Limited Squeezing Restricts Power of Quantum Computations with Light
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Byeongseon Go of the University of Seoul and colleagues have identified squeezing-level thresholds that distinguish between classically tractable and intractable regimes in measurement-based linear optics, revealing a squeezing-driven complexity phase transition. The analysis provides a framework for understanding finite-squeezing noise and demonstrates a change in the classical simulation complexity of output states, quantified by a key number of Ω(M). This work pinpoints a limitation in the computational ability of continuous-variable quantum computers, which use ‘squeezing’ to manipulate quantum states. The level of squeezing directly impacts the complexity of problems these computers can solve effectively. Achieving greater computational power, therefore, requires either sharply enhanced squeezing or the implementation of methods to correct for inevitable errors during processing. This work demonstrates a fundamental limit to the computational power of continuous-variable quantum computers, machines that encode information using properties of light. These computers rely on a technique called ‘squeezing’, which reduces quantum noise, similar to sharpening the focus on a blurry image to reveal finer details. Continuous-variable quantum computation differs from the more commonly publicised qubit-based quantum computing, offering potential advantages in scalability and compatibility with existing optical technologies. The analysis reveals that the level of squeezing directly impacts the complexity of calculations these computers can handle, identifying thresholds beyond which problems become classically intractable. Specifically, the team analysed how the squeezing level governs the classical simulation of output states, finding a ‘complexity phase transition’ where computational difficulty changes abruptly. This establishes a framework for understanding the squeezing resources needed for meaningful quantum computation and raises whether achieving sufficient squeezing is practically feasible, or if alternative error-correction methods are essential for large-scale quantum processing. The implications extend to the broader field of quantum information science, informing resource allocation and guiding the development of more robust quantum algorithms. Squeezing level defines the boundary between tractable and intractable simulation of linear optics The classical simulation complexity of measurement-based linear optics (MBLO) utilising continuous-variable cluster states now transitions from classically tractable to intractable at a squeezing level of Ω(M), representing a strong improvement over previous analyses. Previously, accurately simulating the output states of MBLO with finite squeezing required computational resources scaling polynomially with the system size. This meant that as the size of the quantum computation increased, the classical computer’s required resources grew at a manageable rate. Exceeding this threshold demonstrates a complexity phase transition, rendering classical simulation exponentially harder, meaning the computational cost increases dramatically with even small increases in system size. This transition is crucial because it signifies the point at which a quantum computer can potentially outperform classical computers for specific tasks. This finding establishes a clear boundary, indicating that achieving sufficient squeezing is vital for realising a quantum advantage with this architecture, or that strong error correction strategies are essential. A specific framework was developed by the team, utilising brickwork graphs with width and height proportional to M, to implement any M-mode linear optical circuit. Brickwork graphs are particularly well-suited for representing the connectivity of cluster states, allowing for efficient analysis of measurement-based quantum computation. The analysis accounts for realistic finite squeezing, revealing how Gaussian noise introduced during quantum computation impacts simulation complexity. Gaussian noise arises from the inherent uncertainty in quantum measurements and the imperfections in the preparation of squeezed states.
The team meticulously modelled displacement and second-moment noise arising from imperfect cluster states, providing a more accurate representation of real-world quantum devices. Continuous-variable quantum computing, utilising properties of light rather than traditional bits, holds promise for scaling up quantum processors. Photons, the particles of light, are ideal carriers of quantum information due to their low decoherence rates and ease of transmission. While this work establishes a clear benchmark for achieving quantum advantage, it also highlights the need to address practical limitations in generating and maintaining highly squeezed states. Current squeezing technologies are limited by factors such as optical losses and technical noise. Further investigation will focus on quantifying the overhead required to overcome these limitations, guiding efforts to improve hardware and develop effective error correction methods for continuous-variable systems. This includes exploring techniques like homodyne detection and advanced feedback control to mitigate noise and enhance squeezing levels. Defining the squeezing threshold for demonstrable quantum advantage Precisely how much squeezing is needed before classical computers are unable to simulate quantum calculations is now clarified by this work, revealing a key threshold. Scientists analysing measurement-based linear optics identified a ‘complexity phase transition’ directly linked to the level of squeezing applied, dictating the difficulty for conventional computers to simulate the quantum system. This transition isn’t merely a gradual increase in difficulty; it represents a fundamental shift in computational complexity. This establishes a clear boundary between classical and quantum regimes for continuous-variable quantum computation, utilising light to process information. The ability to define this boundary is significant because it allows researchers to focus their efforts on achieving squeezing levels that demonstrably surpass this threshold, paving the way for practical quantum applications. Rather than dismissing the challenge of building powerful quantum computers, this research precisely defines a critical threshold for this technique to reduce errors. The research builds upon the established principles of measurement-based quantum computation, where quantum computations are performed by making a series of measurements on a highly entangled multi-photon state known as a cluster state. The quality of this cluster state, and specifically the degree of squeezing, is paramount to the success of the computation. The Ω(M) threshold represents a scaling relationship, indicating that the required squeezing level increases with the number of modes (M) in the quantum circuit. This is a crucial consideration for scaling up continuous-variable quantum computers to tackle more complex problems.
The team’s work provides a valuable roadmap for future research, highlighting the importance of both improving squeezing technology and developing robust error correction schemes to unlock the full potential of continuous-variable quantum computation. Scientists determined a clear relationship between the level of squeezing and the computational complexity of measurement-based linear optics. This finding establishes a threshold beyond which classical computers struggle to simulate quantum systems utilising continuous-variable cluster states. The research reveals that the required squeezing level scales with the number of modes in the quantum circuit, informing efforts to improve the performance of these systems. Authors suggest that either increasing squeezing or incorporating error-correction schemes is necessary for reliable, large-scale quantum computation. 👉 More information 🗞 Complexity phase transition for continuous-variable cluster state 🧠 ArXiv: https://arxiv.org/abs/2604.07804 Tags: