accuracy by fitting exponential decay curves of eigenvector magnitudes.

Mira: They also included a diagonalization convergence test, which checks if the calculated eigenfrequencies and eigenvectors are trustworthy by verifying that the error metric epsilon is less than epsilon star.

Title and authors: Lev: Those reliability checks are essential because without them, you're just optimizing based on noisy data from an unreliable simulation, so having those built-in safeguards is smart engineering.

Kai: So, to summarize this paper, it presents a general framework for gradient-based optimization of superconducting quantum circuits using qubit discovery as a case study by integrating automatic differentiation into existing software like SQcircuit.

Mira: This framework allows for the calculation of gradients for various circuit properties and applies them to search problems where you want to maximize metrics like gate count subject to physical constraints, utilizing a dual optimization problem.

Lev: It's a method that automates the Hamiltonian design process by tackling the difficulty of calculating those gradients of eigenvalues and eigenvectors through perturbation theory approximations.

Kai: The implications are pretty significant because it moves us toward an AI-driven quantum hardware designer capable of autonomously searching for qubit designs that maximize performance metrics like gate count while respecting physical limits.

Mira: If this method can reliably find novel qubit topologies, it could significantly accelerate the path toward realizing fault-tolerant quantum computation by discovering systems inherently more resilient to fabrication errors and environmental noise.

Lev: It would give us a tool to rapidly prototype and identify candidate circuits that are already performing better than what we currently have in literature, which is a massive time saver for experimentalists.

Kai: So, wrapping up this discussion on "A General Framework for Gradient-Based Optimization of Superconducting Quantum Circuits using Qubit Discovery as a Case Study," it seems like the authors have developed a solid methodology to bridge the gap between complex quantum simulation and automated design search.

Mira: The focus on using automatic differentiation to compute gradients for eigenvalues and eigenvectors, even with perturbation theory approximations, shows a clever way to make high-dimensional quantum problems tractable for optimization methods that rely on those derivatives.

Lev: My main thought remains about the reliability of the results when we try to translate this into real hardware; we need confidence that these optimized designs aren't just theoretical constructs.

Kai: Exactly, and while they show promising results on fluxonium qubits, the next step is definitely verifying those performance metrics under actual experimental conditions.

Mira: And I think this paper opens the door for repurposing this methodology to optimize other quantum hardware components or even different types of quantum systems if we adjust the loss function appropriately.

Lev: So, for me, it’s a framework that gives us a powerful way to explore design space intelligently rather than relying on brute force searching through parameter space.

The paper's summary: Kai: So, to recap what we just discussed, this paper outlines a comprehensive method for using gradient-based optimization within existing circuit simulation software to automatically design superconducting quantum circuits by focusing on qubit discovery as the main application.

Mira: That’s right, and it boils down to them creating a general framework that uses automatic differentiation to figure out how changing physical circuit parameters affects performance metrics like decoherence time or gate speed.

Lev: I see how that structure connects the high-level search problem with the actual physics calculation; they're using those derivatives to navigate the optimization landscape efficiently without needing brute force.

Kai: Exactly, and what’s really interesting is how they handle the technical hurdle of calculating those derivatives for complex quantum systems, which they do by introducing a custom node that uses perturbation theory to approximate the gradients of eigenvalues and eigenvectors.

Mira: That approximation step is critical because it allows the optimization pipeline to function even when you can't calculate those exact derivatives directly, which is a major practical constraint in this field.

Lev: From my side, I’m thinking about how reliable that approximation needs to be; if the perturbation theory introduces significant error, then any optimized circuit design could turn out to be fundamentally flawed when we actually try to cool and measure it on a real chip.

Kai: That’s a valid concern because the entire point of this framework is that it speeds up the design process so much that we can generate many candidates quickly for experimentalists to check, but accuracy is still paramount.

Mira: The paper addresses this by incorporating rigorous checks, like an automatic truncation number assignment and a diagonalization convergence test, which they use to keep the search reliable and prevent computational waste.

Lev: Those reliability tests are what I’m most interested in; if the system flags that its calculated eigenfrequencies aren't converged enough, then we know we need more simulation time before trusting any design suggestion.

Kai: So, it seems like this work provides a systematic way to move beyond manual trial-and-error and start using AI to search for qubit designs that inherently maximize metrics like gate speed while staying within physical limits.

Mira: It’s about building a system where the optimization loop intelligently guides the design toward superior performance characteristics, rather than just guessing parameters randomly.

Lev: If this works as intended, it means we could start designing qubits specifically engineered to be more resistant to noise or fabrication imperfections from the very beginning of the design process.

Kai: That's what excites me most—the potential for discovering qubit architectures that perform better than anything currently in literature because they were optimized through a rigorous search.

Mira: I think this methodology has broad implications beyond just one specific qubit type, suggesting it could be repurposed to optimize other quantum hardware components or even different types of quantum systems if you adjust the loss function.

Lev: That general applicability is what makes this framework useful for error correction research; we don't want to be stuck optimizing only one specific system design.

Kai: So, this paper isn't just about finding one good circuit; it’s about building a generalized tool that fundamentally improves how quantum hardware is conceived and designed.

Mira: Indeed, it moves the process from heuristic searching to a structured, differentiable optimization search space for superconducting circuits.

Lev: It’s a powerful tool for accelerating prototyping while providing the necessary mathematical backbone to ensure those designs are physically viable before they ever hit the cryogenic stage.

The paper's improvements: Tom: So, we’ve just talked about how they set up the search problem using dual optimization to balance performance metrics against physical constraints in superconducting circuits.

Kai: That's right, and now we’re looking at the specific technical enhancements they added to make this entire framework more robust for real-world application.

Mira: They’ve introduced several improvements that directly address the computational costs and reliability issues we talked about earlier, focusing on making the search process smarter rather than just brute-force.

Lev: I'm paying close attention because if they can truly automate this, it changes how we approach designing systems for fault tolerance; those constraints are where most of our manual tuning time goes.

Kai: One big improvement is the automatic truncation number assignment, which helps minimize the size of the Hilbert space we have to simulate while still keeping the accuracy high.

Mira: That’s clever because it dynamically allocates computational power based on how fast certain quantum modes are expected to decay, preventing us from wasting cycles simulating modes that don't contribute much to the final performance.

Lev: Minimizing K is crucial when you consider the complexity of Hamiltonian simulations; if you can reduce the Hilbert space dimension effectively, it makes running those expensive calculations much more feasible for iterative optimization.

Kai: Then there’s this diagonalization convergence test, which acts as a quality control check to ensure that the eigenfrequencies and eigenvectors calculated during the search are actually trustworthy.

Mira: That test ensures that when we use those gradients to update our circuit parameters, we aren't making adjustments based on noisy or unstable simulation results; it locks in the accuracy of the quantum mechanical inputs.

Lev: Without that kind of built-in validation, I’d have to spend a lot of time post-optimization just trying to debug why a design failed, so having that test integrated into the search loop is a big win for practical use.

Kai: So essentially, they’ve layered in these intelligent management features—the truncation assignment and the convergence check—to turn this framework into an efficient and reliable engine for circuit discovery.

Mira: It shows a strong commitment to making this method tractable; it’s not just a theoretical proposal but a system that anticipates the practical computational bottlenecks of quantum simulation.

Lev: If this holds up, it means we can move from just finding *a* qubit design to systematically finding the *best* qubit design within defined physical boundaries.

Kai: It really does open the door for us to start thinking about AI-driven hardware designers that don't just suggest ideas, but actively optimize them based on a multi-objective loss function.

Mira: I think this is where the real impact lies; it’s moving us toward systems that are intrinsically tailored to be resilient against the noise inherent in superconducting platforms.

Lev: If we can automate the discovery of qubits with superior decoherence times and gate speeds, it significantly shortens the timeline for developing scalable error-correcting codes, which is where we need these robust designs most.

Conclusion: Kai: To wrap things up, this paper presents "A General Framework for Gradient-Based Optimization of Superconducting Quantum Circuits using Qubit Discovery as a Case Study," which establishes a powerful method for using automatic differentiation to automate the design and optimization of superconducting circuits.

Mira: It really provides a concrete way to bridge the gap between abstract quantum simulation and the practical need to actually design high-performing physical hardware by providing an automated search pipeline.

Lev: From my perspective, this is significant because it shows a path toward designing qubits that are inherently better suited for running error correction protocols by optimizing their fundamental parameters directly.

Kai: I think the biggest implication here is that we can start building AI systems capable of autonomously discovering novel qubit architectures that outperform what we currently know in literature.

Mira: That moves us past incremental improvements and toward discovering entirely new physical designs that were previously inaccessible through traditional heuristic searching methods.

Lev: If this method works reliably, it could drastically cut down the years of experimental effort needed to realize fault-tolerant quantum computers by providing optimized starting points for fabrication teams.

Kai: It’s exciting to think about a future where we don't just test circuits; we use AI to intelligently design them based on complex performance targets like gate speed and coherence time.

Mira: The way they structured the dual optimization problem is particularly elegant, showing how you can simultaneously satisfy multiple competing physical requirements in a single mathematical framework.

Lev: I hope this research gets translated quickly into simulation tools that experimentalists can actually trust and use to guide their physical fabrication processes effectively.

Department of Electrical Engineering, Stanford University · E. L. Ginzton Laboratory and the Department of Applied Physics, Stanford University

quant-ph, cond-mat.mes-hall, physics.app-ph

Submitted: 2024-08-22

Updated: 2026-10-06

Comments: 23 pages, 10 figures. Accompanying SQcircuit package on https://sqcircuit.org/

Code: https://github.com/stanfordLINQS/SQcircuit

License: http://creativecommons.org/licenses/by/4.0/

Importance score: 77/100

The gist: Automating Hamiltonian design through gradient-based optimization can dramatically accelerate the process, and this work presents a comprehensive framework for optimizing superconducting quantum

Key concepts

Hamiltonian Transformation: A mathematical process used to simplify the circuit's description. It converts the initial charge and flux operators into a sparse form where off-diagonal elements decay quickly. This structure allows SQcircuit to model the system as uncoupled harmonic oscillators, making numerical simulation much more efficient.
Automatic Differentiation: A computational technique integrated into SQcircuit using PyTorch to calculate gradients. It allows the optimization process to determine how changing circuit parameters affects desired properties like qubit performance, even when direct gradient calculation is difficult.
Perturbation Theory for Gradients: A custom method used to approximate the derivatives of eigenvalues and eigenvectors. Since directly calculating these gradients is hard, this theory provides equations (like Equation 6 and 7) that allow the optimization to proceed by calculating how small changes in circuit elements affect system frequencies.
Qubit Discovery Optimization: The application of the framework to find the best superconducting qubit design. The goal is to maximize performance metrics like coherence time and gate speed while respecting physical constraints, using a dual optimization problem solved by an algorithm like BFGS.

Terminology

Loss Function — 31× in this paper · explained in 2 episodes
Quantum Circuits — 22× in this paper · explained in 2 episodes
Hilbert Space — 19× in this paper · explained in 2 episodes
Accuracy — 10× in this paper · explained in 1 episode
Core — 7× in this paper · explained in 2 episodes
Quantization — 7× in this paper · explained in 12 episodes
Physical Constraints — 5× in this paper · explained in 7 episodes
Bayesian Optimization — 3× in this paper · explained in 3 episodes
Objective Function — 3× in this paper · explained in 2 episodes
Reinforcement Learning — 3× in this paper · explained in 4 episodes
Adam — 2× in this paper · explained in 2 episodes
Benchmarking — 2× in this paper · explained in 3 episodes
Adaptation — 1× in this paper · explained in 1 episode
Alignment — 1× in this paper · explained in 1 episode
Analyzer — 1× in this paper · explained in 1 episode
Artificial Intelligence (AI) — 1× in this paper · explained in 2 episodes
Fidelity — 1× in this paper · explained in 2 episodes
Hybrid System — 1× in this paper · explained in 2 episodes
Latent Space — 1× in this paper · explained in 7 episodes
Meta-learning — 1× in this paper · explained in 2 episodes
Robustness — 1× in this paper · explained in 5 episodes
Trace — 1× in this paper · explained in 2 episodes

Summary

Automating Hamiltonian design through gradient-based optimization can dramatically accelerate the process, and this work presents a comprehensive framework for optimizing superconducting quantum circuits by integrating automatic differentiation into existing software like SQcircuit. The framework addresses the challenge of calculating gradients of eigenvalues and eigenvectors for large, sparse Hamiltonians relative to system properties, demonstrating its effectiveness in qubit discovery to identify designs with superior performance metrics.

The gist: This paper introduces a general framework for gradient-based optimization of superconducting quantum circuits using SQcircuit software, leveraging automatic differentiation to compute gradients for various circuit properties and applying it successfully to the qubit discovery problem.

Circuit Analysis and Transformation

The foundation of the work lies in analyzing an arbitrary superconducting quantum circuit described by its Hamiltonian, which is initially defined in terms of charge operators and flux operators (Equation 1). To enable efficient numerical simulation, a canonical transformation is performed to output a sparse Hamiltonian with rapidly decaying off-diagonal matrix elements. This transformation leads to the division of the transformed charge and flux operators into harmonic components and charge components, which are represented in block diagonal structures (Figure 1). This mathematical structure is crucial because it allows SQcircuit to represent the system dynamics as an ensemble of uncoupled harmonic oscillators and isolated superconducting islands.

Gradient Calculation via Automatic Differentiation

The core innovation is the integration of automatic differentiation into the SQcircuit software using a PyTorch computational graph. The framework computes gradients for loss functions of the form (3), which quantify discrepancies between simulated circuit properties and ideal targets, with respect to circuit element parameters (Equation 4). Since direct implementation of gradients for eigenvalues and eigenvectors is challenging, a custom node is introduced that uses perturbation theory to approximate these derivatives:

The gradient of the eigenfrequency is calculated as: ∂f i/∂x = ⟨f i∂Hˆ/∂x f i⟩ (Equation 6).
The gradient of the eigenvector is calculated as: ∂f i⟩/∂x = Σ E m≠i ⟨f m∂Hˆ/∂x f i⟩ f i − f mf m⟩ (Equation 7).

This approach allows the optimization to proceed by computing dL/dx using the chain rule, even though the charge and flux operators do not depend on circuit elements.

Optimization Pipeline for Qubit Discovery

The framework is applied to qubit discovery, which is framed as a search problem aiming to maximize metrics like the number of gates (N) subject to physical constraints. The optimization problem is formulated as:

max x N s.t. xmin ≤ x ≤ xmax, Si ≤ S∗ i, fq ≤ f∗ q (Equation 15).

This is converted into a dual optimization problem minimizing Lobj + Lconst (Equation 16), where Lobj is the primary objective and Lconst penalizes constraint violations using hinge loss functions. The search utilizes the BFGS algorithm with random restarts, which is accelerated by incorporating automatic truncation number assignment and diagonalization convergence tests to ensure reliable exploration of the search space (Figure 3).

Key Performance Metrics and Results

The optimization process evaluates candidate qubits based on several critical metrics:

Decoherence time (T), defined as T = 1/(1/2T1 + 1/Tφ) (Equation 9).
Single-qubit gate speed (G), determined by the minimum of frequency spacings: G = min i≥2(f i − f 1, f i − 2f 1) (Equation 10).
Number of single-qubit gates (N), expressed as N = T G (Equation 11).
Flux sensitivity (Sφ), defined by the ratio of frequency range to the average minimum and maximum frequencies: Sφ = [fq/φ∗ ext + δ 2] / [-fq/φ∗ ext - δ 2] (Equation 1).
Charge sensitivity (Sn) and Element sensitivity (Se) are also defined using sampling methods.

The optimization pipeline, utilizing a reparameterization technique to optimize over unitless values αx instead of raw element values x, successfully identifies optimized designs. The results show that the fluxonium qubit exhibits the best overall properties for the objective function considered, demonstrating that the optimization pipeline can lead to improved performance metrics compared to existing qubits in literature.

Practical Implementation Details

The framework incorporates several technical features to enhance robustness:

Automatic truncation number assignment (Appendix E) is used to minimize the total Hilbert space dimension K while maximizing accuracy by fitting exponential decay curves of eigenvector magnitudes.
A diagonalization convergence test (Appendix D) ensures that the calculated eigenfrequencies and eigenvectors are trustworthy by checking if the error metric ϵ < ϵ∗.

Improvements for AI systems

As a fastidious and diligent AI researcher, I have analyzed this framework for gradient-based optimization of superconducting quantum circuits using Automatic Differentiation (AD). The core innovation lies in bridging the gap between high-dimensional, sparse Hamiltonian eigenvalue/eigenvector calculations and the differentiable landscape required by modern machine learning optimization techniques (like BFGS).

Here are the specific improvements and capabilities this methodology enables for AI systems:

)1. Improved AI System Capability: Automated Quantum Circuit Design & Discovery

The primary improvement is the creation of an AI-driven Quantum Hardware Designer. This system can autonomously search for and optimize superconducting qubit designs based on complex performance metrics, moving beyond heuristic or evolutionary search methods.

)2. Specific Improvements to the AI System Architecture:

[i] Integration of Automatic Differentiation (AD) into Circuit Simulation: The system uses a PyTorch computational graph where the Hamiltonian, eigenfrequencies, and eigenvectors are computed within custom nodes that calculate gradients with respect to circuit element parameters (capacitors, inductors, Josephson junction energies).
[ii] Robust Optimization Pipeline via BFGS: The AI employs a robust optimization loop using the BFGS algorithm. This allows it to efficiently navigate the non-convex loss landscape defined by circuit properties (e.g., gate count vs. decoherence time) without requiring explicit derivatives for every step, leveraging the calculated gradients for efficient convergence toward local optima.
[iii] Intelligent Search Space Management: The system incorporates an automatic truncation assignment algorithm (Algorithm 1 in Appendix E) and a diagonalization convergence test (Appendix D). This prevents computational waste by dynamically allocating Hilbert space dimensions to modes based on their expected excitation decay rates, ensuring the search remains computationally feasible while maximizing the accuracy of the discovered properties.
[iv] Multi-Objective Optimization Framework: The system utilizes a dual optimization problem framework (Equation 16) to simultaneously maximize desired performance metrics (e.g., gate count, decoherence time) while imposing physical constraints (fabrication limits, flux sensitivity bounds).

)3. Specific Applications and Capabilities of the Improved AI System:

[i] Discovery of Novel Qubit Architectures: The system can autonomously identify entirely new qubit topologies (e.g., JJJ, JL(JC)) that outperform existing literature benchmarks by optimizing their physical parameters, yielding designs with significantly higher gate counts or longer coherence times than known qubits.
[ii] Precision Engineering for Fault Tolerance: By directly optimizing metrics related to noise resilience (dephasing time, sensitivity metrics like Sφ and Se), the AI can discover qubits inherently more robust against fabrication errors and environmental noise, a critical step toward realizing fault-tolerant quantum computation.
[iii] Accelerated Hardware Prototyping: The automated pipeline drastically reduces the manual simulation and trial-and-error cycle required by human researchers. The system can rapidly generate a library of high-performing candidate circuits optimized against specific design goals (e.g., maximizing gate speed under a noise constraint).
[iv] Transfer Learning for Other Quantum Systems: Since the framework is general, the AI methodology can be easily repurposed to optimize other quantum hardware components, such as designing optimal coupling elements between qubits or creating specialized quantum sensors, by simply redefining the loss function (Equation 3) and search constraints.

Abstract

Engineering the Hamiltonian of a quantum system is fundamental to the design of quantum systems. Automating Hamiltonian design through gradient-based optimization can dramatically accelerate this process. However, computing the gradients of eigenvalues and eigenvectors of a Hamiltonian--a large, sparse matrix--relative to system properties poses a significant challenge, especially for arbitrary systems. Superconducting quantum circuits offer substantial flexibility in Hamiltonian design, making them an ideal platform for this task. In this work, we present a comprehensive framework for the gradient-based optimization of superconducting quantum circuits, leveraging the SQcircuit software package. By addressing the challenge of calculating the gradient of the eigensystem for large, sparse Hamiltonians and integrating automatic differentiation within SQcircuit, our framework enables efficient and precise computation of gradients for various circuit properties or custom-defined metrics, streamlining the optimization process. We apply this framework to the qubit discovery problem, demonstrating its effectiveness in identifying qubit designs with superior performance metrics. The optimized circuits show improvements in a heuristic measure of gate count, upper bounds on gate speed, decoherence time, and resilience to noise and fabrication errors compared to existing qubits. While this methodology is showcased through qubit optimization and discovery, it is versatile and can be extended to tackle other optimization challenges in superconducting quantum hardware design.