arXiv subjects

Shota Kanasugi

Publications and source records attributed to Shota Kanasugi.

14 recordsLinked to original sources

arXiv2026

Enabling Chemically Accurate Quantum Phase Estimation in the Early Fault-Tolerant Regime

Quantum simulation of molecular electronic structure is one of the most promising applications of quantum computing. However, achieving chemically accurate predictions for strongly correlated systems requires quantum phase estimation (QPE) on fault-tolerant quantum computing (FTQC) devices. Existing resource estimates for typical FTQC architectures suggest that such calculations demand millions of physical qubits, thereby placing them beyond the reach of near-term devices. Here, we investigate the feasibility of performing QPE for chemically relevant molecular systems in an early-FTQC regime, characterized by partial fault tolerance, constrained qubit budgets, and limited circuit depth. Our framework is based on single-ancilla, Trotter-based QPE implementations combined with partially randomized time evolution. Within this framework, we develop a novel Hamiltonian optimization strategy, termed unitary weight concentration, that reduces algorithmic cost by reshaping linear-combination-of-unitaries representations. Applying this framework to active-space models of iron-sulfur clusters, cytochrome P450 active sites, and CO$_2$-utilization catalysts, we perform end-to-end resource estimation using the latest version of the space-time efficient analog rotation (STAR) architecture. Our results indicate that ground-state energy estimation for active spaces of approximately 20 to 50 spatial orbitals, well beyond the reach of classical full configuration interaction, is achievable using $\sim 10^5$ physical qubits, with runtimes on the order of days to weeks. These findings demonstrate that while full-fledged fault-tolerant quantum computers will be required for even larger molecular simulations, chemically meaningful quantum chemistry problems are already within reach in an experimentally relevant, early-FTQC regime.

quant-ph↗

arXiv2026

STAR-Magic Mutation: Even More Efficient Analog Rotation Gates for Early Fault-Tolerant Quantum Computer

We introduce STAR-magic mutation, an efficient protocol for implementing logical rotation gates on early fault-tolerant quantum computers. This protocol judiciously combines two of the latest state preparation protocols: transversal multi-rotation protocol and magic state cultivation. It achieves a logical rotation gate with a favorable error scaling of $\mathcal{O}(\theta_L^{2(1-\Theta(1/d))}p_{\text{ph}})$, while requiring only the ancillary space of a single surface code patch. Here, $\theta_L$ is the logical rotation angle, $p_{\text{ph}}$ is the physical error rate, and $d$ is the code distance. This scaling marks a significant improvement over the previous state-of-the-art, $\mathcal{O}(\theta_L p_{\text{ph}})$, making our protocol particularly powerful for implementing a sequence of small-angle rotation gates, like Trotter-based circuits. Notably, for $\theta_L \lesssim 10^{-5}$, our protocol achieves a two-order-of-magnitude reduction in both the execution time and the error rate of analog rotation gates compared to the standard $T$-gate synthesis using cultivated magic states. Building upon this protocol, we also propose a novel quantum computing architecture designed for early fault-tolerant quantum computers, dubbed ``STAR ver.~3". It employs a refined circuit compilation strategy based on Clifford+$T$+$\phi$ gate set, rather than the conventional Clifford+$T$ or Clifford+$\phi$ gate sets. We establish a theoretical bound on the feasible circuit size on this architecture and illustrate its capabilities by analyzing the spacetime costs for simulating the dynamics of quantum many-body systems. Specifically, we demonstrate that our architecture can simulate biologically-relevant molecules or lattice models at scales beyond the reach of exact classical simulation, with only a few hundred thousand physical qubits, even assuming a realistic error rate of $p_{\text{ph}}=10^{-3}$.

quant-ph↗

arXiv2025

Mirror subspace diagonalization: A quantum Krylov algorithm with near-optimal sampling cost

Quantum Krylov algorithms have emerged as a promising approach for ground-state energy estimation in the near-term quantum computing era. A major challenge, however, lies in their inherently substantial sampling cost, primarily due to the individual measurement of each term in the Hamiltonian. While various techniques have been proposed to mitigate this issue, the sampling overhead remains a significant bottleneck, especially for practical large-scale electronic structure problems. In this work, we introduce an alternative method, dubbed mirror subspace diagonalization (MSD), which approaches the theoretical lower bound of the sampling cost for quantum Krylov algorithms. MSD leverages a finite-difference formula to express the Hamiltonian operator as a linear combination of time-evolution unitaries with symmetrically shifted timesteps, enabling efficient estimation of the Hamiltonian matrix within the Krylov subspace. In this scheme, the finite difference and statistical errors are simultaneously minimized by optimizing the timestep parameter and shifting the energy spectrum. Consequently, MSD attains the lower bound of the sampling cost of the quantum Krylov algorithms up to a logarithmic factor. Furthermore, we employ classical post-processing to infer Hamiltonian moments, which are used to mitigate the ground state energy error based on the Lanczos scheme. Through theoretical analysis of the sampling cost, we demonstrate that MSD is particularly effective when the spectral norm of the Hamiltonian is significantly smaller than its 1-norm. Such a situation arises, for example, in high-accuracy simulations of molecules using large basis sets that incorporate strong electronic correlations. Numerical results for various molecular models reveal that MSD can achieve sampling cost reductions ranging from approximately 10 to 10,000 times compared to the conventional quantum Krylov algorithm.

quant-ph↗

arXiv2025

Quantum many-body simulation of finite-temperature systems with sampling a series expansion of a quantum imaginary-time evolution

Simulating thermal-equilibrium properties at finite temperature is crucial for studying quantum many-body systems. Quantum computers are expected to enable us to simulate large systems at finite temperatures, overcoming challenges faced by classical computers, like the sign problem of the quantum Monte-Carlo technique. Conventional methods suitable for fault-tolerant quantum computing (FTQC) devices are designed for studying large-scale quantum many-body systems but require a large number of ancilla qubits and a deep quantum circuit with many basic gates, making them unsuitable for the early stage of the FTQC era, at which the availability of qubits and quantum gates is limited. In this paper, we propose a method suitable for quantum devices in this early stage to calculate the thermal-equilibrium expectation value of an observable at finite temperatures. Our proposal, named the Markov-chain Monte Carlo with sampled pairs of unitaries (MCMC-SPU) algorithm, involves sampling simple quantum circuits and generating the corresponding statistical ensembles. This approach addresses the issues of resource demand and the decay in probability associated with postselection of measurement outcomes on ancilla qubits. We validate our proposal with numerical simulation on the one-dimensional transverse-field Ising model as an illustrative example.

quant-ph↗

arXiv2025

Fast-forwardability of Qubit-mapped Fermion models based on Cartan decomposition

We study the Hamiltonian algebra of qubit-mapped interacting fermion models and their fast-forwardability. We prove that the dimension of the Hamiltonian algebra of the fermion model with single-site Coulomb interaction is bounded from below by the exponential function of the number of sites, and the circuit depth of the Cartan-based fast-forwarding method for such a model also exhibits the same scaling. We apply this proposition to the Anderson impurity model and the Hubbard model and show that the dimension of the Hamiltonian algebra of these models scales exponentially with the number of sites. These behaviors of the Hamiltonian algebras imply that, under fermion-qubit mappings that map Majorana operators to single-term Pauli strings, the qubit models obtained from these fermion models cannot be efficiently simulated using the Cartan-based fast-forwarding method.

quant-ph↗

arXiv2024

Subspace-Based Local Compilation of Variational Quantum Circuits for Large-Scale Quantum Many-Body Simulation

Simulation of quantum many-body systems is a promising application of quantum computers. However, implementing the time-evolution operator as a quantum circuit efficiently on near-term devices with limited resources is challenging. Standard approaches like Trotterization often require deep circuits, making them impractical. This paper proposes a hybrid quantum-classical algorithm called Local Subspace Variational Quantum Compilation (LSVQC) for compiling the time-evolution operator. The LSVQC uses variational optimization to reproduce the action of the target time-evolution operator within a physically reasonable subspace. Optimization is performed on small local subsystems based on the Lieb-Robinson bound, allowing for cost function evaluation using small-scale quantum devices or classical computers. Numerical simulations on a spin-lattice model and an $\mathit{\text{ab initio}}$ effective model of strongly correlated material Sr$_2$CuO$_3$ demonstrate the algorithm's effectiveness. It is shown that the LSVQC achieves a 95% reduction in circuit depth compared to Trotterization while maintaining accuracy. The subspace restriction also reduces resource requirements and improves accuracy. Furthermore, we estimate the gate count needed to execute the quantum simulations using the LSVQC on near-term quantum computing architectures in the noisy intermediate-scale or early fault-tolerant quantum computing era. Our estimation suggests that the acceptable physical gate error rate for the LSVQC can be significantly larger than for Trotterization.

quant-ph↗

arXiv2023

Computation of Green's function by local variational quantum compilation

Computation of the Green's function is crucial to study the properties of quantum many-body systems such as strongly correlated systems. Although the high-precision calculation of the Green's function is a notoriously challenging task on classical computers, the development of quantum computers may enable us to compute the Green's function with high accuracy even for classically-intractable large-scale systems. Here, we propose an efficient method to compute the real-time Green's function based on the local variational quantum compilation (LVQC) algorithm, which simulates the time evolution of a large-scale quantum system using a low-depth quantum circuit constructed through optimization on a smaller-size subsystem. Our method requires shallow quantum circuits to calculate the Green's function and can be utilized on both near-term noisy intermediate-scale and long-term fault-tolerant quantum computers depending on the computational resources we have. We perform a numerical simulation of the Green's function for the one- and two-dimensional Fermi-Hubbard model up to $4\times4$ sites lattice (32 qubits) and demonstrate the validity of our protocol compared to a standard method based on the Trotter decomposition. We finally present a detailed estimation of the gate count for the large-scale Fermi-Hubbard model, which also illustrates the advantage of our method over the Trotter decomposition.

quant-ph↗

arXiv2023

Quantum-geometry-induced anapole superconductivity

Anapole superconductivity recently proposed for multiband superconductors Commun. Phys. $\bm 5$, 39\ (2022) (at https://www.nature.com/articles/s42005-022-00804-7) is a key feature of time-reversal ($\mathcal{T}$)-symmetry-broken polar superconductors. The anapole moment was shown to arise from the asymmetric Bogoliubov spectrum, which induces a finite center of mass momenta of Cooper pairs at the zero magnetic field. In this paper, we show an alternative mechanism of anapole superconductivity: the quantum geometry induces the anapole moment when the interband pairing and Berry connection are finite. Thus, the anapole superconductivity is a ubiquitous feature of $\mathcal{T}$-broken multiband polar superconductors. Applying the theory to a minimal model of UTe$_2$, we demonstrate the quantum-geometry-induced anapole superconductivity. Furthermore, we show the Bogoliubov Fermi surfaces (BFS) in an anapole superconducting state and predict an unusual temperature dependence of BFS due to the quantum geometry. Experimental verification of these phenomena may clarify the superconducting state in UTe$_2$ and reveal the ubiquitous importance of quantum geometry in exotic superconductors.

cond-mat.supr-con↗

arXiv2022

Piezoelectric effect and diode effect in anapole and monopole superconductors

Superconductors lacking both inversion symmetry and time-reversal symmetry have been attracting much attention as a platform for exotic superconducting phases and anomalous phenomena, including the superconducting diode effect. Recent studies revealed intrinsic phases with this symmetry, named anapole superconductivity and monopole superconductivity, which are $PT$-symmetric superconducting states with and without Cooper pairs' total momentum, respectively. To explore characteristic phenomena in these states, we calculate and predict the superconducting piezoelectric effect and superconducting diode effect. A close relationship with the finite-$q$ pairing, asymmetric Bogoliubov spectrum, and quantum geometry is discussed. This study reveals the piezoelectric and diode effects as potential probes to elucidate exotic superconducting phases.

cond-mat.supr-con↗

arXiv2021

Anapole superconductivity from $\mathcal{PT}$-symmetric mixed-parity interband pairing

Recently, superconductivity with spontaneous time-reversal or parity symmetry breaking is attracting much attention owing to its exotic properties, such as nontrivial topology and nonreciprocal transport. Particularly fascinating phenomena are expected when the time-reversal and parity symmetry are simultaneously broken. This work shows that time-reversal symmetry-breaking mixed-parity superconducting states generally exhibit an unusual asymmetric Bogoliubov spectrum due to nonunitary interband pairing. For generic two-band models, we derive the necessary conditions for the asymmetric Bogoliubov spectrum. We also demonstrate that the asymmetric Bogoliubov quasiparticles lead to the effective anapole moment of the superconducting state, which stabilizes a nonuniform Fulde-Ferrell-Larkin-Ovchinnikov state at zero magnetic fields. The concept of anapole order employed in nuclear physics, magnetic materials science, strongly correlated electron systems, and optoelectronics is extended to superconductors by this work. Our conclusions are relevant for any multiband superconductors with competing even- and odd-parity pairing channels. Especially, we discuss the superconductivity in UTe$_2$.

cond-mat.supr-con↗

arXiv2020

Ferroelectricity-induced multiorbital odd-frequency superconductivity in SrTiO$_3$

We demonstrate that SrTiO$_3$ can be a platform for observing the bulk odd-frequency superconducting state owing to the multiorbital/multiband nature. We consider a three-orbital tight-binding model for SrTiO$_3$ in the vicinity of a ferroelectric critical point. Assuming an intraorbital spin-singlet $s$-wave superconducting order parameter, it is shown that the odd-frequency pair correlations are generated due to the intrinsic LS coupling which leads to the local orbital mixing. Furthermore, we show the existence of additional odd-frequency pair correlations in the ferroelectric phase, which is induced by an odd-parity orbital hybridization term proportional to the ferroelectric order parameter. We also perform a group theoretical classification of the odd-frequency pair amplitudes based on the fermionic and space group symmetries of the system. The classification table enables us to predict dominant components of the odd-frequency pair correlations based on the symmetry of the normal state Hamiltonian that we take into account. Furthermore, we show that experimental signatures of the odd-parity orbital hybridization, which is an essential ingredient for the ferroelectricity-induced odd-frequency pair correlations, can be observed in the spectral functions and density of states.

cond-mat.supr-con↗

arXiv2020

Multiple odd-parity superconducting phases in bilayer transition metal dichalcogenides

We study unconventional superconductivity in a two-dimensional locally noncentrosymmetric triangular lattice. The model is relevant to bilayer transition metal dichalcogenides with 2H$_b$ stacking structure, for example. The superconducting instability is analyzed by solving the linearized Eliashberg equation within the random phase approximation. We show that ferromagnetic fluctuations are dominant owing to the existence of disconnected Fermi pockets near van Hove singularity, and hence odd-parity spin-triplet superconductivity is favored. In the absence of the spin-orbit coupling, we find that odd-parity $f$-wave superconducting state is stabilized in a wide range of carrier density and interlayer coupling. Furthermore, we investigate impacts of the layer-dependent staggered Rashba and Zeeman spin-orbit coupling on the superconductivity. Multiple odd-parity superconducting phase diagrams are obtained as a function of the spin-orbit coupling and Coulomb interaction. Especially, a topological chiral $p$-wave pairing state is stabilized in the presence of a moderate Zeeman spin-orbit coupling. Our results shed light on a possibility of odd-parity superconductivity in various ferromagnetic van der Waals materials.

cond-mat.supr-con↗

arXiv2019

Multiorbital Ferroelectric Superconductivity in doped SrTiO3

SrTiO$_3$ is a unique example of a system which exhibits both quantum paraelectricity and superconductivity. Thus, it is expected that the superconducting state is closely related to the intrinsic ferroelectric instability. Indeed, recent experiments suggest existence of a coexistent phase of superconductivity and ferroelectricity in Ca-substituted SrTiO$_3$. In this paper, we propose that SrTiO$_3$ can be a platform of the ferroelectric superconductivity, which is characterized by a ferroelectric transition in the superconducting state. By analyzing a multiorbital model for $t_{2g}$ electrons, we show that the ferroelectric superconductivity is stabilized through two different mechanisms which rely on the presence of the spin-orbit coupling. First, the ferroelectric superconducting state is stabilized in the dilute carrier density regime due to a ferroelectricity-induced Lifshitz transition. Second, it is stabilized under a magnetic field independent of the carrier density. The importance of the multiorbital or multiband nature for the ferroelectric superconductivity is clarified. Then, we predict a topological Weyl superconducting state in the ferroelectric superconducting phase of SrTiO$_3$.

cond-mat.supr-con↗

arXiv2018

Spin-orbit-coupled ferroelectric superconductivity

Motivated by recent studies on ferroelectric-like order coexisting with metallicity, we investigate ferroelectric (FE) superconductivity in which a FE-like structural phase transition occurs in the superconducting state. We consider a two-dimensional s-wave superconductor with Rashba-type antisymmetric spin-orbit coupling (ASOC). Assuming linear relationship between polar lattice displacement and strength of the ASOC, we treat the Rashba-type ASOC as a molecular field of FE-like order. It is shown that the FE-like order is induced by the magnetic field when the system is superconducting. Furthermore, we clarify the FE superconductivity in a low carrier density regime, which was recently discovered in doped SrTiO$_3$. It is demonstrated that the FE superconducting state can be stable in this regime in the absence of the magnetic field. Our results open a way to control the electric polarization by superconductivity, that is, superconducting multiferroics.

cond-mat.supr-con↗