arXiv subjects

Hayata Morisaki

Publications and source records attributed to Hayata Morisaki.

7 recordsLinked to original sources

arXiv2025

Explicit quantum surrogates for quantum kernel models

Quantum machine learning (QML) leverages quantum states for data encoding, with key approaches being explicit models that use parameterized quantum circuits and implicit models that use quantum kernels. Implicit models often have lower training errors but face issues such as overfitting and high prediction costs, while explicit models can struggle with complex training and barren plateaus. We propose a quantum-classical hybrid algorithm to create an explicit quantum surrogate (EQS) for trained implicit models. This involves diagonalizing an observable from the implicit model and constructing a corresponding quantum circuit using an extended automatic quantum circuit encoding algorithm. The EQS framework reduces prediction costs, provides a powerful strategy to mitigate barren plateau issues, and combines the strengths of both QML approaches.

quant-ph↗

arXiv2025

Asymptotic Gate Count Bounds for Ancilla-Free Single-Qubit Synthesis with Arithmetic Gates

We study ancilla-free approximation of single-qubit unitaries $U\in {\rm SU}(2)$ by gate sequences over Clifford+$G$, where $G\in\{T,V\}$ or their generalization. Let $p$ denote the characteristic factor of the gate set (e.g., $p=2$ for $G=T$ and $p=5$ for $G=V$). We prove three asymptotic bounds on the minimum $G$-count required to achieve approximation error at most $\varepsilon$. First, for Haar-almost every $U$, we show that $3\log_{p}(1/\varepsilon)$ $G$-count is both necessary and sufficient; moreover, probabilistic synthesis improves the leading constant to $3/2$. Second, for unitaries whose ratio of matrix elements lies in a specified number field, $4\log_p(1/\varepsilon)$ $G$-count is necessary. Again, the leading constant can be improved to $2$ by probabilistic synthesis. Third, there exist unitaries for which the $G$-count per $\log_{p}(1/\varepsilon)$ fails to converge as $\varepsilon\to 0^+$. These results partially resolve a generalized form of the Ross--Selinger conjecture.

quant-ph↗

arXiv2025

Optimal ancilla-free Clifford+T synthesis for general single-qubit unitaries

We propose two Clifford+$T$ synthesis algorithms that are optimal with respect to $T$-count. The first algorithm, called deterministic synthesis, approximates any single-qubit unitary by a single-qubit Clifford+$T$ circuit with the minimum $T$-count. The second algorithm, called probabilistic synthesis, approximates any single-qubit unitary by a probabilistic mixture of single-qubit Clifford+$T$ circuits with the minimum $T$-count. For most of single-qubit unitaries, the runtimes of deterministic synthesis and probabilistic synthesis are $\varepsilon^{-1/2 - o(1)}$ and $\varepsilon^{-1/4 - o(1)}$, respectively, for an approximation error $\varepsilon$. Although this complexity is exponential in the input size, we demonstrate that our algorithms run in practical time at $\varepsilon \approx 10^{-15}$ and $\varepsilon \approx 10^{-22}$, respectively. Furthermore, we show that, for most single-qubit unitaries, the deterministic synthesis algorithm requires at most $3\log_2(1/\varepsilon) + o(\log_2(1/\varepsilon))$ $T$-gates, and the probabilistic synthesis algorithm requires at most $1.5\log_2(1/\varepsilon) + o(\log_2(1/\varepsilon))$ $T$-gates. Remarkably, complexity analyses in this work do not rely on any numerical or number-theoretic conjectures.

quant-ph↗

arXiv2025

Classical variational optimization of PREPARE circuit for quantum phase estimation of quantum chemistry Hamiltonians

We propose a method for constructing $\texttt{PREPARE}$ circuits for quantum phase estimation of a molecular Hamiltonian in quantum chemistry by using variational optimization of quantum circuits solely on classical computers. The $\texttt{PREPARE}$ circuit generates a quantum state which encodes the coefficients of the terms in the Hamiltonian as probability amplitudes and plays a crucial role in the state-of-the-art efficient implementations of quantum phase estimation. We employ the automatic quantum circuit encoding algorithm [Shirakawa $\textit{et al.}$, arXiv:2112.14524] to construct $\texttt{PREPARE}$ circuits, which requires classical simulations of quantum circuits of $O(\log N)$ qubits with $N$ being the number of qubits of the Hamiltonian. The generated $\texttt{PREPARE}$ circuits do not need any ancillary qubit. We demonstrate our method by investigating the number of $T$-gates of the obtained $\texttt{PREPARE}$ circuits for quantum chemistry Hamiltonians of various molecules, which shows a constant-factor reduction compared to previous approaches that do not use ancillary qubits. Since the number of available logical qubits and $T$ gates will be limited at the early stage of the fault-tolerant quantum computing, the proposed method is particularly of use for performing the quantum phase estimation with such limited capability.

quant-ph↗

arXiv2025

Error Crafting in Mixed Quantum Gate Synthesis

In fault-tolerant quantum computing, errors in unitary gate synthesis is comparable with noise inherent in the gates themselves. While mixed synthesis can suppress such coherent errors quadratically, there is no clear understanding on its remnant error, which hinders us from designing a holistic and practical error countermeasure. In this work, we propose that the classical characterizability of synthesis error can be exploited; remnant errors can be crafted to satisfy desirable properties. We prove that we can craft the remnant error of arbitrary single-qubit unitaries to be Pauli and depolarizing errors, while the conventional twirling cannot be applied in general. For Pauli rotation gates, in particular, the crafting enables us to suppress the remnant error up to cubic order, which results in synthesis with a T-count of $\log_2(1/\varepsilon)$ up to accuracy of $\varepsilon=10^{-9}$. Our work opens a novel avenue in quantum circuit design and architecture that orchestrates error countermeasures.

quant-ph↗

arXiv2024

End-to-end complexity for simulating the Schwinger model on quantum computers

The Schwinger model is one of the simplest gauge theories. It is known that a topological term of the model leads to the infamous sign problem in the classical Monte Carlo method. In contrast to this, recently, quantum computing in Hamiltonian formalism has gained attention. In this work, we estimate the resources needed for quantum computers to compute physical quantities that are challenging to compute on classical computers. Specifically, we propose an efficient implementation of block-encoding of the Schwinger model Hamiltonian. Considering the structure of the Hamiltonian, this block-encoding with a normalization factor of $\mathcal{O}(N^3)$ can be implemented using $\mathcal{O}(N+\log^2(N/\varepsilon))$ T gates. As an end-to-end application, we compute the vacuum persistence amplitude. As a result, we found that for a system size $N=128$ and an additive error $\varepsilon=0.01$, with an evolution time $t$ and a lattice spacing a satisfying $t/2a=10$, the vacuum persistence amplitude can be calculated using about $10^{13}$ T gates. Our results provide insights into predictions about the performance of quantum computers in the FTQC and early FTQC era, clarifying the challenges in solving meaningful problems within a realistic timeframe.

quant-ph↗

arXiv2023

MNISQ: A Large-Scale Quantum Circuit Dataset for Machine Learning on/for Quantum Computers in the NISQ era

We introduce the first large-scale dataset, MNISQ, for both the Quantum and the Classical Machine Learning community during the Noisy Intermediate-Scale Quantum era. MNISQ consists of 4,950,000 data points organized in 9 subdatasets. Building our dataset from the quantum encoding of classical information (e.g., MNIST dataset), we deliver a dataset in a dual form: in quantum form, as circuits, and in classical form, as quantum circuit descriptions (quantum programming language, QASM). In fact, also the Machine Learning research related to quantum computers undertakes a dual challenge: enhancing machine learning exploiting the power of quantum computers, while also leveraging state-of-the-art classical machine learning methodologies to help the advancement of quantum computing. Therefore, we perform circuit classification on our dataset, tackling the task with both quantum and classical models. In the quantum endeavor, we test our circuit dataset with Quantum Kernel methods, and we show excellent results up to $97\%$ accuracy. In the classical world, the underlying quantum mechanical structures within the quantum circuit data are not trivial. Nevertheless, we test our dataset on three classical models: Structured State Space sequence model (S4), Transformer and LSTM. In particular, the S4 model applied on the tokenized QASM sequences reaches an impressive $77\%$ accuracy. These findings illustrate that quantum circuit-related datasets are likely to be quantum advantageous, but also that state-of-the-art machine learning methodologies can competently classify and recognize quantum circuits. We finally entrust the quantum and classical machine learning community the fundamental challenge to build more quantum-classical datasets like ours and to build future benchmarks from our experiments. The dataset is accessible on GitHub and its circuits are easily run in qulacs or qiskit.

quant-ph↗