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Kazuto Oshima

Publications and source records attributed to Kazuto Oshima.

17 recordsLinked to original sources
arXiv2025

Construction of Superposition States of Energy Eigenstates via Classically Emulated Digital Quantum Simulation: The Hydrogen Molecule as an Example

We construct superposition states of energy eigenstates of the hydrogen molecule using classically emulated digital quantum simulation. We generate the ground state and excited states of the system via the twirling operation method, and construct superposition states of the ground state and an excited state of the system by applying a controlled excitation unitary transformation on the ground state with one ancillary qubit as the control. To verify the correctness of the resulting superposition state, we calculate matrix elements of several physical observables.

quant-ph↗
arXiv2024

Twirling Operations to Produce Energy Eigenstates of a Hamiltonian by Classically Emulated Quantum Simulation

We propose a simple procedure to produce energy eigenstates of a Hamiltonian with discrete eigenvalues. We use ancilla qubits and quantum entanglement to separate an energy eigenstate from the other energy eigenstates. We exhibit a few examples derived from the (1+1)-dimensional massless Schwinger model. Our procedure in principle will be applicable for a Hamiltonian with a finite dimensional Hilbert space. Choosing an initial state properly, we can in principle produce any energy eigenstate of the Hamiltonian.

quant-ph↗
arXiv2023

Extracting vacuum expectation values from approximate vacuum prepared by the adiabatic quantum computation

We propose a procedure to extract vacuum expectation values from approximate vacuum prepared by the adiabatic quantum computation. We use plural ancilla bits with hierarchical structure, intending to gradually put up approximate precision. We exhibit simulation results for a typical one-qubit system and a two-qubits system based on the (1+1)-dimensional Schwinger model using classically emulated digital quantum simulator.

quant-ph↗
arXiv2022

Improving approximate vacuum prepared by the adiabatic quantum computation

According to the quantum adiabatic theorem, we can in principle obtain a true vacuum of a quantum system starting from a trivial vacuum of a simple Hamiltonian. In actual adiabatic digital quantum simulation with finite time length and non-infinitesimal time steps, we can only obtain an approximate vacuum that is supposed to be a superposition of a true vacuum and excited states. We propose a procedure to improve the approximate vacuum.

quant-ph↗
arXiv2021

Remark on using quantum states prepared by the adiabatic quantum computation

We indicate that there are points to keep in mind in utilizing quantum states prepared by the adiabatic quantum computation. Even if an instantaneous expectation value of a physical quantity for the adiabatically prepared quantum state is close to an expectation value for the true vacuum, this does not assure us that the prepared vacuum is close to the true vacuum. In general time average of the expectation value tend to systematically differ from the true value. Using a simple model we discuss how to diminish this systematic difference.

quant-ph↗
arXiv2018

Channel fidelities for high-fidelity approach in KLM scheme

We study channel fidelity for the high-fidelity approach in the Knill-Laflamme-Milburn (KLM) scheme. We examine an optimal channel fidelity $f_{opt}$ and identify the corresponding KLM ancilla state. In the limit of large $n$, where $2n$ is the number of the ancilla qubits, we find $f_{opt}=1-{π^{2} \over 6n^{2}}+{2π^{2} \over 9n^{3}}$. We see that as $n$ increases $f_{opt}$ approaches to 1 slightly faster than $f=1-{2 \over n^{2}}$ which is the channel fidelity computed by Franson et. al. in the limit of large $n$. We also compute the channel fidelity for the ancilla state that gives a lower bound of success probability of quantum teleportation.

quant-ph↗
arXiv2017

Lower Bounds of Success Probabilities for High-Fidelity Approach in KLM Scheme

In the Knill-Laflamme-Milburn (KLM) scheme, the success probability of quantum teleportation is given by ${n \over n+1}$, wehre $2n$ is the number of the ancilla qubits. For the high-fidelity approach in the KLM scheme, the success probability is approximately given by $1-{1 \over n^{2}}$ for large $n$. We give an explicit prescription to prepare an optimal ancilla state and give an exact lower bound of the success probability for the high-fidelity approach for arbitrary $n$.

quant-ph↗
arXiv2009

Classical signal-flow in cluster-state quantum computation

We study concretely how classical signals should be processed in quantum cluster-state computation. Deforming corresponding quantum teleportation circuit, we find a simple rule of a classical signal-flow to obtain correct quantum computation results.

quant-ph↗
arXiv2003

Proper magnetic fields for nonadiabatic geometric quantum gates in NMR

In a scheme of nonadiabatic purely geometric quantum gates in nuclear magnetic resonance(NMR) systems we propose proper magnitudes of magnetic fields that are suitable for an experiment. We impose a natural condition and reduce the degree of freedom of the magnetic fields to the extent. By varying the magnetic fields with essentially one-dimensional degree of freedom, any spin state can acquire arbitrary purely geometric phase ϕ_{g}=-2π(1-cos{theta}), 0 < cosθ < 1. This is an essential ingredient for constructing universal geometric quantum gates.

quant-ph↗
arXiv2001

Driving Hamiltonian in a Quantum Search Problem

We examine the driving Hamiltonian in the analog analogue of Grover's algorithm by Farhi and Gutmann. For a quantum system with a given Hamiltonian $E|w> < w|$, we explicitly show that while the driving Hamiltonian $E|s> < s|$ optimally produces the state $|w>$ from an initial state $|s>$, the driving Hamiltonian $E^{\prime}|s> < s|(E^{\prime} \ne E)$ does not provide any speedup compared even with a classical computation.

quant-ph↗
arXiv2001

Critical Coupling in (1+1)-Dimensional Light-Front $ϕ^{4}$ Theory. II -effects of non-diagonal interactionof non-diagonal interactions-

Spontaneous symmetry breaking in (1+1)-dimensional $ϕ^{4}$ theory is studied with discretized light-front quantization. Taking effects of non-diagonal interactions into account, the first few terms of the commutation relations $[a_{0},a_{n}]$ are recalculated in the $\hbar$ expansion. Our result of the critical coupling is still consistent with the equal-time result $22μ^{2}/\hbar \le λ_{\rm{cr}} \le 55.5μ^{2}/\hbar$. We also have examined effects of regarding the ratio of the bare coupling constant to a renormalized mass as an independent parameter in the $\hbar$ expansion.

hep-th↗
arXiv1998

Critical coupling in (1+1)-dimensional light-front $ϕ^{4}$ theory

The spontaneous symmetry breaking in (1+1)-dimensional $ϕ^{4}$ theory is studied with discretized light-front quantization, that is, by solving the zero-mode constraint equation. The symmetric ordering is assumed for the operator-valued constraint equation. The commutation relation between the zero mode and each oscillator mode is calculated with $\hbar$ expansion. A critical coupling evaluated from the first some terms in the expansion is $28.8μ^{2}/\hbar \le λ_{cr} \le 31.1μ^{2}/\hbar$ consistent with the equal-time one $22μ^{2}/\hbar \le λ_{cr} \le 55.5μ^{2}/\hbar$. The same analysis is also made under another operator ordering.

hep-th↗
arXiv1998

de Rham cohomology of SO(n) and some related manifolds by supersymmetric quantum mechanics

We study supersymmetric quantum mechanics on RP_{n},SO(n),G_{2} and U(2) to examine Witten's Morse theory concretely. We confirm the simple instanton picture of the de Rham cohomology that has been given in a previous paper. We use a reflection symmetry of each theory to select the true vacuums. The number of selected vacuums agrees with the de Rham cohomology for each of the above manifolds.

hep-th↗
arXiv1996

De Rham Cohomology of SO(n) by Supersymmetric Quantum Mechanics

We give an elementary derivation of the de Rham cohomology of SO(n) in terms of supersymmetric quantum mechanics. Our analysis is based on Witten's Morse theory. We show reflection symmetries of the theory are useful to select true vacuums. The number of the selected vacuums will agree with the de Rham cohomology of SO(n).

hep-th↗
arXiv1995

Instanton effects and Witten complex in supersymmetric quantum mechanics on SO(4)

We examine supersymmetric quantum mechanics on $SO(4)$ to realize Witten's idea. We find instanton solutions connecting approximate vacuums. We calculate Hessian matrices for these solutions to determine true vacuums. Our result is in agreement with de Rham cohomology of $SO(4)$. We also give a criterion for cancellation of instanton effects for a pair of instanton paths.

hep-th↗
arXiv1994

Gap Equations of O(N) Non-linear Sigma Model in Three Dimensions

We study the $O(N)$ non-linear $σ$ model on three-dimensional manifolds of constant curvature by means of the large $N$ expansion at the critical point. We examine saddle point equations imposing anti-periodic boundary condition in time direction. In the case $S^1 \times S^2$ we find that a solution is inevitably unstable. We briefly refer to the case $S^1 \times S^1 \times S^1$.

hep-th↗