arXiv subjects

Takuya Hatomura

Publications and source records attributed to Takuya Hatomura.

At least 19 recordsLinked to original sources

arXiv2026

Feedback-based quantum optimization and its classical counterpart: quantum advantage and the power of classical algorithms

Feedback-based quantum optimization is a quantum approach to combinatorial optimization. In this paper, we introduce the classical counterpart of feedback-based quantum optimization by using the quantum-classical correspondence of spin systems to discuss the possibility of quantum advantage. It also enables us to develop higher-order theory of a previously proposed classical approach to feedback-based quantum optimization. First, we compare the feedback-based algorithm for quantum optimization (FALQON) and its variant with their classical counterparts. Then, we perform benchmark tests of various quantum and classical algorithms with small-scale instances, and of classical algorithms with large-scale instances. Main findings are that (i) quantum algorithms can be advantageous to classical algorithms in terms of the quality of solutions, while classical algorithms tend to show faster convergence than quantum ones, and (ii) one of the classical algorithms discussed in this paper shows significant scalability for higher-order unconstrained binary optimization problems. These findings highlight the importance of quantumness and the usefulness of classical approaches.

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arXiv2026

Universal Digitized Counterdiabatic Driving

Counterdiabatic driving realizes parameter displacement of an energy eigenstate of a given parametrized Hamiltonian using the adiabatic gauge potential. In this paper, we propose a universal method of digitized counterdiabatic driving, constructing the adiabatic gauge potential in a digital way with the idea of universal counterdiabatic driving. This method has three advantages over existing universal counterdiabatic driving and/or digitized counterdiabatic driving: it does not introduce any many-body and/or nonlocal interactions to an original target Hamiltonian; it can incorporate infinite nested commutators, which constitute the adiabatic gauge potential; and it gives explicit expression of rotation angles for digital implementation. We show the consistency of our method to the exact theory in an analytical way and the effectiveness of our method with the aid of numerical simulations.

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arXiv2025

Reducing errors and gate operations in digitized quantum annealing with local counterdiabatic driving

Local counterdiabatic driving is a method of improving the performance of adiabatic control and digital implementation of quantum annealing with local counterdiabatic driving has been discussed. In this paper, we propose a decomposition formula which enables us to reduce digitization errors and the number of gate operations in digitized quantum annealing with local counterdiabatic driving.

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arXiv2025

Classical algorithm inspired by the feedback-based algorithm for quantum optimization and local counterdiabatic driving

We propose a quantum-inspired classical algorithm for combinatorial optimization problems, named the counterdiabaticity-assisted classical algorithm for optimization (CACAO). In this algorithm, a solution of a given combinatorial optimization problem is heuristically searched with classical spin dynamics based on quantum Lyapunov control of local counterdiabatic driving. We compare the performance of CACAO with that of quantum time-evolution algorithms, i.e., quantum annealing, the feedback-based algorithm for quantum optimization (known as FALQON), and the counterdiabatic feedback-based quantum algorithm (known as CD-FQA). We also study the performance of CACAO applied to large systems up to $10,000$ spins.

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arXiv2025

Improving Variational Counterdiabatic Driving with Weighted Actions and Computer Algebra

Variational counterdiabatic (CD) driving is a disciplined and widely used method to robustly control quantum many-body systems by mimicking adiabatic processes with high fidelity and reduced duration. Central to this technique is a universal structure of the adiabatic gauge potential (AGP) over a parameterized Hamiltonian. Here, we reveal that introducing a new degree of freedom into the theory of the AGP can significantly improve variational CD driving. Specifically, we find that the algebraic characterization of the AGP is not unique, and we exploit this nonuniqueness to develop the weighted variational method for deriving a refined driving protocol. This approach extends the conventional method in two aspects: it assigns customized weights to matrix elements relevant to specific problems, and it effectively incorporates nonlocal information into local driving coefficients. We also develop an efficient numerical algorithm to compute the refined driving protocol using computer algebra. Our framework is broadly applicable and, in principle, it can replace any previous use of variational CD driving. We demonstrate its practicality by applying it to adiabatic evolution along the ground state of a parameterized Hamiltonian. This proposal outperforms the conventional method in terms of fidelity, as confirmed by extensive numerical simulations on quantum Ising models.

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arXiv2025

Geometrical scheduling of adiabatic control without information of energy spectra

Adiabatic control is a fundamental technique for manipulating quantum systems, guided by the quantum adiabatic theorem, which ensures suppressed nonadiabatic transitions under slow parameter variations. Quantum annealing, a heuristic algorithm leveraging adiabatic control, seeks the ground states of Ising spin glass models and has drawn attention for addressing combinatorial optimization problems. However, exponentially small energy gaps in such models often necessitate impractically long runtime to satisfy the adiabatic condition. Despite this limitation, improving the quality of approximate solutions remains crucial for practical applications. The quantum adiabatic brachistochrone provides a method to enhance adiabaticity by minimizing an action representing nonadiabaticity via the variational principle. While effective, its implementation requires detailed energy spectra, complicating its use in quantum annealing. Shortcuts to adiabaticity by counterdiabatic driving offer alternative approaches for accelerating adiabatic processes. However, the theory of shortcuts to adiabaticity often faces challenges such as nonlocal control requirements, high computational cost, and trade-offs between speed and energy efficiency. In this work, we propose a novel quantum adiabatic brachistochrone protocol tailored for quantum annealing that eliminates the need for energy spectrum information. Our approach builds on advancements in counterdiabatic driving to design efficient parameter schedules. We demonstrate the effectiveness of our method through numerical simulations on the transverse-field Ising chain and axial next-nearest neighbor Ising models.

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arXiv2024

Energy-saving fast-forward scaling

We propose energy-saving fast-forward scaling. Fast-forward scaling is a method which enables us to speed up (or slow down) given dynamics in a certain measurement basis. We introduce energy costs of fast-forward scaling, and find possibility of energy-saving speedup for time-independent measurement bases. As concrete examples, we show such energy-saving fast-forward scaling in a two-level system and quantum annealing of a general Ising spin glass. We also discuss the influence of a time-dependent measurement basis, and give a remedy for unwanted energy costs. The present results pave the way for realization of energy-efficient quantum technologies.

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arXiv2024

Benchmarking adiabatic transformation by alternating unitaries

Adiabatic transformation can be approximated as alternating unitary operators of a Hamiltonian and its parameter derivative as proposed in a gate-based approach to counterdiabatic driving (van Vreumingen, arXiv:2406.08064). In this paper, we conduct numerical benchmarking of this alternating unitary method in a finite-parameter range against adiabatic driving in nonadiabatic timescale. We find that the alternating unitary method results in broader distribution on energy eigenstates than that obtained by adiabatic driving, but it has ability to sample low-energy eigenstates when an energy gap of a given Hamiltonian is small. It indicates that the alternating unitary method may be able to find good approximate solutions in quantum annealing applied to hard instances.

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arXiv2024

Shortcuts to adiabaticity: theoretical framework, relations between different methods, and versatile approximations

Shortcuts to adiabaticity guide given systems to final destinations of adiabatic control via fast tracks. Various methods were proposed as varieties of shortcuts to adiabaticity. Basic theory of shortcuts to adiabaticity was established in the 2010s, but it has still been developing and many fundamental findings have been reported. In this Topical Review, we give a pedagogical introduction to theory of shortcuts to adiabaticity and revisit relations between different methods. Some versatile approximations in counterdiabatic driving, which is one of the methods of shortcuts to adiabaticity, will be explained in detail. We also summarize recent progress in studies of shortcuts to adiabaticity.

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arXiv2023

The first-order Trotter decomposition in the dynamical-invariant basis

The Trotter decomposition is a basic approach to Hamiltonian simulation (digital quantum simulation). The first-order Trotter decomposition is the simplest one, whose deviations from target dynamics are of the first order of a small coefficient in terms of the infidelity. In this paper, we consider the first-order Trotter decomposition in the dynamical-invariant basis. By using a state-dependent inequality, we point out that deviations of this decomposition are of the second order of a small coefficient. Moreover, we also show that this decomposition includes a useful example, i.e., digital implementation of shortcuts to adiabaticity by counterdiabatic driving.

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arXiv2023

Time rescaling of nonadiabatic transitions

Applying time-dependent driving is a basic way of quantum control. Driven systems show various dynamics as its time scale is changed due to the different amount of nonadiabatic transitions. The fast-forward scaling theory enables us to observe slow (or fast) time-scale dynamics during moderate time by applying additional driving. Here we discuss its application to nonadiabatic transitions. We derive mathematical expression of additional driving and also find a formula for calculating it. Moreover, we point out relation between the fast-forward scaling theory for nonadiabatic transitions and shortcuts to adiabaticity by counterdiabatic driving.

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arXiv2023

Scaling of errors in digitized counterdiabatic driving

We study errors caused by digitization of shortcuts to adiabaticity by counterdiabatic driving. We find possibility of error scaling $\mathcal{O}(M^{-2})$ with the number of time slices $M$, whereas worse error scaling $\mathcal{O}(M^{-1})$ is predicted in the conventional theory of the first-order Suzuki-Trotter decomposition. We point out this possibility by considering a state-dependent error bound and confirm emergence of this error scaling $\mathcal{O}(M^{-2})$ by numerical simulation. Moreover, we numerically show that intermediate error scaling can be observed in digitization of approximate counterdiabatic driving. These results reveal usefulness of digitized counterdiabatic driving from the viewpoints of both cost and performance.

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arXiv2022

State-dependent error bound for digital quantum simulation of driven systems

Digital quantum simulation is a promising application of quantum computers, where quantum dynamics is simulated by using quantum gate operations. Many techniques for decomposing a time-evolution operator of quantum dynamics into simulatable quantum gate operations have been proposed, while these methods cause some errors. To evaluate these errors, we derive a lower bound for overlap between true dynamics and digital simulated dynamics at the final time. Our result enables us to guarantee how obtained digital simulated dynamics is close to unknown true dynamics. We also extend our formalism to error evaluation of digital quantum simulation on noisy quantum computers.

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arXiv2021

Performance evaluation of invariant-based inverse engineering by quantum speed limit

Quantum speed limits for two time-evolved states are introduced and applied to overlap between true dynamics and approximate dynamics. In particular, we point out that the present idea is suitable for invariant-based inverse engineering, i.e., the worst case performance of invariant-based inverse engineering can be evaluated by using a designed time-evolved state. As demonstrations, we apply the present method to stimulated Raman adiabatic passage and quantum annealing, and then we find that the present idea brings valuable insight to control scheduling.

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arXiv2021

Quantum metrology based on symmetry-protected adiabatic transformation: Imperfection, finite time duration, and dephasing

The aim of quantum metrology is to estimate target parameters as precisely as possible. In this paper, we consider quantum metrology based on symmetry-protected adiabatic transformation. We introduce a ferromagnetic Ising model with a transverse field as a probe and consider the estimation of a longitudinal field. Without the transverse field, the ground state of the probe is given by the Greenberger-Horne-Zeilinger state, and thus the Heisenberg limit estimation of the longitudinal field can be achieved through parity measurement. In our scheme, full information of the longitudinal field encoded on parity is exactly mapped to global magnetization by symmetry-protected adiabatic transformation, and thus the parity measurement can be replaced with global magnetization measurement. Moreover, this scheme requires neither accurate control of individual qubits nor that of interaction strength. We discuss the effects of the finite transverse field and nonadiabatic transitions as imperfection of adiabatic transformation. By taking into account finite time duration for state preparation, sensing, and readout, we also compare performance of the present scheme with a classical scheme in the absence and presence of dephasing.

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arXiv2020

Controlling and exploring quantum systems by algebraic expression of adiabatic gauge potential

Adiabatic gauge potential is the origin of nonadiabatic transitions. In counterdiabatic driving, which is a method of shortcuts to adiabaticity, adiabatic gauge potential can be used to realize identical dynamics to adiabatic time evolution without requiring slow change of parameters. We introduce an algebraic expression of adiabatic gauge potential. Then, we find that the explicit form of adiabatic gauge potential can be easily determined by some algebraic calculations. We demonstrate this method by using a single-spin system, a two-spin system, and the transverse Ising chain. Moreover, we derive a lower bound for fidelity to adiabatic time evolution based on the quantum speed limit. This bound enables us to know the worst case performance of approximate adiabatic gauge potential. We can also use this bound to find dominant terms in adiabatic gauge potential to suppress nonadiabatic transitions. We apply this bound to magnetization reversal of the two-spin system and to quantum annealing of the transverse Ising chain. Adiabatic gauge potential reflects structure of energy eigenstates, and thus we also discuss detection of quantum phase transitions by using adiabatic gauge potential. We find a signature of a quantum phase transition in the transverse Ising chain.

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arXiv2020

Bounds for nonadiabatic transitions

We discuss bounds for nonadiabatic transitions from the viewpoints of the adiabatic perturbation theory and the quantum speed limit. We show that the amount of nonadiabatic transitions from the $n$th level to the $m$th level is bounded by a function of the quantum geometric tensor for the $m$th level. We analyze this bound from the viewpoint of the adiabatic perturbation theory. In addition, this bound and the viewpoint of the quantum speed limit suggest nontrivial relationship between the dynamical transformation and the adiabatic transformation. We also derive a universal bound for any nonadiabatic transition. This bound is written in terms of the counterdiabatic Hamiltonian.

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arXiv2019

Iterative classical superadiabatic algorithm for combinatorial optimization

We consider a classical and superadiabatic version of an iterative quantum adiabatic algorithm to solve combinatorial optimization problems. This algorithm is deterministic because it is based on purely classical dynamics, that is, it does not rely on any stochastic approach to mimic quantum dynamics. Moreover, use of shortcuts to adiabaticity makes the algorithm independent of the annealing time. We apply this algorithm to a certain class of hard instances of the 3-SAT problem. We find that more than 90\% of such 64-bits hard instances can be resolved by a few iteration. Our approach can also be used to analyze properties of instances themselves apart from stochastic uncertainty and shortage of adiabaticity.

cond-mat.stat-mech↗