arXiv subjects

Kou Hamada

Publications and source records attributed to Kou Hamada.

5 recordsLinked to original sources

arXiv2026

Bounded-depth spacetime lattice surgery for resource-efficient fault-tolerant quantum computation

Fault-tolerant quantum computing based on lattice surgery requires place-and-route compilation with low spacetime overhead. Routing, in particular, faces a basic tension between suppressing path conflicts through greater spatial allocation and exploiting the time direction to realize ancilla-efficient spacetime routing. Existing approaches do not fully resolve this trade-off while retaining compatibility with inner factory layouts and termination guarantees. Here we introduce double-slice routing, a constant-depth spacetime-routing method that uses two consecutive time slices with a guarantee that its kink-parity correction terminates under both planar and stacked architectures. We numerically benchmark the resulting compiler on Hamiltonian-simulation workloads to show that double-slice routing reduces compilation cost by up to a factor of 2.4 over a single-slice baseline. Compared to projective routing, an existing method that allows an unbounded number of time slices per path, double-slice routing achieves smaller circuit volume with only a marginal execution-time penalty. Combined with a cultivation-compatible mapping optimization, the overall improvement reaches up to 7.5-fold over a naive single-slice compilation baseline. These results identify double-slice routing as a practically useful operating point in lattice-surgery compilation and show the substantial benefit in joint optimization of mapping and routing.

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arXiv2024

A Simple Representation of Tree Covering Utilizing Balanced Parentheses and Efficient Implementation of Average-Case Optimal RMQs

Tree covering is a technique for decomposing a tree into smaller-sized trees with desirable properties, and has been employed in various succinct data structures. However, significant hurdles stand in the way of a practical implementation of tree covering: a lot of pointers are used to maintain the tree-covering hierarchy and many indices for tree navigational queries consume theoretically negligible yet practically vast space. To tackle these problems, we propose a simple representation of tree covering using a balanced parenthesis representation. The key to the proposal is the observation that every micro tree splits into at most two intervals on the BP representation. Utilizing the representation, we propose several data structures that represent a tree and its tree cover, which consequently allow micro tree compression with arbitrary coding and efficient tree navigational queries. We also applied our data structure to average-case optimal RMQ by Munro et al.~[ESA 2021] and implemented the RMQ data structure. Our RMQ data structures spend less than $2n$ bits and process queries in a practical time on several settings of the performance evaluation, reducing the gap between theoretical space complexity and actual space consumption. We also implement tree navigational operations while using the same amount of space as the RMQ data structures. We believe the representation can be widely utilized for designing practically memory-efficient data structures based on tree covering.

cs.DS↗

arXiv2024

Faster computation of nonstabilizerness

The characterization of nonstabilizerness is fruitful due to its application in gate synthesis and classical simulation. In particular, the resource monotone called the stabilizer extent is a useful tool to estimate the simulation cost using rank-based simulators, one of the state-of-the-art simulators of Clifford+$T$ circuits. In this work, we propose faster numerical algorithms to compute the stabilizer extent. Our algorithm utilizes the Column Generation method, which iteratively updates the subset of pure stabilizer states used for calculation. This subset is selected based on the overlaps between all stabilizer states and a target state. In order to update the subset, we make use of a newly proposed subroutine for calculating the stabilizer fidelity that (i) achieves linear time complexity with respect to the number of stabilizer states, (ii) super-exponentially reduces the space complexity by in-place calculation, and (iii) prunes unnecessary states for the computation. As a result, our algorithm can compute the stabilizer fidelity and the stabilizer extent for Haar random pure states up to $n=9$ qubits, which naively requires a memory of 305 EiB. We further show that our algorithm runs faster when the target state vector is real. We prove that the problem size is reduced by $\mathcal{O}(2^n)$ compared to the general cases, which makes it computable for the case of $n=10$ qubits.

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arXiv2024

Efficient and high-performance routing of lattice-surgery paths on three-dimensional lattice

Encoding logical qubits with surface codes and performing multi-qubit logical operations with lattice surgery is one of the most promising approaches to demonstrate fault-tolerant quantum computing. Thus, a method to efficiently schedule a sequence of lattice-surgery operations is vital for high-performance fault-tolerant quantum computing. A possible strategy to improve the throughput of lattice-surgery operations is splitting a large instruction into several small instructions, such as Bell state preparation and measurements, and executing a part of them in advance. However, scheduling methods to fully utilize this idea have yet to be explored. In this paper, we propose a fast and high-performance scheduling algorithm for lattice-surgery instructions leveraging this strategy. We achieved this by converting the scheduling problem of lattice-surgery instructions to a graph problem of embedding 3D paths into a 3D lattice, which enables us to explore efficient scheduling by solving path search problems in the 3D lattice. Based on this reduction, we propose a method to solve the path-finding problems, the look-ahead Dijkstra projection. We numerically show that this method reduced the execution time of benchmark programs generated from quantum phase estimation algorithms by 3.8 times compared with a naive method based on greedy algorithms. Our study establishes the relation between the lattice-surgery scheduling and graph search problems, which leads to further theoretical analysis on compiler optimization of fault-tolerant quantum computing.

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arXiv2023

Handbook for Quantifying Robustness of Magic

The nonstabilizerness, or magic, is an essential quantum resource to perform universal quantum computation. Robustness of magic (RoM) in particular characterizes the degree of usefulness of a given quantum state for non-Clifford operation. While the mathematical formalism of RoM can be given in a concise manner, it is extremely challenging to determine the RoM in practice, since it involves superexponentially many pure stabilizer states. In this work, we present efficient novel algorithms to compute the RoM. The crucial technique is a subroutine that achieves the remarkable features in calculation of overlaps between pure stabilizer states: (i) the time complexity per each stabilizer is reduced exponentially, (ii) the space complexity is reduced superexponentially. Based on this subroutine, we present algorithms to compute the RoM for arbitrary states up to $n=7$ qubits on a laptop, while brute-force methods require a memory size of 86 TiB. As a byproduct, the proposed subroutine allows us to simulate the stabilizer fidelity up to $n=8$ qubits, for which naive methods require memory size of 86 PiB so that any state-of-the-art classical computer cannot execute the computation. We further propose novel algorithms that utilize the preknowledge on the structure of target quantum state such as the permutation symmetry of disentanglement, and numerically demonstrate our state-of-the-art results for copies of magic states and partially disentangled quantum states. The series of algorithms constitute a comprehensive ``handbook'' to scale up the computation of the RoM, and we envision that the proposed technique applies to the computation of other quantum resource measures as well.

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