Quantum control papers on arXiv, selected and classified automatically by QOC. https://llorebaga.github.io/QOC/topics/propagation-methods/ 2026-10-06T00:00:00Z QOC https://arxiv.org/abs/2610.08235 2026-10-06T00:00:00Z 2026-10-06T00:00:00Z Julián Ferreiro-VélezFrancisco Andrés Cárdenas-LópezFelix MotzoiXi Chen

We introduce an inertial counterdiabatic (CD) protocol that reformulates shortcut-to-adiabaticity design as a moving-frame diagonalization problem. The method employs the Magnus expansion to construct a variational propagator generated by an accessible CD ansatz. In the new rotating frame, the controls are optimized to suppress the off-diagonal Hamiltonian terms, and the CD terms are defined to counteract the corresponding inertial contribution. The propagator generated with the Magnus expansion naturally exploits additional control directions generated through its nested commutator, while the sequential design of the propagator introduces temporal nonlocality into the optimization. We benchmark the method on a two-qubit system and on the one-dimensional quantum Ising chain, where it consistently outperforms variational CD protocols based on action minimization. The largest improvements are observed near gap-closing regions, demonstrating the advantage of combining temporal and algebraic nonlocality for suppressing diabatic excitations.

https://arxiv.org/abs/2608.04850 2026-08-05T00:00:00Z 2026-08-14T00:00:00Z Urei Miura

Although Arnoldi reduction of a generally non-Hermitian Hamiltonian yields an upper Hessenberg matrix rather than the tridiagonal form of Hermitian Lanczos theory, we show that a closed Toda sector survives in its diagonal and subdiagonal coefficients. For a fixed finite-dimensional Hamiltonian and a cyclic state vector deformed holomorphically, the Krylov Gram determinants are $τ$ functions of the finite two-dimensional Toda lattice, whose Flaschka variables coincide exactly with these Arnoldi coefficients. The Toda dynamics therefore closes on this sector without determining the remaining upper Hessenberg entries. The subdiagonal part of the same sector also has a direct geometric meaning: the squared subdiagonal coefficients determine both the Fubini--Study metric and the Berry curvature of holomorphic Krylov subspaces, whereas the geometric quantities associated with subspaces lost at Arnoldi breakdown cease to be defined. Along a smooth real path in the cyclic region, the Arnoldi-frame connection further provides a Hermitian tridiagonal generator of exact isospectral transport. When added to the Arnoldi matrix, this generator cancels transitions between instantaneous eigenspaces and realizes counterdiabatic driving whenever the matrix is diagonalizable with a nondegenerate spectrum.

https://arxiv.org/abs/2608.03702 2026-08-04T00:00:00Z 2026-08-06T00:00:00Z Anastasia PipiValentin DuruisseauxEmily M. BeenXuecheng TaoTaylor L. PattiAnima AnandkumarPrineha Narang

Quantum optimal control is a key tool for steering quantum dynamics, but its computational cost grows rapidly with the Hilbert space dimension. Here, we introduce a Fourier Neural Operator (FNO)-based framework for learning high dimensional molecular quantum dynamics and accelerating the inverse design of control protocols. Given an initial molecular population distribution, laser frequency, and polarization, the FNO predicts molecular-motional population dynamics up to $10^7$ times faster than GPU-accelerated numerical propagation with CUDA-Q Dynamics. Using this fast and differentiable surrogate, we develop the FNO stochastic pulse-measurement planner (FNO-SPMP), which constructs pulse sequences to purify an initially mixed Boltzmann distribution. We demonstrate the protocol in an 888-dimensional subspace of the hydronium molecule at 20 K, achieving a target-state population of 0.98 with a sequence success rate of up to 86.2%. In a shared discrete control space, FNO-SPMP achieves nearly twice the success rate of a reinforcement-learning baseline while using roughly half as many quantum control pulses and reducing pulse-sequence generation time from approximately 10 hours to 10-20 minutes. These results show that operator-learning surrogates can enable inverse design in quantum systems whose Hilbert spaces are too large for conventional direct optimization.

https://arxiv.org/abs/2607.07802 2026-07-08T00:00:00Z 2026-07-08T00:00:00Z Ankit Wenju ShresthaBudhaditya BhattacharjeeAdolfo del Campo

Shortcuts to adiabaticity (STA) reproduce adiabatic dynamics in finite time, but their counterdiabatic implementation relies on the adiabatic gauge potential (AGP), which is difficult to compute and implement in many-body systems and whose extension to open and non-Hermitian settings has remained largely model-specific. Here, we develop a general, diagonalization-free framework for engineering STA in non-Hermitian systems by representing the AGP in Krylov space. Starting from an integral representation of the counterdiabatic control, we recast the AGP as a nested-commutator series with controlled locality and generate the associated Krylov basis using the bi-Lanczos and Arnoldi algorithms. This reduces the exact or truncated AGP to a sparse tridiagonal or upper-Hessenberg matrix equation that generalizes the Hermitian construction. We demonstrate the method on a decaying two-level atom, where it recovers the exact drive and signals the exceptional point; on the interacting Hatano-Nelson model, where truncated controls rapidly suppress nonadiabatic excitations; and on a PT-symmetric Heisenberg chain, whose AGP norm detects the PT-symmetry-breaking transition. Throughout, the expansion converges with only a small fraction of the full Krylov space, offering a practical route to fast, accurate control of many-body non-Hermitian systems.

https://arxiv.org/abs/2606.02014 2026-06-01T00:00:00Z 2026-06-01T00:00:00Z Piero LuchiFrancesco Pederiva

We present a framework combining Lie group theory and feed-forward neural networks to efficiently generate quantum optimal control pulses for arbitrary unitary operations in superconducting qubit systems, bypassing the need for explicit optimization at inference time. The exponential scaling of the Hilbert space dimension with qubit number makes standard optimization approaches computationally prohibitive when large ensembles of distinct propagators must be processed, a bottleneck that is particularly acute in Trotterized quantum simulation. Our method addresses this limitation by pre-computing a representative set of control pulses via Lie group theory and training neural networks to map target propagators to their corresponding pulses. We demonstrate the approach on superconducting qubit systems of 2, 3, and 4 qubits, finding high reconstruction fidelity for specific combinations of Lie algebra parameters. As a physically motivated benchmark, we apply the methodology to reconstruct control pulses for the Trotter propagators of a neutrino system undergoing collective flavor oscillations. The successful generalization across system types demonstrates that a single model -- trained once on hardware-specific random propagators -- can serve as a universal control-pulse generator for any target quantum system of compatible Hilbert space dimension, offering a promising route toward scalable quantum simulation.

https://arxiv.org/abs/2605.07668 2026-05-08T00:00:00Z 2026-05-08T00:00:00Z Shuo ZhangYuzhi TongPengfei ZhangZeyu Liu

Quantum simulation of complex many-body systems beyond classical computational capabilities provides a promising route toward understanding novel quantum phases and their transitions. In particular, analog quantum simulators with global control fields have attracted considerable attention due to their potential to simulate arbitrary Hamiltonians and perform quantum computing tasks. However, a clear, quantitative measure for the complexity of implementing specific quantum operations in such systems is still lacking. In this Letter, we address this challenge by introducing generalized Krylov complexity, a concept originating from operator growth dynamics, as a direct diagnosis for this synthesis complexity. We construct the block Krylov basis generated by a set of Hamiltonians, which naturally organizes the operator space achievable through the simulator's native interactions and their nested commutators. By analyzing representative systems including Rydberg atom arrays, we demonstrate that the generalized Krylov complexity of a target operation serves as a strong predictor of the minimum time required for its realization. Our results establish Krylov complexity as an intuitive and predictive tool for designing efficient control protocols in analog quantum simulators.

https://arxiv.org/abs/2605.05290 2026-05-06T00:00:00Z 2026-05-15T00:00:00Z András GrabaritsE. Medina-GuerraAdolfo del Campo

We study quantum dynamics generated by time-dependent Hamiltonians in Krylov space, the minimal subspace in which the evolution takes place. We establish a direct link between dynamics in the time-dependent Krylov subspace and the underlying Lie-algebraic structure of the Hamiltonian. We develop a general framework in which the dynamics in the time-dependent Krylov subspace is generated by ladder operators of the associated Lie algebra. In particular, we identify the minimal conditions under which the exact time-dependent Krylov dynamics is naturally determined by the interaction-picture Hamiltonian and governed by an embedded $\mathfrak{sl}(2,\mathbb{C})$ subalgebra. We further show that an exact single-exponential representation of the time-evolution operator gives rise to a distinct time-independent Krylov dynamics in a unitarily related basis, from which the exact time-dependent Krylov dynamics can nevertheless be recovered. We also extend the framework to the oscillator algebra as the simplest extension of the nilpotent Heisenberg--Weyl algebra, and provide further examples, including the translated and dilated harmonic oscillator, systems governed by closed Virasoro subalgebras, a spin in a rotating magnetic field, and higher-dimensional generalizations for multi-level systems. In addition, we introduce a new quantum speed limit to the complexity growth rate generated by a time-dependent generator and show that, for evolutions governed by a Lie algebra, it retains the same functional form as in the time-independent case. Remarkably, saturation of this bound is strongly affected by temporal driving and persists only when the Hamiltonian commutes with itself at different times. These results establish a unified framework for characterizing operator growth and Krylov complexity in time-dependent quantum systems with underlying Lie-algebraic structures.

https://arxiv.org/abs/2604.26663 2026-04-29T00:00:00Z 2026-04-29T00:00:00Z F. S. LuizPaulo Henrique Dias FerreiraMurilo Henrique de Oliveira

Compiling time-evolution operators of the form $U(t)=e^{-iHt}$ into hardware-native gate sequences is a central bottleneck for digital quantum simulation on noisy intermediate-scale quantum (NISQ) devices. Generic transpilation treats $U(t)$ as an arbitrary unitary, discarding the structure of Hamiltonian dynamics and producing circuits whose depth exceeds hardware coherence limits. We introduce a structure-aware compilation framework that treats product-formula decompositions as synthesis primitives rather than simulation approximations. The method combines (i) native placement of Hamiltonian terms onto the hardware coupling map, (ii) adaptive selection of Trotter blocks via a greedy discretization procedure, and (iii) variational refinement using a Trotter-initialized ansatz. Across Heisenberg, Ising, and XY models with $n=3$--$8$ qubits, the compiled circuits achieve fidelities $F>0.996$ with approximately linear scaling in the number of entangling gates, while generic synthesis produces circuits that are orders of magnitude deeper. On IBM Torino hardware, we observe a regime in which shorter approximate circuits outperform deeper exact decompositions: a 27-CX circuit achieves higher hardware fidelity ($F_{\mathrm{hw}}=0.987$) than a 187-CX exact circuit. These results demonstrate that, in the NISQ regime, structure-aware approximate compilation can outperform exact structure-agnostic synthesis, providing a practical pathway for executing Hamiltonian dynamics without requiring pulse-level control.

https://arxiv.org/abs/2604.13923 2026-04-15T00:00:00Z 2026-04-15T00:00:00Z Rahul GuptaFlorian MintertHimadri Shekhar Dhar

We present a Krylov space based theoretical framework for modeling inhomogeneous spin ensembles with arbitrary distributions of spin frequencies and couplings. The framework is then used to asymptotically large spin ensemble. In the single-excitation subspace, the Krylov construction allows for to derive exact expressions for the Lieb-Robinson velocity and quantum speed limit, and figure of merit such as Krylov complexity. Our work reveals a strong dependence of the speed of information flow on the statistical distribution of resonance frequencies in the spin ensemble with immediate implications for the design of components for quantum technologies, realized for example with nitrogen vacancy centers, nuclear spins or ultracold atoms.

https://arxiv.org/abs/2603.26619 2026-03-27T00:00:00Z 2026-08-21T00:00:00Z Swati ChoudharySukrut MondkarUjjwal Sen

A recently developed notion, known as spread complexity, captures how a quantum state spreads in Krylov space under unitary evolution. Related Krylov-space approaches are increasingly being investigated for applications in quantum control, simulation, and metrology, as well as are being considered for implementation in near-term quantum platforms. However, its connection to fundamental quantum resources such as entanglement and quantum coherence remains unclear. We show that the dynamics of entanglement is constrained by the extent of spreading in Krylov space. For multipartite systems, we relate state delocalization in the Krylov basis, quantified by the inverse participation ratio, to geometric measures of multipartite quantum correlations. Furthermore, we derive analytical relations between the quantum coherence of the initial state in the energy eigenbasis and spread complexity for qubit and qutrit systems. Our results make progress towards understanding the subtle interplay between the dynamical spreading in Krylov space and fundamental quantum resources.

https://arxiv.org/abs/2603.18052 2026-03-17T00:00:00Z 2026-09-09T00:00:00Z Rylan Malarchick

Dense Lindblad propagation at the Hilbert-space sizes of near-term transmon control ($d = 3$, $9$, $27$) sits in a regime where cache boundaries, launch overhead, and fixed latency decide which hardware is useful, not peak arithmetic rate. This paper characterizes that regime on two x86 CPUs, two NVIDIA GPUs, and a low-cost FPGA. Each implementation is stated as an algorithm in $d$ with an idealized cost built from separately measured ceilings, and the measured gaps are attributed to specific mechanisms: thread fork/join, the strided read of the propagator, PCI Express (PCIe) transfers, and propagator re-upload. An end-to-end gradient-ascent (GRAPE-style) benchmark against released QuTiP 5.2.3 shows that fast propagation does not imply fast control optimization: the C path wins by up to two orders of magnitude at $d = 3$ but loses at $d = 27$, where the dense LU solve inside the Padé propagator build takes over $90\%$ of the cost. The FPGA contributes a deterministic-latency operating point, $95$ cycles per step at a stress-characterized $108$ MHz with zero cycle spread over $1000$ trials, and its Q1.15 fixed-point drift is measured on the device. The results are a map of operating regimes for the measured grid, with the propagator build, not propagation, as the dominant cost at the largest size.

https://arxiv.org/abs/2603.11697 2026-03-12T00:00:00Z 2026-03-12T00:00:00Z Boris WembeUsman AliTorsten MeierSina Ober-Blöbaum

This paper presents a class of structure-preserving numerical methods for quantum optimal control problems, based on commutator-free Cayley integrators. Starting from the Krotov framework, we reformulate the forward and backward propagation steps using Cayley-type schemes that preserve unitarity and symmetry at the discrete level. This approach eliminates the need for matrix exponentials and commutators, leading to significant computational savings while maintaining higher-order accuracy. We first recall the standard linear setting and then extend the formulation to nonlinear Schrödinger and Gross-Pitaevskii equations using a Cayley-polynomial interpolation strategy. Numerical experiments on state-transfer problems illustrate that the CF-Cayley method achieves the same accuracy as high-order exponential or Cayley-Magnus schemes at substantially lower cost, especially for longtime or highly oscillatory dynamics. In the nonlinear regime, the structure-preserving properties of the method ensure stability and norm conservation, making it a robust tool for large-scale quantum control simulations. The proposed framework thus bridges geometric integration and optimal control, offering an efficient and reliable alternative to existing exponential-based propagators.

https://arxiv.org/abs/2512.22636 2025-12-27T00:00:00Z 2026-06-12T00:00:00Z Mara VizzusoGianluca PassarelliGiovanni CanteleProcolo LucignanoXi ChenKoushik Paul

Trotter errors in digitized quantum dynamics arise from approximating time-ordered evolution under noncommuting Hamiltonian terms with a product formula. In the adiabatic regime, such errors are known to exhibit long-time self-healing [Phys. Rev. Lett. \textbf{131}, 060602 (2023)], where discretization effects are effectively suppressed. Here we show that self-healing persists at finite evolution times once nonadiabatic errors induced by finite-speed ramps are compensated. Using counterdiabatic driving to cancel diabatic transitions and isolate discretization effects, we study both noninteracting and interacting spin models and characterize the finite-time scaling with the Trotter steps and the total evolution time. In the instantaneous eigenbasis of the driven Hamiltonian, the leading digital error maps to an effective harmonic perturbation whose dominant Fourier component yields an analytic upper bound on the finite-time Trotter error and reveals the phase-cancellation mechanism underlying self-healing. Our results establish finite-time self-healing as a generic feature of digitized counterdiabatic protocols, clarify its mechanism beyond the long-time adiabatic limit, and provide practical guidance for high-fidelity state preparation on gate-based quantum processors.

https://arxiv.org/abs/2512.20359 2025-12-23T00:00:00Z 2026-02-09T00:00:00Z Mohsen AlishahihaSouvik Banerjee

We show that Hall's exact uncertainty relation acquires a simple geometric form in the Krylov basis generated by the Liouvillian. In this canonical operator frame, the uncertainty equality implies that the operator amplitude vector evolves on the unit Krylov sphere with constant speed fixed solely by the first Lanczos coefficient. This yields an exact linear bound on geometric operator evolution, independent of higher Lanczos coefficients and valid for arbitrary Hamiltonians, integrable or chaotic. Our results provide the first unified geometric interpretation of exact quantum speed limits and operator growth, identifying the first Lanczos coefficient as the intrinsic speed scale of quantum dynamics.

https://arxiv.org/abs/2512.04494 2025-12-04T00:00:00Z 2025-12-04T00:00:00Z Wen Ting HsiehDries Sels

This study explores the use of subspace methods in combination with counterdiabatic driving in a Rydberg atom system to solve the Maximum Independent Set (MIS) problem. Although exact counterdiabatic driving offers excellent performance, it comes at an unscalable computational cost. In this work, we demonstrate that counterdiabatic driving can be significantly improved by restricting the analysis to a relevant subspace of the system. We first show that both direct diagonalization and the Krylov method for obtaining the counterdiabatic matrix can be accelerated through the use of subspace techniques, while still maintaining strong performance. We then demonstrate that the cost function used in the standard Krylov method can be further optimized by employing a subspace-based cost function. These findings open up new possibilities for applying counterdiabatic driving in a practical and efficient manner to a variety of quantum systems.

https://arxiv.org/abs/2503.01952 2025-03-03T00:00:00Z 2025-11-01T00:00:00Z Stewart MorawetzAnatoli Polkovnikov

Local counterdiabatic (CD) driving provides a systematic way of constructing a control protocol to approximately suppress the excitations resulting from changing some parameter(s) of a quantum system at a finite rate. However, designing CD protocols typically requires knowledge of the original Hamiltonian a priori. In this work, we design local CD driving protocols in Krylov space using only the characteristic local time scales of the system set by e.g. phonon frequencies in materials or Rabi frequencies in superconducting qubit arrays. Surprisingly, we find that convergence of these universal protocols is controlled by the asymptotic high frequency tails of the response functions. This finding hints at a deep connection between the long-time, low frequency response of the system controlling non-adiabatic effects, and the high-frequency response determined by the short-time operator growth and the Krylov complexity, which has been elusive until now.

https://arxiv.org/abs/2408.06855 2024-08-13T00:00:00Z 2025-04-28T00:00:00Z Ankit GillTapobrata Sarkar

We investigate the relationship between Krylov complexity and operator quantum speed limits (OQSLs) of the complexity operator and level repulsion in random/integrable matrices and many-body systems. An enhanced level-repulsion corresponds to increased OQSLs in random/integrable matrices. However, in many-body systems, the dynamics is more intricate due to the tensor product structure of the models. Initially, as the integrability-breaking parameter increases, the OQSL also increases, suggesting that breaking integrability allows for faster evolution of the complexity operator. At larger values of integrability-breaking, the OQSL decreases, suggesting a slowdown in the operator's evolution speed. Information-theoretic properties, such as scrambling, coherence and entanglement, of Krylov basis operators in many-body systems, are also investigated. The scrambling behaviour of these operators exhibits distinct patterns in integrable and chaotic cases. For systems exhibiting chaotic dynamics, the Krylov basis operators remain a reliable measure of these properties of the time-evolved operator at late times. However, in integrable systems, the Krylov operator's ability to capture the entanglement dynamics is less effective, especially during late times.

https://arxiv.org/abs/2408.00826 2024-08-01T00:00:00Z 2026-01-21T00:00:00Z Rathindra Nath DasTakato Mori

In quantum systems, purification can map mixed states into pure states and a non-unitary evolution into a unitary one by enlarging the Hilbert space. We establish a connection between the complexities of mixed quantum states and their purification, proposing new inequalities among these complexities. By examining single qubits, two-qubit Werner states, eight-dimensional Gaussian random unitary ensembles, and infinite-dimensional systems, we demonstrate how these relationships manifest across a broad class of systems. We find that the spread complexity of purification of a vacuum state evolving into a thermal state equals the average number of Rindler particles. This complexity is also shown to adhere to the Lloyd-like bound, indicating a further relation to the quantum speed limit. Finally, using mutual Krylov complexity, we observe subadditivity of the Krylov complexities, which contrasts with known results from holographic volume complexity. We put forward Krylov mutual complexity as a diagnosis of a potential gravity dual of Krylov complexities.

https://arxiv.org/abs/2405.15609 2024-05-24T00:00:00Z 2024-10-21T00:00:00Z Modesto Orozco-RuizNguyen H. LeFlorian Mintert

We show that combining ideas from the fields of quantum invariants and of optimal control can be used to design optimal quantum control solutions without explicit reference to quantum states. The states are specified only implicitly in terms of operators to which they are eigenstates. The scaling in numerical effort of the resultant approach is not given by the typically exponentially growing effort required for the specification of a time-evolved quantum state, but it is given by the effort required for the specification of a time-evolved operator. For certain Hamiltonians, this effort can be polynomial in the system size. We describe how control problems for state preparation and the realization of propagators can be formulated in this approach, and we provide explicit control solutions for a spin chain with an extended Ising Hamiltonian. The states considered for state-preparation protocols include eigenstates of Hamiltonians with more than pairwise interactions, and these Hamiltonians are also used for the definition of target propagators. The cost of describing suitable time-evolving operators grows only quadratically with the system size, allowing us to construct explicit control solutions for up to 50 spins. While sub-exponential scaling is obtained only in special cases, we provide several examples that demonstrate favourable scaling beyond the extended Ising model.

https://arxiv.org/abs/2405.09628 2024-05-15T00:00:00Z 2025-05-15T00:00:00Z Pratik NandyApollonas S. Matsoukas-RoubeasPablo Martinez-AzconaAnatoly DymarskyAdolfo del Campo

The dynamics of quantum systems unfolds within a subspace of the state space or operator space, known as the Krylov space. This review presents the use of Krylov subspace methods to provide an efficient description of quantum evolution and quantum chaos, with emphasis on nonequilibrium phenomena of many-body systems with a large Hilbert space. It provides a comprehensive update of recent developments, focused on the quantum evolution of operators in the Heisenberg picture as well as pure and mixed states. It further explores the notion of Krylov complexity and associated metrics as tools for quantifying operator growth, their bounds by generalized quantum speed limits, the universal operator growth hypothesis, and its relation to quantum chaos, scrambling, and generalized coherent states. A comparison of several generalizations of the Krylov construction for open quantum systems is presented. A closing discussion addresses the application of Krylov subspace methods in quantum field theory, holography, integrability, quantum control, and quantum computing, as well as current open problems.

https://arxiv.org/abs/2402.01498 2024-02-02T00:00:00Z 2024-02-02T00:00:00Z Michael SchillingFrancesco PretiMatthias M. MüllerTommaso CalarcoFelix Motzoi

The effort to generate matrix exponentials and associated differentials, required to determine the time evolution of quantum systems, frequently constrains the evaluation of problems in quantum control theory, variational circuit compilation, or Monte-Carlo sampling. We introduce two ideas for the time-efficient approximation of matrix exponentials of linear multi-parametric Hamiltonians. We modify the Suzuki-Trotter product formula from an approximation to an interpolation schemes to improve both accuracy and computational time. This allows us to achieve high fidelities within a single interpolation step, which can be computed directly from cached matrices. We furthermore define the interpolation on a grid of system parameters, and show that the infidelity of the interpolation converges with $4^\mathrm{th}$ order in the number of interpolation bins.

https://arxiv.org/abs/2312.01115 2023-12-02T00:00:00Z 2025-12-31T00:00:00Z Taner M. TureSeogjoo J. Jang

Magnus expansion (ME) provides a general way to expand the real-time propagator of a time-dependent Hamiltonian within the exponential such that the unitarity is satisfied at any order. We use this property and explicit integration of Lagrange interpolation formulas for the time-dependent Hamiltonian within each time interval and derive approximations that preserve unitarity for the differential time evolution operators of general time-dependent Hamiltonians. The resulting second-order approximation is the same as using the average of Hamiltonians for two end points of time. We identify three fourth-order approximations involving commutators of Hamiltonians at different times and also derive a sixth-order expression. A test of these approximations along with other available expressions for a two-state time-dependent Hamiltonian with sinusoidal time dependences provides information on the relative performance of these approximations and suggests that the derived expressions can serve as useful numerical tools for time evolution in time-resolved spectroscopy, quantum control, quantum sensing, real-time ab initio quantum dynamics, and open system quantum dynamics.

https://arxiv.org/abs/2308.15100 2023-08-29T00:00:00Z 2023-08-29T00:00:00Z Takuya Hatomura

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.

https://arxiv.org/abs/2306.08613 2023-06-14T00:00:00Z 2024-03-13T00:00:00Z Farhan T. ChowdhuryMatt C. J. DentonDaniel C. BonserDaniel R. Kattnig

We realize arbitrary waveform-based control of spin-selective recombination reactions of radical pairs in the low magnetic field regime. To this end, we extend the Gradient Ascent Pulse Engineering (GRAPE) paradigm to allow for optimizing reaction yields. This overcomes drawbacks of previously suggested time-local optimization approaches for the reaction control of radical pairs, which were limited to high biasing fields. We demonstrate how efficient time-global optimization of the recombination yields can be realized by gradient based methods augmented by time-blocking, sparse sampling of the yield, and evaluation of the central single time-step propagators and their Fréchet derivatives using iterated Trotter-Suzuki splittings. Results are shown for both a toy model, previously used to demonstrate coherent control of radical pair reactions in the simpler high-field scenario, and furthermore for a realistic exciplex-forming donor-acceptor system comprising 16 nuclear spins. This raises prospects for the spin-control of actual radical pair systems in ambient magnetic fields, by suppressing or boosting radical reaction yields using purpose-specific radio-frequency waveforms, paving the way for reaction-yield-dependent quantum magnetometry and potentially applications of quantum control to biochemical radical pair reactions. We demonstrate the latter aspect for two radical pairs implicated in quantum biology.

https://arxiv.org/abs/2304.06200 2023-04-13T00:00:00Z 2023-04-13T00:00:00Z Yunwei LuSandeep JoshiVinh San DinhJens Koch

Gradient Ascent Pulse Engineering (GRAPE) is a popular technique in quantum optimal control, and can be combined with automatic differentiation (AD) to facilitate on-the-fly evaluation of cost-function gradients. We illustrate that the convenience of AD comes at a significant memory cost due to the cumulative storage of a large number of states and propagators. For quantum systems of increasing Hilbert space size, this imposes a significant bottleneck. We revisit the strategy of hard-coding gradients in a scheme that fully avoids propagator storage and significantly reduces memory requirements. Separately, we present improvements to numerical state propagation to enhance runtime performance. We benchmark runtime and memory usage and compare this approach to AD-based implementations, with a focus on pushing towards larger Hilbert space sizes. The results confirm that the AD-free approach facilitates the application of optimal control for large quantum systems which would otherwise be difficult to tackle.

https://arxiv.org/abs/2302.05460 2023-02-10T00:00:00Z 2024-03-07T00:00:00Z Kazutaka TakahashiAdolfo del Campo

Shortcuts to adiabaticity provide fast protocols for quantum state preparation in which the use of auxiliary counterdiabatic controls circumvents the requirement of slow driving in adiabatic strategies. While their development is well established in simple systems, their engineering and implementation are challenging in many-body quantum systems with many degrees of freedom. We show that the equation for the counterdiabatic term, equivalently the adiabatic gauge potential, is solved by introducing a Krylov basis. The Krylov basis spans the minimal operator subspace in which the dynamics unfolds and provides an efficient way to construct the counterdiabatic term. We apply our strategy to paradigmatic single- and many-particle models. The properties of the counterdiabatic term are reflected in the Lanczos coefficients obtained in the course of the construction of the Krylov basis by an algorithmic method. We examine how the expansion in the Krylov basis incorporates many-body interactions in the counterdiabatic term.

https://arxiv.org/abs/2210.11595 2022-10-20T00:00:00Z 2023-06-06T00:00:00Z Daniel PuzzuoliSophia Fuhui LinMoein MalekakhlaghEmily PritchettBenjamin RosandChristopher J. Wood

We develop general purpose algorithms for computing and utilizing both the Dyson series and Magnus expansion, with the goal of facilitating numerical perturbative studies of quantum dynamics. To enable broad applications to models with multiple parameters, we phrase our algorithms in terms of multivariable sensitivity analysis, for either the solution or the time-averaged generator of the evolution over a fixed time-interval. These tools simultaneously compute a collection of terms up to arbitrary order, and are general in the sense that the model can depend on the parameters in an arbitrary time-dependent way. We implement the algorithms in the open source software package \qiskitdynamics{}, utilizing the JAX array library to enable just-in-time compilation, automatic differentiation, and GPU execution of all computations. Using a model of a single transmon, we demonstrate how to use these tools to approximate fidelity in a region of model parameter space, as well as construct perturbative robust control objectives. We also derive and implement Dyson and Magnus-based variations of the recently introduced Dysolve algorithm [Shillito et al., Physical Review Research, 3(3):033266] for simulating linear matrix differential equations. We show how the pre-computation step can be phrased as a multivariable expansion computation problem with fewer terms than in the original method. When simulating a two-transmon entangling gate on a GPU, we find the Dyson and Magnus-based solvers provide a speedup over traditional ODE solvers, ranging from roughly $2\times$ to $4\times$ for a solution and $10\times$ to $60\times$ for a gradient, depending on solution accuracy.

https://arxiv.org/abs/2205.15044 2022-05-27T00:00:00Z 2022-12-01T00:00:00Z Michael H. GoerzSebastian C. CarrascoVladimir S. Malinovsky

We develop a framework of "semi-automatic differentiation" that combines existing gradient-based methods of quantum optimal control with automatic differentiation. The approach allows to optimize practically any computable functional and is implemented in two open source Julia packages, GRAPE.jl and Krotov.jl, part of the QuantumControl.jl framework. Our method is based on formally rewriting the optimization functional in terms of propagated states, overlaps with target states, or quantum gates. An analytical application of the chain rule then allows to separate the time propagation and the evaluation of the functional when calculating the gradient. The former can be evaluated with great efficiency via a modified GRAPE scheme. The latter is evaluated with automatic differentiation, but with a profoundly reduced complexity compared to the time propagation. Thus, our approach eliminates the prohibitive memory and runtime overhead normally associated with automatic differentiation and facilitates further advancement in quantum control by enabling the direct optimization of non-analytic functionals for quantum information and quantum metrology, especially in open quantum systems. We illustrate and benchmark the use of semi-automatic differentiation for the optimization of perfectly entangling quantum gates on superconducting qubits coupled via a shared transmission line. This includes the first direct optimization of the non-analytic gate concurrence.

https://arxiv.org/abs/2205.02520 2022-05-05T00:00:00Z 2022-10-24T00:00:00Z Xiaodong YangXinfang NieYunlan JiTao XinDawei LuJun Li

In designing quantum control, it is generally required to simulate the controlled system evolution with a classical computer. However, computing the time evolution operator can be quite resource-consuming since the total Hamiltonian is often hard to diagonalize. In this paper, we mitigate this issue by substituting the time evolution segments with their Trotter decompositions, which reduces the propagator into a combination of single-qubit operations and fixed-time system evolutions. The resulting procedure can provide substantial speed gain with acceptable costs in the propagator error. As a demonstration, we apply the proposed strategy to improve the efficiency of the gradient ascent pulse engineering algorithm for searching optimal control fields. Furthermore, we show that the higher-order Trotter decompositions can provide efficient Ansätze for the variational quantum algorithm, leading to improved performance in solving the ground-state problem. The strategy presented here is also applicable for many other quantum optimization and simulation tasks.

https://arxiv.org/abs/2110.06187 2021-10-12T00:00:00Z 2022-03-24T00:00:00Z Mogens DalgaardFelix Motzoi

Quantum optimal control theory is becoming increasingly crucial as quantum devices become more precise, but the need to quickly optimize these systems classically remains a significant bottleneck in their operation. Here we present a new theoretical quantum control framework for much faster optimization than the state of the art by replacing standard time propagation with a product of short-time propagators, each calculated using the Magnus expansion. The derived formulas for exact series terms and their gradients, based on earlier approximate integrals in a simulation setting, allow us to subsume the high cost of calculating commutators and integrals as an initial overhead. This provides an order of magnitude speedup for quantum control optimization.