Quantum Processor Achieves Verification of Four Computational Phases of Quantum Matter Predictions

The quest to understand exotic phases of quantum matter has taken a significant step forward with new research demonstrating the practical implications of ‘computational phases’. Ryohei Weil, from the University of Chicago, alongside Dmytro Bondarenko, Arnab Adhikary, and Robert Raussendorf from the University of British Columbia and Leibniz Universität Hannover, have experimentally verified key theoretical predictions regarding these phases using a superconducting quantum processor. Their work focuses on measurement-based quantum computation, revealing how imperfections affect computational power and demonstrating methods to mitigate logical decoherence. This research is particularly important as it confirms the operational stability of quantum algorithms within these phases, suggesting a pathway towards robust and scalable quantum technologies. The team’s findings validate the principle that even with correlated measurements, densely packed algorithms remain the most efficient, solidifying the potential of symmetry-protected phases for future quantum computation.

Their work focuses on measurement-based quantum computation, revealing how imperfections affect computational power and demonstrating methods to mitigate logical decoherence. This research is particularly important as it confirms the operational stability of quantum algorithms within these phases, suggesting a pathway towards robust and scalable quantum technologies. The team’s findings validate the principle that densely packed algorithms remain the most efficient, solidifying the potential of symmetry-protected phases for future quantum computation.

The study of symmetry protected or symmetry enriched phases of quantum matter has revealed that every ground state within a given phase offers the same computational power for measurement-based quantum computation. These phases, termed ‘computational phases of quantum matter’, represent a promising avenue for robust quantum information processing. Researchers have now experimentally verified four theoretical predictions relating to these phases using an IBM superconducting quantum device. A comprehensive investigation determined how symmetric imperfections within the resource states contribute to logical decoherence, and crucially, how this decoherence can be effectively mitigated.

The central experiment probes the scaling law for this decoherence, providing insight into the stability of computations performed within these phases. The research team engineered a superconducting device to verify theoretical predictions concerning computational phases of matter, specifically focusing on how imperfections in resource states impact measurement-based computation. Central to the study was an investigation into logical decoherence , the loss of quantum information , and the mechanisms to mitigate its effects. Experiments employed a precise methodology to probe the scaling laws governing the uniformity of computational power inherent in these phases, alongside analysis of correlated regimes where local measurements enact logical operations.

Scientists developed a technique to assess the impact of symmetric imperfections, deliberately introducing deviations from a symmetry-respecting basis to observe the resulting entanglement between logical and ‘junk’ registers, inducing logical decoherence. To counteract this, the study pioneered the use of an ‘oblivious wire’, a trailing component in a measurement pattern designed to drive the junk subsystem towards a fixed point, preserving the integrity of the logical subsystem. This approach enables the creation of reproducible, factorized conditions essential for computationally favourable states. The team then implemented logical rotations using specific measurement angles, carefully characterizing the resulting logical action as a combination of unitary transformation and decoherent noise.

The system delivers precise control over measurement angles, allowing researchers to quantify the relationship between the logical rotation angle and the error parameter. Equations demonstrate that for small angles, the gate action dominates over decoherence, a crucial property underpinning the uniformity of computational power. Experiment #2 directly tested the prediction that the physical and computational order parameters are equivalent, confirming their agreement. This meticulous approach validated the operational stability of measurement-based computation within phases of matter exhibiting symmetry.

Further innovation lay in the ‘splitting’ technique, where a single operation is replaced by multiple operations with halved measurement angles. This method achieves a reduction in logical error proportional to the number of splits, as described by the scaling relation. The team defined logical error as the Frobenius norm of the difference between the target unitary and the implemented channel, using a measure of resource state quality. By demonstrating that the error can be arbitrarily reduced with increased resources, the study establishes a pathway for extending measurement-based quantum computation into more complex, symmetry-protected topological phases.

Scientists have experimentally verified four theoretical predictions concerning computational phases of matter using a superconducting device. The research meticulously investigates how imperfections in resource states translate into logical decoherence, and importantly, how this decoherence can be effectively mitigated during quantum computation. Experiments focused on probing the scaling law that dictates the uniformity of computational power, revealing crucial insights into the behaviour of these phases. Analysis extended to the correlated regime, demonstrating that local measurements can collectively generate logical operations, and confirming that densest packing of measurement-based algorithms remains the most efficient approach even with these correlations present.

The team measured logical decoherence, an effect arising from particularities within a given symmetry-protected topological (SPT) phase, despite precise knowledge of resource state properties and perfect measurements. This logical decoherence stems from uncontrolled residual entanglement beyond the symmetry-protected entanglement, presenting a key challenge for utilising SPT-ordered states as computational resources. However, the study demonstrates that this complication can be counteracted through established formalisms, paving the way for more robust quantum computation. Researchers employed both the Matrix Product State (MPS) and Coding Theory (CT) formalisms, finding the CT-formalism currently provides more quantitative predictions while the MPS-formalism aids in conceptual understanding.

Experiments revealed that quantum wire, the ability to transmit quantum information across a spin chain via local measurements, remains uniform across suitable SPT phases. Any ground state within these phases reliably supports quantum wire with perfect accuracy, a significant step towards stable quantum information transfer. The work demonstrates that ground states in these phases possess a unique MPS representation, where tensor components take a specific form. Within this framework, the matrices acting on the logical subspace are unitary and constant across the phase, enabling the storage and teleportation of quantum information.

Further tests confirmed that as long as measurements are performed in a symmetric basis, the evolution described by the MPS representation remains consistent. The research establishes that the discrete group of gates generated by these measurements is the primary means of enacting logical operations within these symmetry-protected systems. This breakthrough delivers operational stability to measurement-based computation in phases of matter exhibiting symmetry, opening possibilities for future investigations into the universality of computational phases and more complex quantum algorithms.

This work presents experimental verification of key theoretical predictions concerning computational phases of matter, specifically demonstrating operational stability in measurement-based quantum computation within systems possessing symmetry. Researchers investigated how imperfections in resource states contribute to logical decoherence and, crucially, how this decoherence can be effectively mitigated. Experiments confirmed a predicted scaling law underpinning the uniformity of computational power across these phases, alongside analysis of correlated regimes where local measurements collectively enact logical operations.

The findings establish that, for small measurement angles, the action of a quantum gate outweighs decoherence, a fundamental property enabling consistent computational power. Through the ‘splitting’ technique, where operations are divided into multiple steps, the researchers demonstrated a reduction in logical errors without sacrificing the overall rotation angle, effectively extending the scope of measurement-based quantum computation into phases beyond ideal resource states. The experiments also linked the quality of the resource state to a parameter, which dictates the computational cost associated with error correction.

The authors acknowledge limitations stemming from the chosen error metric and the dependence of this parameter on the order parameter and its correlations. Future research may focus on exploring the boundaries of these phases and optimising resource states to minimise this parameter, thereby reducing the resources required for accurate computation. These results represent a significant step towards realising robust and scalable quantum computation leveraging the unique properties of symmetry-protected phases of matter.