arXiv subjects

Soichiro Yamazaki

Publications and source records attributed to Soichiro Yamazaki.

5 recordsLinked to original sources

arXiv2026

Multi-qubit controlled gate with optimal T-count

Controlled gates are key components in various quantum algorithms. Improving on the prior work of Gosset et al., we show that, for an allowed error $\varepsilon$, $3\log_2(1/\varepsilon) + o(\log(1/\varepsilon))$ $T$ gates are sufficient to approximate most multi-qubit controlled SU(2)s. We also show that this T-count matches the lower bound when the use of an almost controlled gate is prohibited. As an application, general controlled gate synthesis and efficient SU(4) gate synthesis are given.

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arXiv2026

Quantum simulation of Burgers turbulence: Nonlinear transformation and direct evaluation of statistical quantities

Fault-tolerant quantum computing is a promising technology to solve linear partial differential equations that are classically demanding to integrate. It is still challenging to solve non-linear equations in fluid dynamics, such as the Burgers equation, using quantum computers. We propose a novel quantum algorithm to solve the Burgers equation. With the Cole-Hopf transformation that maps the fluid velocity field $u$ to a new field $ψ$, we apply a sequence of quantum gates to solve the resulting linear equation and obtain the quantum state $\vertψ\rangle$ that encodes the solution $ψ$. We also propose an efficient way to extract stochastic properties of $u$, namely the multi-point functions of $u$, from the quantum state of $\vertψ\rangle$. Our algorithm offers an exponential advantage over the classical finite difference method in terms of the number of spatial grids when a perturbativity condition in the information-extracting step is met.

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arXiv2025

Clifford+V synthesis for multi-qubit unitary gates

We developed a general framework for synthesizing target gates by using a finite set of basic gates, which is a crucial step in quantum compilation. When approximating a gate in SU($n$), a naive brute-force search requires a computational complexity of $O(1/\varepsilon^{(n^2 - 1)})$ to achieve an approximation with error $\varepsilon$. In contrast, by using our method, the complexity can be reduced to $O(-n^2 \log\varepsilon/\varepsilon^{((n^2 - 1)/2)})$. This method requires almost no assumptions and can be applied to a variety of gate sets, including Clifford+$T$ and Clifford+$V$. Further, we introduce a suboptimal but short run-time algorithm for synthesizing multi-qubit controlled gates. This approach highlights the role of subgroup structures in reducing synthesis complexity and opens a new direction of study on the compilation of multi-qubit gates. The framework is broadly applicable to different universal gate sets, and our analysis suggests that it can serve as a foundation for resource-efficient quantum compilation in near-term architectures.

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arXiv2024

Quantum algorithm for collisionless Boltzmann simulation of self-gravitating systems

The collisionless Boltzmann equation (CBE) is a fundamental equation that governs the dynamics of a broad range of astrophysical systems from space plasma to star clusters and galaxies. It is computationally expensive to integrate the CBE directly in a multi-dimensional phase space, and thus the applications to realistic astrophysical problems have been limited so far. Recently, Todorova & Steijl (2020) proposed an efficient quantum algorithm to solve the CBE with significantly reduced computational complexity. We extend the algorithm to perform quantum simulations of self-gravitating systems, incorporating the method to calculate gravity with the major Fourier modes of the density distribution extracted from the solution-encoding quantum state. Our method improves the dependency of time and space complexities on Nv , the number of grid points in each velocity coordinate, compared to the classical simulation methods. We then conduct some numerical demonstrations of our method. We first run a 1+1 dimensional test calculation of free streaming motion on 64*64 grids using 13 simulated qubits and validate our method. We then perform simulations of Jeans collapse, and compare the result with analytic and linear theory calculations. It will thus allow us to perform large-scale CBE simulations on future quantum computers.

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arXiv2024

Quantum algorithm for the Vlasov simulation of the large-scale structure formation with massive neutrinos

Investigating the cosmological implication of the fact that neutrino has finite mass is of importance for fundamental physics. In particular, massive neutrino affects the formation of the large-scale structure (LSS) of the universe, and, conversely, observations of the LSS can give constraints on the neutrino mass. Numerical simulations of the LSS formation including massive neutrino along with conventional cold dark matter is thus an important task. For this, calculating the neutrino distribution in the phase space by solving the Vlasov equation is a suitable approach, but it requires solving the PDE in the $(6+1)$-dimensional space and is thus computationally demanding: Configuring $n_\mathrm{gr}$ grid points in each coordinate and $n_t$ time grid points leads to $O(n_\mathrm{gr}^6)$ memory space and $O(n_tn_\mathrm{gr}^6)$ queries to the coefficients in the discretized PDE. We propose a quantum algorithm for this task. Linearizing the Vlasov equation by neglecting the relatively weak self-gravity of the neutrino, we perform the Hamiltonian simulation to produce quantum states that encode the phase space distribution of neutrino. We also propose a way to extract the power spectrum of the neutrino density perturbations as classical data from the quantum state by quantum amplitude estimation with accuracy $ε$ and query complexity of order $\widetilde{O}((n_\mathrm{gr} + n_t)/ε)$. Our method also reduces the space complexity to $O(\mathrm{polylog}(n_\mathrm{gr}/ε))$ in terms of the qubit number, while using quantum random access memories with $O(n_\mathrm{gr}^3)$ entries. As far as we know, this is the first quantum algorithm for the LSS simulation that outputs the quantity of practical interest with guaranteed accuracy.

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