Quantum Computational Advantage Of Noisy Boson Sampling
QCA: Quantum Computational Advantage Secured Quantum Computational Advantage: Logarithmic Noise Threshold Proves Boson Sampling Intractability
Hyunseok Jeong, Changhun Oh, Byeongseon Go. Proving Quantum Computational Advantage (QCA), the point at which a quantum device performs a task beyond traditional supercomputers, is critical. One of the most promising QCA approaches, Boson Sampling (BS), provides strong complexity-theoretical evidence for its ability to endure a lot of experimental noise while maintaining classical intractability. Boson sampling, known for its convincing proof of computational complexity and experimental viability, has recently reached system sizes big enough to prove QCA in several studies. Near-term quantum devices will have physical faults including photon loss and imperfect distinguishability, which is a major hurdle. Quantum Classical algorithms can mimic the process if the noise rate is too high, “ruling out” the quantum advantage. Thus, employing near-term noisy devices to demonstrate QCA requires a precise characterisation of the noise rate limit that preserves traditional intractability. Finding the Logarithmic Noise Boundary Go, Oh, and Jeong's main contribution is characterising partial-distinguishability noise, a major obstacle to Quantum Computational Advantage QCA in optical systems and more recent bosonic platforms like atomic arrays and ion traps used for boson sampling. Quantum computing is difficult because photons are indistinguishable. Even when input photons average out to be distinct, Boson Sampling remains as difficult as ideal boson sampling. This result improves calculated noise robustness for traditional hardness arguments. Previously, photon loss studies only showed that complexity equivalence was retained if a maximum number of input photons were lost. Current research shows that the number of acceptable noisy photons scales logarithmically with system size, contrary to prior findings. The improved threshold allows Quantum Computational Advantage QCA with noisy boson samplers. Reduction-Theoretical Complexity Equivalence Ideal Boson Sampling is traditionally hard since it requires anticipating the ideal output probability within error bounds. This problem may be #P-hard. If an effective classical algorithm solves this estimate problem, the polynomial hierarchy is unlikely to collapse. This study, like photon loss studies, showed that perfect boson sampling might be approximated by noisy boson sampling. The authors formalised the noisy system problem of estimating noisy output probability given an indistinguishability rate. The drop shows that solving the noisy problem is as difficult as solving the ideal problem if the noise rate is below the logarithmic threshold. A low-degree polynomial approximation and polynomial interpolation are the main methods that enable this finding. The noisy output probability is polynomial in the indistinguishability rate. If the whole degree polynomial were interpolated to calculate the ideal output probability, exponential imprecision would result. Logarithmically scaled degree polynomial approximation was achieved by researchers. With the average number of identifiable photons preserved, this low-degree approximation can infer the ideal output probability (via interpolation) without an exponentially large imprecision blowup.
Combine Noise and Future Challenges The method was generalised to cover real-world situations with photon loss and partial distinguishability. The results show that ideal Boson Sampling remains classically intractable even with an average number of identifiable photons and photon loss. These results help academics comprehend classical intractability regimes for noisy boson sampling and provide a baseline for the amount of physical noise needed in near-term studies to prove Quantum Computational Advantage QCA. There are many unanswered questions. Only when the average number of noisy photons scales logarithmically does the current finding hold. Experimental implementations often have indistinguishability or a constant fraction of noisy photons. To expand the hardness proof to this constant noise rate domain, new sophisticated approaches must be developed since the low-degree polynomial approximation strategy fails. Gaussian Boson Sampling (GBS), which often fits better with Gaussian state inputs in experimental setups, needs additional theoretical study on its classical simulation hardness. Using non-uniform noise models instead of idealised uniform distinguishability noise with a single parameter is another exciting future challenge.
