Distillation boosts surface code links without discarding qubits

Researchers from The University of Tokyo and NTT have developed a new scheme for distributed surface-code quantum computing that improves upon existing methods by using entanglement distillation without relying on postselection. This approach addresses a key limitation of scaling up quantum computers, where connecting multiple processing units requires high-fidelity entangled states.

Numerical simulations demonstrate lower logical error rates with this distillation scheme compared to those without it, and further reductions are possible by using the unique characteristics of errors within the surface code. The proposed scheme offers a practical and simple path toward distributed quantum computing with surface codes.

Entanglement Distillation Enables Distributed Surface Code Computation

A new entanglement distillation scheme allows for connections between surface code quantum computing patches without discarding potentially useful qubits, a significant simplification for scaling up these systems. Unlike typical distillation protocols that rely on postselection, a process of filtering results by discarding unsuccessful attempts, this approach retains output states even when a distillation attempt appears to fail, streamlining implementation.

The team’s work addresses a core challenge in distributed quantum computing: the low encoding rate of surface codes, which limits the number of physical qubits that can be accommodated on a single processor. By distributing physical qubits across multiple nodes and connecting them with shared entangled pairs, researchers aim to overcome this limitation and build larger, more powerful quantum computers.

This scheme uses a 2-to-1 distillation protocol to improve the reliability of remote lattice surgery, a technique for performing operations between distant qubits, without the need for complex scheduling or long waiting times associated with postselection. The researchers retain the output state and use it to perform internode gates even when a rejection outcome is obtained. Exploiting the asymmetry between errors in the surface code further enhances performance.

The simulations revealed that both X and Z errors play important roles in determining the optimized logical error rate when moving a logical qubit across the connection seam between processing units. To address this, the team implemented a strategy of alternating between X and Z distillation variants, selecting X distillation with probability q and Z distillation with 1-q. The work builds on recent progress in experimental demonstrations of the surface code, offering a promising solution to the challenges of scaling up fault-tolerant quantum computation.

Surface Code Limitations Drive Need for Distributed Approach

The architecture relies on connecting “patches” of the surface code, a two-dimensional arrangement of qubits where data and ancilla qubits alternate on a lattice. Stabilizer generators, defined as tensor products of Pauli X or Z operators, are important for maintaining the integrity of the quantum information. This distributed approach addresses the inherent limitations of accommodating a sufficient number of physical qubits on a single processor for complex calculations.

The work builds on the established foundation of the surface code, known for its high threshold and support for universal logical operations. A key innovation lies in the avoidance of “postselection” during entanglement distillation, a process that normally discards some entangled states to improve fidelity. By retaining all output states, even those initially deemed imperfect, the researchers simplify implementation and reduce overhead. This is achieved by using the probabilities conditioned on distillation outcomes to set decoder weights, as described in the paper.

This careful balance ensures that both error types are effectively mitigated, capitalizing on the unique information each variant provides. The resulting scheme offers a streamlined path toward building scalable quantum computers, bypassing the need for complex post-processing steps. The researchers’ work demonstrates a significant step toward overcoming the scalability challenges inherent in fault-tolerant quantum computation.

Error-Detecting vs. Error-Correcting Distillation Trade-offs

Error-detecting distillation protocols, known for compact circuits, traditionally require postselection, a process of repeating distillation until success or sourcing successful pairs externally, introducing delays or complex routing. This reliance on postselection creates a fundamental compromise in protocol design, forcing a choice between efficient, yet potentially time-consuming, error detection or inefficient, but immediate, error correction. The work detailed in this paper proposes a scheme that circumvents this trade-off, enabling remote lattice surgery with error-detecting entanglement distillation without discarding any output states.

Conventional error-correcting distillation avoids postselection by estimating and correcting errors based on measurement outcomes, but protocols like the [[5,1,3]] code demand more input Bell pairs and more detailed circuits than the simpler 2-to-1 protocols often used in error-detecting schemes. The team focused on these simpler error-detecting protocols using two initial entangled pairs, assuming ideal local operations and measurements and isotropic input states with a fidelity, F.

This approach allows for distillation without the need to discard imperfect pairs, streamlining the process and potentially reducing overhead. Marginal error probabilities for X distillation are key to understanding the performance of this method, with success and failure rows providing probabilities conditioned on measurement outcome agreement or disagreement. The proposed architecture balances the suppression of both logical X and Z errors, critical for surface code functionality.

In scenarios where seam errors dominate, increasing syndrome measurement rounds minimizes logical Z errors, while a higher ratio of X distillation to Z distillation effectively reduces logical X errors. Conversely, when bulk errors are prevalent, increasing syndrome measurement rounds can actually increase errors due to accumulation. This highlights a detailed interplay between measurement rounds and distillation ratios, demanding careful optimization. The optimal number of syndrome measurement rounds and distillation ratio are therefore determined by the specific error landscape.

The study demonstrates that logical error rates are lower when distillation is employed, even without postselection, compared to using raw entangled pairs. Additionally, the authors demonstrate that the logical error rates can be suppressed further by exploiting the asymmetry between spacelike and timelike errors in the surface code. The findings suggest that a carefully tuned balance between X and Z distillation can further suppress logical error rates, offering a practical route toward scalable quantum computation.

to-1 Distillation Improves Logic Rates Without Postselection

Entanglement distillation, a technique for improving the quality of quantum connections, now demonstrates benefits even when a common filtering step is bypassed. This simplification could accelerate the development of distributed quantum computing architectures. The team’s work focuses on surface codes, a promising method for protecting quantum information from errors. Their scheme uses the outputs of distillation circuits, retaining data even when the distillation process itself fails to yield a perfect entangled state.

This approach avoids the delays and complexities of waiting for and scheduling successful distillations, a significant hurdle in scaling up quantum systems. Numerical simulations reveal a threshold improvement from 15% to 18% when distillation is applied, indicating a greater tolerance for noise in the initial entangled states. The optimization of syndrome measurement rounds and distillation protocol selection further refines performance.

By carefully balancing the number of error checks and the type of distillation used, focusing on either X or Z errors, the researchers achieved additional reductions in logical error rates. Analysis of the results reveals a subtle interplay between error types and distillation outcomes. Even unsuccessful distillation attempts provide valuable information about potential errors, aiding in error correction. Z) distillation succeeds or fails provides information about whether an X (resp.

Z) error has occurred,” the researchers explain in their paper. This means that the system can still glean useful data from imperfect distillations, enhancing the overall robustness of the quantum computation. The team explored the optimal ratio of syndrome measurement rounds to distillation attempts, finding that the ideal parameters depend on the initial infidelity of the entangled pairs.

In scenarios with high infidelity, simply increasing the number of syndrome measurements does not necessarily improve performance. Instead, a carefully tuned balance between the two is key for minimizing logical errors.

The ratio r_opt/d, where r is the distillation ratio and d is the code distance, varies as a function of the initial infidelity, indicating a need for dynamic adjustment based on the quality of the initial entangled states. “The results indicate that logical error rates can be suppressed and a higher threshold for the noise of entangled states can be achieved by applying entanglement distillation, even without postselection,” the researchers state.

Distillation Measurement Outcomes Inform Surface Code Decoding

Using distillation outcomes to refine error estimation is central to a new approach for connecting surface code quantum computing patches, as the success or failure of distillation protocols now directly informs the decoding process. Rather than discarding imperfect distillations through postselection, this scheme incorporates the probabilities of both bit and phase errors, X and Z errors, into the surface code decoder, enabling more accurate error correction.

The team’s architecture uses two distillation variants, selecting between them probabilistically to provide the decoder with conditioned error probabilities for each entangled pair. This method avoids the need for more complex circuits typically required by error-correcting distillation codes like the [[5,1,3]] code, which often demand a larger number of initial entangled states. By retaining every output pair, regardless of distillation success, the system gains additional information from measurement outcomes during the protocol, allowing for a subtle assessment of error probabilities.

The decoder then uses these probabilities, rather than simple averages, to weight edges in the decoding graph, improving the accuracy of identifying the most probable error configuration. This approach is particularly effective when moving a logical qubit, as it accounts for both logical X and Z error mechanisms. The decoding process itself relies on a minimum weight perfect matching (MWPM) algorithm, assigning weights to edges based on their error probabilities.

The decoder then identifies the set of edges with the minimal total weight that aligns with the observed stabilizer measurement results. By incorporating distillation outcomes, the decoder can more effectively distinguish between genuine errors and noise, leading to a reduction in logical error rates. This balanced approach ensures that the impact of both error types is properly evaluated during the logical qubit movement process. The team’s noise model and decoding strategy build upon existing surface code formulations, refining them with the added layer of distillation-informed error estimation.

Asymmetry of Spacelike and Timelike Errors in Surface Codes

Exploiting the differing characteristics of errors propagating through a quantum network can further refine the performance of distributed quantum computing, according to new work focused on surface codes. Researchers demonstrated that suppressing timelike logical errors requires only increased measurement rounds, a computational cost but not a spatial one. This allows for a strategic bias toward distillation protocols that reveal information about other error types, even if they slightly elevate the rate of the suppressed error.

The team’s analysis reveals an asymmetry in how errors manifest at the boundaries between separate quantum processing units, or “patches,” connected via entanglement distillation. Specifically, the length of the shortest error chains impacting logical Z errors differs from those affecting logical X errors, a distinction linked to spacelike and timelike behavior. Increasing a parameter, denoted ‘r’, demonstrably suppresses seam errors contributing to the logical Z-error rate, a finding important for optimizing the overall system.

The approach avoids a common limitation in entanglement distillation, postselection, which discards some data, simplifying implementation. Instead, the researchers use probabilities conditioned on distillation outcomes to weight the decoder, a technique detailed in Section III. The team’s simulations show that simply defining a logical qubit across multiple chips can underestimate the impact of Z errors, highlighting the importance of a detailed approach to error analysis. By strategically using the asymmetry between error types, the researchers present a pathway toward more robust and scalable quantum networks.

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