Researchers have demonstrated a method for performing parallel quantum gates on superconducting-qubit arrays scaling up to 200 qubits, an important step toward building more powerful quantum computers. The team from Shenzhen University and the Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area overcame the challenge of qubit crosstalk by focusing on “crosstalk-robust control over constant-sized subsystems,” dramatically reducing the computational demands of gate optimization.

This approach effectively eliminates the leading-order deviations caused by crosstalk, reducing noise scaling from exponential to linear for single-qubit gates and achieving order-of-magnitude reductions for multi-qubit operations. The method requires no prior knowledge of crosstalk strengths and functions across diverse qubit architectures, including nitrogen-vacancy centers and nuclear-spin processors.

Scalable Subsystem Division for Parallel Gate Design

This approach addresses the challenge of crosstalk, unwanted interactions between qubits, by reformulating the optimization of parallel gates as a robust control problem for these smaller, localized units. The entire system is partitioned according to the structure of the gates being executed, assuming minimal interaction between these subsystems, allowing for a significant reduction in computational complexity. This division isn’t static; the paper explains that the system, denoted as S, is broken into L disjoint subsystems S₁∪…∪S_L, and this division can change for different parallel gates within a quantum circuit.

The researchers mathematically describe the system Hamiltonian as H_S = H₀ + H₁ = sum_{(k = +, where represents the internal Hamiltonian of subsystem S_k, and accounts for crosstalk between subsystems S_k and S_j. By focusing on minimizing the effects of these inter-subsystem interactions, the team achieved substantial gains in gate fidelity.}

The core innovation lies in the suppression of leading-order errors caused by crosstalk, directly impacting the scalability of quantum computation. Numerical simulations demonstrate a shift in noise scaling for parallel single-qubit gates, moving from an exponential decay to a linear one. This improvement is visualized in the paper’s data, which compares the fidelities achieved with their robust pulse design against a primitive rectangular pulse across varying numbers of repeated parallel gates.

The researchers observed that the primitive pulse predictably exhibits exponential fidelity decay, while their robust pulse maintains a linear decay, a substantial improvement for building larger, more reliable quantum computers. This linear scaling is achieved because the robust pulses strongly suppress the dominant lowest-order errors, making the overall infidelity *ε* sufficiently small. As a result, the exponential decay e^(-εM), where M is the number of repeated gates, is well approximated by its linear expansion *1-εM*.

The team validated this approach numerically across multiple platforms, including coupled nitrogen-vacancy centers, a nuclear-spin processor, and the aforementioned superconducting-qubit arrays. They also demonstrated an order-of-magnitude reduction in error rates for parallel multi-qubit gates, further highlighting the method’s effectiveness. This adaptability allows for accommodating the varied designs and limitations of different quantum computing platforms.

Crosstalk-Robust Control via Inverse Geometric Optimization

The ability to independently address each qubit within a larger system is critical for scaling quantum computation, and a new method achieves this by focusing on optimizing control at the level of constant-sized subsystems. This approach dramatically reduces the computational burden of full system optimization, a longstanding barrier to building more powerful quantum processors. By reducing the problem’s scale, researchers have designed pulses that effectively eliminate the leading-order deviations in gate operations caused by crosstalk, directly suppressing error rates.

This reduction in computational complexity stems from a novel optimization strategy: inverse geometric optimization. The team constructed analytical pulse solutions for parallel single-qubit gates, and numerical pulses for multi-qubit operations, by focusing on crosstalk-robust control over these smaller, manageable subsystems. This allows each interaction between qubit pairs to be evaluated independently, avoiding calculations across the entire system.

The resulting robust control problem then becomes a multi-objective optimization focused on these subsystems, maximizing fidelity while minimizing crosstalk-induced errors. The team also demonstrated the approach on a superconducting-qubit array, a significant step towards larger, more practical quantum computers. As a result, the noise scaling is reduced from exponential to linear for parallel single-qubit gates, and an order-of-magnitude reduction is achieved for parallel multi-qubit gates.

Analytical Pulses for Parallel Single-Qubit Gates

Analytical pulses designed within a new framework enable high-fidelity parallel single-qubit gates across increasingly complex quantum systems, an important step toward scalable quantum computation. This numerical demonstration represents a significant expansion beyond previous parallel gate implementations, suggesting a pathway toward larger, more powerful quantum processors. A key innovation lies in the reduction of computational complexity through “crosstalk-robust control over constant-sized subsystems,” which dramatically lowers the resources needed for optimization.

This method effectively eliminates the leading-order deviations induced by crosstalk, directly addressing a major source of error in quantum computing. The team observed that primitive pulse implementations of parallel gates exhibit an exponential fidelity decay with repeated application, a predictable outcome given the accumulation of even small errors. In contrast, their robust pulses demonstrate a linear decay, indicating a substantial suppression of these initial errors and a marked improvement in gate performance.

This shift from exponential to linear noise scaling for single-qubit gates is a substantial advancement for scalable quantum computation, allowing for more reliable operation as the number of gates increases. The researchers demonstrated this improvement by comparing the fidelity of parallel CZ gates under both primitive and robust pulses, revealing a clear advantage for the new method. Simulation results show that the robust pulses maintain higher fidelity even with increased coupling strength, a critical parameter for quantum operations.

The method’s independence from precise crosstalk parameters and qubit connectivity broadens its applicability to a wider range of quantum architectures. The team’s analysis reveals a general principle of subsystem-level robustness, suggesting that scalable quantum control can be built from robust solutions on smaller, manageable building blocks. The team’s analytical framework expresses the norm of the directional deviation for parallel single-qubit quantum gates, allowing for precise characterization and optimization of gate performance. By carefully controlling the frequency of the first qubit in each subsystem, the team implemented CZ gates with improved fidelity and reduced error rates.

Numerical Pulses for Parallel Multi-Qubit Operations

The ability to perform parallel quantum operations has expanded significantly, now demonstrated numerically on superconducting-qubit arrays, a scale previously challenging due to the pervasive issue of crosstalk. This achievement stems from a new approach that shifts the focus from optimizing the entire quantum system at once to instead implementing “crosstalk-robust control over constant-sized subsystems,” a strategy that dramatically reduces computational demands.

Researchers achieved this by designing control pulses using inverse geometric optimization for single-qubit gates, and a combination of quantum optimal control with the Van Loan integral technique for multi-qubit gates, avoiding the need for complex simulations of crosstalk effects. This is particularly valuable for near-term quantum computing platforms where crosstalk is a dominant source of error, and full Hilbert-space optimization is computationally intractable.

The team’s analysis reveals that dividing the system into L disjoint subsystems, S = $S_{1}$ ∪…∪ $S_{L}$ , allows for a manageable reduction in complexity, provided there are only a few comparatively small crosstalk couplings between those subsystems. This new method doesn’t just improve gate fidelity. It fundamentally alters the scaling of noise accumulation.

The implications of this work extend beyond quantum computation itself, offering a pathway toward large-scale quantum simulation and metrology on existing hardware. By slowing the rate at which noise accumulates during parallel operations, the method enables the execution of deeper and more complex quantum circuits, expanding the computational reach of current devices.

Reduced Noise Scaling to Linearity in Single-Qubit Gates

Numerical validations of this new approach extend to quantum systems of considerable scale, with successful demonstrations on superconducting-qubit arrays and coupled nitrogen-vacancy centers, and a 12-qubit nuclear-spin processor, indicating a clear trajectory toward more complex and powerful quantum processors. This level of simulation provides strong evidence for the method’s viability beyond smaller, proof-of-concept demonstrations and suggests its potential for implementation in larger devices currently under development.

Beyond superconducting qubits, the framework has also been successfully tested on coupled nitrogen-vacancy centers and a 12-qubit nuclear-spin processor, highlighting its adaptability across diverse physical platforms. This improvement is not merely incremental. The researchers demonstrate that the robust pulses exhibit a linear fidelity decay with repeated applications, contrasting sharply with the exponential decay observed with conventional pulse designs. For parallel CNOT gates, the reduction in decay rate is approximately a factor of 13 compared to primitive pulse designs, further emphasizing the effectiveness of the new method.

The team’s success stems from a novel optimization strategy that breaks down the complex problem of controlling many qubits simultaneously into a series of smaller, more manageable tasks focused on “crosstalk-robust control over constant-sized subsystems.” This approach significantly reduces the computational cost associated with designing high-fidelity gates, a major bottleneck in scaling up quantum computers. The researchers found that the number of directional derivatives needed for optimization is limited by the size of these subsystems, typically containing only a few qubits, making the process far more efficient.

The analytical pulses developed within this framework enable high-fidelity parallel single-qubit gates on coupled nitrogen-vacancy centers, while numerical pulses achieve similar results for multi-qubit operations. This combination of analytical and numerical techniques provides a versatile toolkit for designing robust quantum circuits.

The researchers also demonstrate that the norm of the directional deviation, a key metric for quantifying gate error, can be expressed in a simplified form, further streamlining the control design process. The ability to reduce noise scaling and simplify control design represents a step toward building more reliable and powerful quantum systems, capable of tackling increasingly complex problems.

👉 More information
🗞 Scalable subsystem-optimized robust control for parallel quantum gates
✍️ Xiaodong Yang, Ran Liu and Jun Li
🧠 DOI: http://link.aps.org/doi/10.1103/qdlj-d839

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