Quantum Computing Advances Show GKP Fidelity Is Not Guaranteed by Stabilizers

Robust quantum computing depends on encoding information in states that are resilient to errors, and Gottesman–Kitaev–Preskill (GKP) states are a leading candidate for achieving this goal. Aaron Z. Goldberg of the National Research Council of Canada and collaborators challenge a widely used assumption for evaluating the quality of these states. Their research shows that stabilizer expectation values—commonly used indicators of error resistance—do not reliably measure how close a physical state is to an ideal GKP state.

The study demonstrates that stabilizer expectation values provide only an upper bound on the fidelity between a physical state and an ideal GKP state. As a result, a qubit encoded in a harmonic oscillator can exhibit seemingly excellent stabilizer measurements while still being far from the ideal GKP state when assessed using fidelity-based distance measures. This finding overturns the common belief that strong stabilizer performance guarantees high-quality logical qubits.

Because many quantum error-correcting codes rely on stabilizers that can be measured without disturbing the encoded information, this result has broad implications for quantum information processing. When such codes are implemented in physical platforms like optical or microwave oscillators, unavoidable imperfections in state preparation and measurement can significantly affect code performance. The work highlights the need to rethink benchmarking methods for GKP codes and develop more reliable metrics for assessing the true quality of encoded quantum states.

GKP States for Bosonic Quantum Error Correction

Scientists are exploring Gottesman-Kitaev-Preskill (GKP) states as a promising approach to bosonic quantum error correction, a method for protecting quantum information. This research investigates how to encode qubits using continuous degrees of freedom, like the amplitude and phase of light, potentially creating more robust quantum computers. Bosonic quantum error correction differs from traditional qubit-based schemes by encoding information in the continuous properties of bosonic systems. A key challenge lies in overcoming decoherence, the loss of quantum information due to environmental interactions, and implementing effective error correction.

This work focuses on achieving scalability and fault tolerance in GKP-based quantum computing, addressing the practical limitations of real-world quantum devices. The team performs detailed simulations and analyses to evaluate the performance of GKP codes under realistic conditions, identifying key bottlenecks and challenges. A significant focus is on preparing GKP cluster states, essential for measurement-based quantum computation, and generating these states efficiently with high fidelity. The research also investigates techniques to make GKP codes more resilient to photon loss, a major source of error in photonic quantum computing. By integrating GKP-based quantum computing with existing photonic and microwave technologies, scientists aim to create more versatile and powerful quantum systems, representing a significant step towards building practical quantum computers.

High Stabilizer Values Do Not Guarantee GKP Fidelity

Scientists have discovered a surprising relationship between the quality of quantum states known as Gottesman-Kitaev-Preskill (GKP) states and measurements of their stabilizers. The research reveals that a good stabilizer expectation value, traditionally thought to indicate a high-quality GKP state, actually only provides an upper bound on the state’s fidelity to an ideal GKP state. This means that a state can exhibit strong stabilizer signals while still being quite different from a true GKP state when measured by fidelity, a key metric for quantum information processing. The team constructed specific quantum states designed to mimic the characteristics of GKP states, while simultaneously minimizing their overlap with actual GKP states.

Measurements confirmed this counterintuitive result, establishing a mathematical relationship that defines the limit on fidelity based on stabilizer values. This finding fundamentally alters the understanding of how to assess the quality of GKP states. Further investigation involved defining and analyzing the maximum fidelity achievable between a given state and any possible GKP state. The work demonstrates that simpler measurements of stabilizer expectation values can only rule out the presence of ideal GKP states, and different metrics are required to confirm a state’s high quality for quantum computation. The research provides a crucial insight into the limitations of using stabilizer measurements as a sole indicator of GKP state quality, paving the way for more accurate assessment techniques.

Stabilizer Values Limit GKP State Fidelity

The research demonstrates a counterintuitive relationship between the quality of Gottesman-Kitaev-Preskill (GKP) states and their stabilizer expectation values. Contrary to common assumptions, the team found that a high stabilizer expectation value does not guarantee a GKP state is close to an ideal state in terms of fidelity. Instead, the fidelity to an ideal GKP state is fundamentally upper bounded by these stabilizer values, meaning arbitrarily low fidelities can exist even with near-perfect stabilizer measurements. This finding stems from a detailed analysis of both ideal and approximate GKP states, addressing the challenges posed by the infinite number of coefficients inherent in defining these states.

By employing Gaussian approximations to create normalizable GKP states, the researchers were able to analytically and geometrically demonstrate the origin of this unexpected result. Calculations involving these approximate states confirm that even with minimal variance, arbitrarily small fidelities are possible despite high stabilizer expectation values. The authors acknowledge that their analysis relies on approximations, specifically the use of Gaussian distributions to represent position states. These approximations, while necessary for mathematical tractability, introduce limitations to the precision of the results. Future work could explore the impact of different approximation methods or investigate the robustness of these findings in more complex scenarios.