Efficient Simulation of Leakage Errors in Quantum Error Correcting Codes Using Tensor Network Methods

Leakage errors, in which a qubit is excited to a level outside the qubit subspace, represent a significant obstacle in the development of robust quantum computers. We present a computationally efficient simulation methodology for studying leakage errors in quantum error correcting codes (QECCs) using tensor network methods, specifically Matrix Product States (MPS). Our approach enables the simulation of various leakage processes, including thermal noise and coherent errors, without approximations (such as the Pauli twirling approximation) that can lead to errors in the estimation of the logical error rate. We apply our method to two QECCs: the one-dimensional (1D) repetition code and a thin $3\times d$ surface code. By leveraging the small amount of entanglement generated during the error correction process, we are able to study large systems, up to a few hundred qudits, over many code cycles. We consider a realistic noise model of leakage relevant to superconducting qubits to evaluate code performance and a variety of leakage removal strategies. Our numerical results suggest that appropriate leakage removal is crucial, especially when the code distance is large.Comment: 14 pages, 12 figure

Seasonal variation of air transport in the Antarctic and Atmospheric Circulation in 1997

To better understand how present and past climates at Syowa Station, Antarctica relate to climate elsewhere, we analyzed the tropospheric air transport to Syowa Station for the year 1997 using a dataset from the European Centre for Medium Range Weather Forecasts(ECMWF). The five-day trajectories of the air parcels were estimated and analyzed. In the middle troposphere in winter, air parcels were usually from the lower troposphere over the Atlantic. However, in January, most of the air parcels came from latitudes higher than 60°S . The trajectories had little vertical motion and were associated with a low pressure system that forms along the coastal region of Antarctica only in summer. In the lower troposphere, trajectories could be classified as originating in one of three regions: the Southern Ocean, the continental interior, and the east coast. In contrast to the middle troposphere, air parcels from the Southern Ocean had the lowest frequency, irrespective of the time of year. This is partially due to a low pressure system that blocks air parcels from outside the continent. Most trajectories are affected by the drainage flow. An amplified quasi-stationary planetary wave for September to November and a blocking circulation in June make trajectories pass over Antarctica

Noise propagation in hybrid tensor networks

The hybrid tensor network (HTN) method is a general framework allowing for the construction of an effective wavefunction with the combination of classical tensors and quantum tensors, i.e., amplitudes of quantum states. In particular, hybrid tree tensor networks (HTTNs) are very useful for simulating larger systems beyond the available size of the quantum hardware. However, while the realistic quantum states in NISQ hardware are highly likely to be noisy, this framework is formulated for pure states. In this work, as well as discussing the relevant methods, i.e., Deep VQE and entanglement forging under the framework of HTTNs, we investigate the noisy HTN states by introducing the expansion operator for providing the description of the expansion of the size of simulated quantum systems and the noise propagation. This framework enables the general tree HTN states to be explicitly represented and their physicality to be discussed. We also show that the expectation value of a measured observable exponentially vanishes with the number of contracted quantum tensors. Our work will lead to providing the noise-resilient construction of HTN states.Comment: 20 pages, 8 figure

Virtual quantum error detection

Quantum error correction and quantum error detection necessitate syndrome measurements to detect errors. Performing syndrome measurements for each stabilizer generator can be a significant overhead, considering the fact that the readout fidelity in the current quantum hardware is generally lower than gate fidelity. Here, by generalizing a quantum error mitigation method known as symmetry expansion, we propose a protocol called virtual quantum error detection (VQED). This method virtually allows for evaluating computation results corresponding to post-selected quantum states obtained through quantum error detection during circuit execution, without implementing syndrome measurements. Unlike conventional quantum error detection, which requires the implementation of Hadamard test circuits for each stabilizer generator, our VQED protocol can be performed with a constant depth shallow quantum circuit with an ancilla qubit, irrespective of the number of stabilizer generators. Furthermore, for some simple error models, the computation results obtained using VQED are robust against the noise that occurred during the operation of VQED, and our method is fully compatible with other error mitigation schemes, enabling further improvements in computation accuracy and facilitating high-fidelity quantum computing.Comment: 10 pages, 8 figures, 1 tabl

Hunting for quantum-classical crossover in condensed matter problems

The intensive pursuit for quantum advantage in terms of computational complexity has further led to a modernized crucial question: {\it When and how will quantum computers outperform classical computers?} The next milestone is undoubtedly the realization of quantum acceleration in practical problems. Here we provide a clear evidence and arguments that the primary target is likely to be condensed matter physics. Our primary contributions are summarized as follows: 1) Proposal of systematic error/runtime analysis on state-of-the-art classical algorithm based on tensor networks; 2) Dedicated and high-resolution analysis on quantum resource performed at the level of executable logical instructions; 3) Clarification of quantum-classical crosspoint for ground-state simulation to be within runtime of hours using only a few hundreds of thousand physical qubits for 2d Heisenberg and 2d Fermi-Hubbard models, assuming that logical qubits are encoded via the surface code with the physical error rate of $p=10^{-3}$. To our knowledge, we argue that condensed matter problems offer the earliest platform for demonstration of practical quantum advantage that is order-of-magnitude more feasible than ever known candidates, in terms of both qubit counts and total runtime.Comment: 14+41 pages, 8+24 figure

Fine Particulate Matter and Diabetes Prevalence in Okayama, Japan

Many studies have shown an association between long-term exposure to particulate matter having an aerodynamic diameter of 2.5 μm or less (PM2.5) and diabetes mellitus (DM), but few studies have focused on Asian subjects. We thus examined the association between long-term exposure to PM2.5 and DM prevalence in Okayama City, Japan. We included 76,591 participants who had received basic health checkups in 2006 and 2007. We assigned the census-level modeled PM2.5 data from 2006 and 2007 to each participant and defined DM using treatment status and the blood testing. PM2.5 was associated with DM prevalence, and the prevalence ratio (95% confidence interval) was 1.10 (1.00-1.20) following each interquartile range increase (2.1 μg/m3) in PM2.5. This finding is consistent with previous results and suggests that long-term exposure to PM2.5 is associated with an increased prevalence of DM in Okayama City, Japan, where the PM2.5 level is lower than in other cities in Asian countries