⚛️ quantum physics

Measurement-free Preparation of Surface-Code States with Digital-Analog Counterdiabatic Drivings

This paper introduces a digital-analog counterdiabatic driving method that leverages the structural properties of the adiabatic gauge potential to efficiently prepare surface-code ground states on near-term superconducting architectures, significantly outperforming bare adiabatic evolution and reducing entangling depth by an order of magnitude for measurement-free initialization.

Original authors: Shubham Kumar Balaganchi A. Bhargava, Paolo A. Erdman, Anne-Maria Visuri, Jose D. Martın-Guerrero, Yolanda Vives-Gilabert, Enrique Solano, Narendra N. Hegade

Published 2026-10-06

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CC BY 4.0

Original authors: Shubham Kumar Balaganchi A. Bhargava, Paolo A. Erdman, Anne-Maria Visuri, Jose D. Martın-Guerrero, Yolanda Vives-Gilabert, Enrique Solano, Narendra N. Hegade

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

Quantum computers promise to solve problems that would take ordinary machines thousands of years, but they are notoriously fragile. The bits of information they use, called qubits, lose their delicate quantum state the moment they interact too much with the outside world or make a mistake. To fix this, scientists use a strategy called quantum error correction, which spreads information across many qubits so that if one fails, the others can hold the truth. This requires arranging the qubits in a specific pattern and forcing them to agree with each other in a strict set of rules. Before the computer can start its work, it must first be initialized into this perfect, rule-following state. Doing this quickly and accurately without stopping to measure and correct the qubits along the way is a major hurdle for building useful machines today.

A team of researchers has developed a new way to prepare these essential states on superconducting quantum processors, the type of hardware currently used by many labs. Instead of trying to build the complex state piece by piece using a long sequence of digital instructions, they used a method that blends continuous, natural interactions with short, precise digital adjustments. Their approach, tested in detailed computer simulations, successfully prepares the required quantum patterns much faster and more reliably than previous methods, all without needing to pause and measure the system. This work offers a practical path to getting quantum computers ready for their jobs without the heavy overhead of constant checking.

The challenge the researchers tackled is known as state preparation. In a quantum computer designed to correct its own errors, the qubits must be arranged in a grid where they form specific groups, or "plaquettes," that act together. For the computer to work, these groups must settle into a state where they all agree on a shared property, a condition physicists call a stabilizer code. The standard way to get there is to slowly guide the system from a simple starting point to the complex target state, a process known as adiabatic evolution. However, if this process is too slow, the computer loses its quantum coherence before it finishes. If it is too fast, the system gets confused and ends up in the wrong state. To speed things up without losing accuracy, scientists have tried adding a "counterdiabatic" push, an extra force that cancels out the confusion caused by moving too quickly. The problem is that this extra force usually requires complex, multi-qubit interactions that current hardware cannot perform directly.

The authors of this study, working with superconducting circuits, found a way to generate these complex pushes using the hardware's native capabilities. Their processors naturally allow qubits to interact with their immediate neighbors in a specific, continuous way. The researchers realized that by applying short, fixed digital rotations to the qubits before and after these natural interactions, they could "dress" the simple interactions to create the complex, multi-qubit forces needed for the counterdiabatic push. They did not try to build the complex force from scratch; instead, they let the hardware's natural physics do the heavy lifting, using the digital steps only to steer the outcome. This digital-analog hybrid method allowed them to create the necessary four-qubit correlations using only the two-qubit connections available on their chips.

To test their idea, the team simulated the process on grids of qubits ranging from small 2-by-3 arrangements up to 4-by-4 squares, which represent the building blocks of larger quantum error-correcting codes. They compared their new digital-analog method against two other approaches: a purely digital method that tries to build every step from scratch, and a standard adiabatic method that moves slowly without the extra push. In these simulations, the new method proved highly effective. It reached the correct target state with a high degree of accuracy in a very short time, performing nearly as well as the best purely digital method but using far fewer complex operations. Crucially, it vastly outperformed the slow, standard method, which failed to reach the correct state within the same short timeframe.

The researchers also examined how their method holds up when the hardware is imperfect, which is always the case in real life. They introduced a realistic model of noise, simulating the small errors and signal losses that occur in actual superconducting devices. In these noisy conditions, the purely digital method struggled because its long sequence of instructions accumulated too many mistakes. The standard slow method also failed to reach the target state. The digital-analog approach, however, remained robust. By relying on the hardware's natural interactions rather than long chains of digital gates, it avoided many of the errors that plagued the other methods. While a method that uses measurements to check and fix errors still achieved the highest possible accuracy, the new digital-analog technique came remarkably close to that performance without requiring any measurements, reset operations, or classical computing to intervene during the process.

This work demonstrates that the geometry of the error-correcting code itself can be used to simplify the control of the quantum hardware. By matching the structure of the required quantum state to the natural connections of the processor, the researchers were able to synthesize the necessary complex forces efficiently. Their simulations showed that as the grid of qubits grows larger, the method scales well, requiring only a manageable increase in the complexity of the digital steps. The key finding is that by reversing the usual workflow—first identifying what the hardware can naturally do, and then designing the control strategy around those capabilities—scientists can prepare the essential states for quantum error correction much more effectively. This provides a clear, measurement-free route to initializing quantum computers, a critical step toward building machines that can run complex algorithms without falling apart.

Technical Summary: Measurement-free Preparation of Surface-Code States with Digital-Analog Counterdiabatic Drivings

Problem Statement
Initializing quantum processors into stabilizer-code states is a critical primitive for near-term quantum error correction (QEC), particularly in superconducting architectures. While repeated syndrome extraction relies on measurements and classical decoding, the initial state preparation must be formulated as a coherent Hamiltonian-control problem. Standard adiabatic evolution offers a measurement-free route but suffers from diabatic excitations at experimentally accessible runtimes, limiting ground-state fidelity. Conversely, Counterdiabatic (CD) driving can suppress these transitions by adding an auxiliary Hamiltonian derived from the adiabatic gauge potential (AGP). However, exact AGPs for many-body systems are typically nonlocal and contain high-weight Pauli operators (e.g., four-body terms) that are difficult to implement directly on hardware restricted to native one- and two-qubit controls. Existing digital decompositions of these high-weight terms incur significant entangling depth and gate overhead, degrading performance under noise.

Methodology
The authors propose a Digital-Analog Quantum Computing (DAQC) framework to prepare surface-code ground states. The methodology reverses the conventional workflow: instead of compiling a pre-determined variational AGP into native gates, the method first identifies the many-body operator manifold generatable by the hardware's native interactions and uses this set as the variational ansatz for the AGP.

Hardware-Native Operator Pool: The authors utilize a superconducting layout with tunable couplers providing native $XY$ exchange interactions ( $H_{XY} = \sum J_{ij}(X_i X_j + Y_i Y_j)$ ). By applying "dressing" circuits—comprising fixed-angle two-qubit $XY$ gates and single-qubit rotations on disjoint matchings of the hardware graph—they generate a pool of higher-order Pauli operators (up to four-body) directly from the analog evolution.
Variational CD Synthesis: Within the Sels-Polkovnikov variational framework, the coefficients of these hardware-generated operators are optimized to approximate the exact AGP. The variational principle minimizes the Hilbert-Schmidt action, selecting only the relevant operators and their optimal amplitudes.
Implementation: The resulting CD Hamiltonian is implemented by activating specific analog blocks (with couplings $J_{ij}$ determined by the optimized coefficients) and applying digital dressing layers. Two-body boundary terms are handled digitally, while four-body bulk plaquette terms are realized via the dressed analog blocks.
Benchmarking: The protocol is benchmarked on rotated surface-code patches (checkerboard plaquette-stabilizer grids) ranging from $2\times3$ to $4\times4$ qubits. Performance is evaluated against bare adiabatic evolution, fully digital CD (using nested-commutator and variational ansätze), and a measurement-based stabilizer preparation scheme. Simulations include a hardware-motivated noise model incorporating gate errors and decoherence.

Key Contributions

Hardware-Native CD Construction: The paper introduces a method to map stabilizer-local counterdiabatic terms directly to digital-analog blocks on superconducting layouts, avoiding the need for deep digital decompositions of high-weight operators.
Scalable Synthesis: The authors demonstrate that the dressing rules identified on a $3\times3$ patch can be extended to larger $n \times m$ lattices through repeated matching patterns, allowing the method to scale without requiring new unrestricted many-body decompositions for every system size.
Entangling Depth Reduction: The digital-analog approach reduces the entangling circuit depth by an order of magnitude compared to fully digital implementations of the same variational CD terms.
Noise Robustness: The study shows that while fully digital CD protocols suffer from accumulated gate errors, the digital-analog implementation maintains high fidelity under noise by replacing long digital decompositions with simultaneous analog interactions.

Results

Fidelity Improvement: For short evolution times ( $T=1$ ), the digital-analog CD protocol substantially improves ground-state preparation fidelity compared to bare adiabatic evolution and fully digital CD methods.
Comparison with Measurement-Based Schemes: In noiseless simulations, the measurement-based protocol (using syndrome extraction and correction) achieves the highest fidelity. However, under a realistic noise model, the digital-analog CD protocol approaches the performance of the measurement-based scheme while remaining entirely coherent and measurement-free.
Resource Efficiency: The digital-analog method achieves ground-state fidelities close to the fully digital variational CD (Var-CD) but with significantly fewer entangling gates.
Trotterization Robustness: The digital-analog implementation is less sensitive to the time-step size in Trotterized evolution compared to fully digital Var-CD, as the analog blocks evolve under the complete native interaction rather than a decomposed Pauli sum.
Local vs. Global Stability: In noisy simulations, the digital-analog protocol preserves both global ground-space overlap and local stabilizer correlations more effectively than fully digital coherent protocols.

Significance
The paper establishes a direct connection between the geometry of stabilizer codes, the structure of the counterdiabatic gauge potential, and digital-analog control. It demonstrates that organizing CD construction around native hardware interactions allows for the preparation of stabilizer-code states without measurements, ancillas, or mid-circuit resets. This provides a viable, measurement-free initialization strategy for near-term superconducting architectures, potentially serving as a foundational step for digital-analog quantum error correction where analog blocks handle stabilizer operations and digital operations manage ancilla control and readout. The work does not claim to solve full fault-tolerant error correction but positions this method as a critical primitive for logical-state initialization.

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