Structured decompositions of a desired unitary operator are employed to derive control schemes that achieve certain control objectives for finite-level quantum systems using only sequences of simple control pulses such as square waves with finite rise and decay times or Gaussian wavepackets. The technique is applied to find control schemes that achieve population transfers for pure-state systems, complete inversions of the ensemble populations for mixed-state systems, create arbitrary superposition states and optimize the ensemble average of observables.
We study the emission spectrum and absorption spectrum of a quantum emitter when it is driven by various pulse sequences. We consider the Uhrig sequence of $π_x$ pulses, the periodic sequence of $π_xπ_y$ pulses and the periodic sequence of $π_z$ pulses (phase kicks). We find that, similar to the periodic sequence of $π_x$ pulses, the Uhrig sequence of $π_x$ pulses has emission and absorption that are, with small variations, analogous to those of the resonance fluorescence spectrum. In addition, while the periodic sequence of $π_z$ pulses produces a spectrum that is dependent on the detuning be…
We present three classes of symmetric broadband composite pulse sequences. The composite phases are given by analytic formulas (rational fractions of $π$) valid for any number of constituent pulses. The transition probability is expressed by simple analytic formulas and the order of pulse area error compensation grows linearly with the number of pulses. Therefore, any desired compensation order can be produced by an appropriate composite sequence; in this sense, they are arbitrarily accurate. These composite pulses perform equally well or better than previously published ones. Moreover, the cu…
We introduce universally robust sequences for dynamical decoupling, which simultaneously compensate pulse imperfections and the detrimental effect of a dephasing environment to an arbitrary order, work with any pulse shape, and improve performance for any initial condition. Moreover, the number of pulses in a sequence grows only linearly with the order of error compensation. Our sequences outperform the state-of-the-art robust sequences for dynamical decoupling. Beyond the theoretical proposal, we also present convincing experimental data for dynamical decoupling of atomic coherences in a soli…
A general approach is introduced for the efficient simultaneous optimization of pulses that compensate each other' s imperfections within the same scan. This is applied to broadband Ramsey-type experiments, resulting in pulses with significantly shorter duration compared to individually optimized broadband pulses. The advantage of the cooperative pulse approach is demonstrated experimentally for the case of two-dimensional nuclear Overhauser enhancement spectroscopy. In addition to the general approach, a symmetry-adapted analysis of the optimization of Ramsey sequences is presented. Furthermo…
We investigate the nature of the pulse sequence so that unwanted transitions in quantum systems can be inhibited optimally. For this purpose we show that the sequence of pulses proposed by Uhrig [Phys. Rev. Lett. \textbf{98}, 100504 (2007)] in the context of inhibition of environmental dephasing effects is optimal. We derive exact results for inhibiting the transitions and confirm the results numerically. We posit a very significant improvement by usage of the Uhrig sequence over an equidistant sequence in decoupling a quantum system from unwanted transitions. The physics of inhibition is the …
The control of qubit states is often impeded by systematic control errors. Compensating pulse sequences have emerged as a resource efficient method for quantum error reduction. In this review, we discuss compensating composite pulse methods, and introduce a unifying control-theoretic framework using a dynamic interaction picture. This admits a novel geometric picture where sequences are interpreted as vector paths on the dynamical Lie algebra. Sequences for single-qubit and multi-qubit operations are described with this method.
We propose various composite $π$-pulse sequences for implementing robust z-axis rotation gates widely used in quantum information processing (QIP) scenarios, and discuss their error tolerance of the pulse strength error (PSE) and off-resonance error (ORE), i.e., two typical systematic errors in NMR systems. Compared to existing composite gates, our designed composite pulses exhibit higher gate fidelity and shorter sequence time cost. Furthermore, such short pulse sequences are generalized by simple analytic formulas which can suppress these errors to any desired order simultaneously with linea…
Dynamical decoupling has been actively investigated since Viola first suggested using a pulse sequence to protect a qubit from decoherence. Since then, many schemes of dynamical decoupling have been proposed to achieve high-order suppression, both analytically and numerically. However, hitherto, there has not been a systematic framework to understand all existing uniform $π$-pulse dynamical decoupling schemes. In this report, we use the projection pulse sequences as basic building blocks and concatenation as a way to combine them. We derived a new concatenated-projection dynamical decoupling (…
We examine the question of survival of quantum entanglement between the bipartite states and multiparticle states like GHZ states under the action of a dephasing bath by the application of sequence of $π$ pulses. We show the great advantage of the pulse sequence of Uhrig [ 2007 {\it Phys. Rev. Lett.} {\bf 98} 100504] applied at irregular intervals of time, in controlling quantum entanglement. In particular death of entanglement could be considerably delayed by pulses. We use quantum optical techniques to obtain exact results.
Composite pulse sequences, which produce arbitrary pre-defined rotations of a two-state system at an angle $θ$ on the Bloch sphere, are presented. The composite sequences can contain arbitrarily many pulses and can compensate experimental errors in the pulse amplitude and duration to any desired order. A special attention is devoted to two classes of $π/2$ sequences --- symmetric and asymmetric --- the phases of which are given by simple formulas in terms of rational multiples of $π$ for any number of constituent pulses. This allows one to construct arbitrarily accurate $π/2$ composite rotatio…
Programmable arrays of hundreds of Rydberg atoms have recently enabled the exploration of remarkable phenomena in many-body quantum physics. In addition, the development of high-fidelity quantum gates are making them promising architectures for the implementation of quantum circuits. We present here \textit{Pulser}, an open-source Python library for programming neutral-atom devices at the pulse level. The low-level nature of Pulser makes it a versatile framework for quantum control both in the digital and analog settings. The library also contains simulation routines for studying and exploring…
We propose a new pulse sequence for dynamical averaging of the dipole-dipole interactions and inhomogeneities of the magnetic fields in the nuclear spin system. The sequence contains a short cycle of the periodic resonant pulse excitation that offers new possibilities for implementing the long-lived multi-qubit quantum memory on the condensed spin ensembles that are so important for construction of universal quantum computer and long-distance quantum communications.
A general coherent control scenario to suppress, or accelerate, tunneling of quantum states decaying into a continuum, is investigated. The method is based on deterministic, or stochastic, sequences of unitary pulses that affect the underlying interference phenomena responsible for quantum dynamics, without inducing decoherence, or collapsing the coherent evolution of the system. The influence of control sequences on the ensuing quantum dynamics is analyzed by using perturbation theory to first order in the control pulse fields and compared to dynamical decoupling (DD) protocols and sequences …
Composite pulses --- sequences of pulses with well defined relative phases --- are an efficient, robust and flexible technique for coherent control of quantum systems. Composite sequences can compensate a variety of experimental errors in the driving field (e.g. in the pulse amplitude, duration, detuning, chirp, etc.) or in the quantum system and its environment (e.g. inhomogeneous broadening, stray electric or magnetic fields, unwanted couplings, etc.). The control parameters are the relative phases between the constituent pulses in the composite sequence, an accurate control over which is re…
The pulse control of decoherence in a qubit interacting with a quantum environment is studied with focus on a general case where decoherence is induced by both pure dephasing and population decay. To observe how the decoherence is suppressed by periodic pi pulses, we present a simple method to calculate the time evolution of a qubit under arbitrary pulse sequences consisting of bit-flips and/or phase-flips. We examine the effectiveness of the two typical sequences: bb sequence consisting of only bit-flips, and bp sequence consisting of both bit- and phase-flips. It is shown that the effectiven…
We show how to create quantum gates of arbitrary speed between trapped ions, using a laser walking wave, with complete insensitivity to drift of the optical phase, and requiring cooling only to the Lamb-Dicke regime. We present pulse sequences that satisfy the requirements and are easy to produce in the laboratory.
The amplitude and probability of quantum transitions are represented as a path integrals in energy state space of the investigated multi-level quantum system. Using this approach we consider rotational dynamics of nitrogen molecules $^{14}N_{2}$ and $^{15}N_{2}$ which interact with a sequence of ultrashort laser pulses. Our computer simulations indicate the complex dependency of the high rotation states excitation probability upon ultrashort laser pulses sequence periods. We observe pronounced resonances, which correspond to the results of some experiments.
We demonstrate how NMR can in principle be used to implement all the elements required to build quantum computers, and briefly discuss the potential applications of insights from quantum logic to the development of novel pulse sequences with applications in more conventional NMR experiments.
Loss-aware pulse sequence optimization for generating photonic Fock states
Friedrich Schiller University Jena（耶拿弗里德里希·席勒大学）；Paderborn University（帕德博恩大学）；Fraunhofer Institute for Applied Optics and Precision Engineering IOF（弗劳恩霍夫应用光学和精密工程研究所 IOF）；Institute for Photonic Quantum Systems (PhoQS)（光子量子系统研究所 (PhoQS)）
Composite pulse sequences, which produce arbitrary pre-defined rotations of a qubit on the Bloch sphere, are presented. The composite sequences contain up to 17 pulses and can compensate up to eight orders of experimental errors in the pulse amplitude and the pulse duration. Composite sequences for three basic quantum gates -- X (NOT), Hadamard and arbitrary rotation -- are derived. Three classes of composite sequences are presented -- one symmetric and two asymmetric. They contain as their lowest members two well-known composite sequences -- the three-pulse symmetric SCROFULOUS pulse and the …
Coherent control of two-state systems is traditionally achieved by resonant pulses of specific Rabi frequency and duration, by adiabatic techniques using level crossings or delayed pulses, or by sequences of pulses with precise relative phases (composite pulses). Here we develop a method for high-fidelity coherent control which uses a sequence of detuning pulses. By using the detuning pulse areas as control parameters, and driving on an analogy with composite pulses, we report a great variety of detuning pulse sequences for broadband and narrowband transition probability profiles.
We propose a selective dynamical decoupling scheme on a chain of permanently coupled qubits with XX type interactions, which is capable of dynamically suppressing any coupling in the chain by applying sequences of local pulses to the individual qubits. We demonstrate that high-fidelity single- and two-qubit gates can be achieved by this procedure and that sequences of gates can be implemented by this pulse control alone. We discuss the applicability and physical limitations of our model specifically for strongly coupled superconducting flux qubits. Since dynamically modifying the couplings bet…
Implementing a single qubit unitary is often hampered by imperfect control. Systematic amplitude errors $ε$, caused by incorrect duration or strength of a pulse, are an especially common problem. But a sequence of imperfect pulses can provide a better implementation of a desired operation, as compared to a single primitive pulse. We find optimal pulse sequences consisting of $L$ primitive $π$ or $2π$ rotations that suppress such errors to arbitrary order $\mathcal{O}(ε^{n})$ on arbitrary initial states. Optimality is demonstrated by proving an $L=\mathcal{O}(n)$ lower bound and saturating it w…
The hardware overhead associated with microwave control is a major obstacle to scale-up of superconducting quantum computing. An alternative approach involves irradiation of the qubits with trains of Single Flux Quantum (SFQ) pulses, pulses of voltage whose time integral is precisely equal to the superconducting flux quantum. Here we describe the derivation and validation of compact SFQ pulse sequences in which classical bits are clocked to the qubit at a frequency that is roughly a factor 5 higher than the qubit oscillation frequency, allowing for variable pulse-to-pulse timing. The control s…
We present two methods for efficient detection of chiral molecules based on sequences of single pulses and Raman pulse pairs. The chiral molecules are modelled by a closed-loop three-state system with different signs in one of the couplings for the two enantiomers. One method uses a sequence of three interaction steps: a single pulse, a Raman pulse, and another single pulse. The other method uses a sequence of only two interaction steps: a Raman pulse, and a single pulse. The second method is simpler and faster but requires a more sophisticated Raman pulse than the first one. Both techniques a…
Dynamical decoupling sequences with multiple pulses can be considered to exhibit filter functions for the time evolution of a qubit superposition state. They contribute to the improvement of coherence time and qubit-phase accumulation due to a time-varying field and can thus achieve high-frequency-resolution spectroscopy. Such behaviors find useful application in highly sensitive detection based on qubits for various external fields such as a magnetic field. Hence, decoupling sequences are indispensable tools for quantum sensing. In this study, we experimentally and theoretically investigated …
We introduce flexible high-fidelity passband (PB) composite pulse sequences constructed by concatenation of recently derived arbitrarily large and arbitrarily accurate broadband $\mathcal{B}$ and narrowband $\mathcal{N}$ composite sequences. Our PB sequences allow to produce flexible and tunable nearly rectangular two-state inversion profiles as a function of the individual pulse area because the width and the rectangularity of these profiles can be adjusted at will. Moreover, these PB sequences suppress excitation around pulse area $0$ and $2π$, and suppress deviations from complete populatio…
We present a genetic algorithm for finding a set of pulse sequences, or rotations, for a given quantum logic gate, as implemented by NMR. We demonstrate the utility of the method by showing that shorter sequences than have been previously published can be found for both a CNOT and for the central part of Shor's algorithm (for N=15.) Artificial intelligence techniques like the genetic algorithm here presented have an enormous potential for simplifying the implementation of working quantum computers.
Composite pulse sequences designed for nuclear magnetic resonance experiments are currently being applied in many quantum information processing technologies.We present an analysis of a family of composite pulse sequences used to address systematic pulse-length errors in the execution of quantum gates. It has been demonstrated by Cummins et al. [Phys. Rev. A 67, 042308 (2003)] that for this family of composite pulse sequences, the fidelity of the resulting unitary operation compared with the ideal unitary operation is 1+C*epsilon^6, where epsilon is the fractional error in the length of the pu…
We propose a new protocol to implement ultra-fast two-qubit phase gates with trapped ions using spin-dependent kicks induced by resonant transitions. By only optimizing the allocation of the arrival times in a pulse train sequence the gate is implemented in times faster than the trapping oscillation period $T<2π/ω$. Such gates allow us to increase the number of gate operations that can be completed within the coherence time of the ion-qubits favoring the development of scalable quantum computers.
For a generic dynamical decoupling sequence employing a single-axis control, we study its efficiency in the presence of small errors in direction of the controlling-pulses. In the case that the corresponding ideal dynamical-decoupling sequence produces good results, the impact of the errors is found to scale as $ξ^2$, with negligible first-order effect, where $ξ$ is the dispersion of the random errors. This analytical prediction is numerically tested in a model, in which the environment is modeled by one qubit coupled to a quantum kicked rotator in chaotic motion. In this model, with periodic …
We develop a new class of genetic algorithm that computationally determines efficient pulse sequences to implement a quantum gate U in a three-qubit system. The method is shown to be quite general, and the same algorithm can be used to derive efficient sequences for a variety of target matrices. We demonstrate this by implementing the inversion-on-equality gate efficiently when the spin-spin coupling constants $J_{12}=J_{23}=J$ and $J_{13}=0$. We also propose new pulse sequences to implement the Parity gate and Fanout gate, which are about 50% more efficient than the previous best efforts. Mor…
The vast research conducted on Nitrogen-Vacancy (NV) centers in diamond in recent years opened the door for a wide range of NV based applications. However, some properties of the NV center dynamics and energy levels remain unknown. In this work, we propose a charge conversion pulsed sequence scheme for locating the NV center singlet manifold energy level, by multi-color excitation using a tunable laser. We present two approaches for readout - photo-induced current and NV$^0$ population - and discuss their efficiency for different regimes in the relevant spectrum.
We consider the effect of broadband decoherence on the performance of refocusing sequences, having in mind applications of dynamical decoupling in concatenation with quantum error correcting codes as the first stage of coherence protection. Specifically, we construct cumulant expansions of effective decoherence operators for a qubit driven by a pulse of a generic symmetric shape, and for several sequences of $π$- and $π/2$-pulses. While, in general, the performance of soft pulses in decoupling sequences in the presence of Markovian decoherence is worse than that of the ideal $δ$-pulses, it can…
A vital requirement for a quantum computer is the ability to locally address, with high fidelity, any of its qubits without affecting their neighbors. We propose an addressing method using composite sequences of laser pulses, which reduces dramatically the addressing error in a lattice of closely spaced atoms or ions, and at the same time significantly enhances the robustness of qubit manipulations. To this end, we design novel high-fidelity composite pulses for the most important single-qubit operations. In principle, this method allows one to beat the diffraction limit, for only atoms situat…
We show that the addition of correlated phases to the recently developed method of randomized dynamical decoupling pulse sequences [Physical Review Letters 122, 200403 (2019)] can improve its performance in quantum sensing. In particular, by correlating the relative phases of basic pulse units in dynamical decoupling sequences, we are able to improve the suppression of the signal distortion due to $π$ pulse imperfections and spurious responses due to finite-width $π$ pulses. This enhances selectivity of quantum sensors such as those based on NV centers in diamond.
We propose a scheme for sensing of an oscillating field in systems with large inhomogeneous broadening and driving field variation by applying sequences of phased, adiabatic, chirped pulses. The latter act as a double filter for dynamical decoupling, where the adiabatic changes of the mixing angle during the pulses rectify the signal and partially remove frequency noise. The sudden changes between the pulses act as instantaneous $π$ pulses in the adiabatic basis for additional noise suppression. We also use the pulses' phases to correct for other errors, e.g., due to non-adiabatic couplings. O…
We investigate the rephasing efficiency of sequences of phased pulses for spin echoes and light storage by electromagnetically induced transparency (EIT). We derive a simple theoretical model and show that the rephasing efficiency is very sensitive to the phases of the imperfect rephasing pulses. The obtained efficiency differs substantially for spin echoes and EIT light storage, which is due to the spatially retarded coherence phases after EIT light storage. Similar behavior is also expected for other light-storage protocols with spatial retardation or for rephasing of collective quantum stat…
The aim of dynamical decoupling consists in the suppression of decoherence by appropriate coherent control of a quantum register. Effectively, the interaction with the environment is reduced. In particular, a sequence of $π$ pulses is considered. Here we present exact results on the suppression of the coupling of a quantum bit to its environment by optimized sequences of $π$ pulses. The effect of various cutoffs of the spectral density of the environment is investigated. As a result we show that the harder the cutoff is the better an optimized pulse sequence can deal with it. For cutoffs which…
The performance of sequences of designed pulses of finite length $τ$ is analyzed for a bath of spins and it is compared with that of sequences of ideal, instantaneous pulses. The degree of the design of the pulse strongly affects the performance of the sequences. Non-equidistant, adapted sequences of pulses, which equal instantaneous ones up to $\mathcal{O}(τ^3)$, outperform equidistant or concatenated sequences. Moreover, they do so at low energy cost which grows only logarithmically with the number of pulses, in contrast to standard pulses with linear growth.
We present experimental measurements on a model quantum system that demonstrate our ability to dramatically suppress qubit error rates by the application of optimized dynamical decoupling pulse sequences in a variety of experimentally relevant noise environments. We provide the first demonstration of an analytically derived pulse sequence developed by Uhrig, and find novel sequences through active, real-time experimental feedback. These new sequences are specially tailored to maximize error suppression without the need for a priori knowledge of the ambient noise environment. We compare these s…
One of the most significant hurdles to be overcome on the path to practical quantum information processors is dealing with quantum errors. Dynamical decoupling is a particularly promising approach that complements conventional quantum error correction by eliminating some correlated errors without the overhead of additional qubits. In practice, the control pulses used for decoupling are imperfect and thus introduce errors which can accumulate after many pulses. These instrumental errors can destroy the quantum state. Here we examine several dynamical decoupling sequences, and their concatenated…
We study how to simulate, efficiently, pulse field gradients (PFG) used in nuclear magnetic resonance (NMR). An efficient simulation requires discretization in time and space. We study both discretizations and provide a guideline to choose best discretization values depending on the precision required experimentally. We provide a theoretical study and simulation showing the minimum number of divisions we need in space for simulating, with high precision, a sequence composed of several unitary evolution and PFG. We show that the fast simulation of PFG allow us to optimize sequences composed of …
The Hamiltonian control of n qubits requires precision control of both the strength and timing of interactions. Compensation pulses relax the precision requirements by reducing unknown but systematic errors. Using composite pulse techniques designed for single qubits, we show that systematic errors for n qubit systems can be corrected to arbitrary accuracy given either two non-commuting control Hamiltonians with identical systematic errors or one error-free control Hamiltonian. We also examine composite pulses in the context of quantum computers controlled by two-qubit interactions. For quantu…
Nowadays most of superconducting quantum processors use charge qubits of a transmon type. They require implementation of energy efficient qubit state control scheme. A promising approach is the use of superconducting digital circuits operating with single-flux-quantum (SFQ) pulses. The duration of SFQ pulse control sequence is typically larger than that of conventional microwave drive pulses but its length can be optimized for the system with known parameters. Here we introduce a genetic algorithm for unipolar or bipolar SFQ control sequence search that minimize qubit state leakage from the co…
We study multiple-spin coherence transfers in linear Ising spin chains with nearest neighbor couplings. These constitute a model for efficient information transfers in future quantum computing devices and for many multi-dimensional experiments for the assignment of complex spectra in nuclear magnetic resonance spectroscopy. We complement prior analytic techniques for multiple-spin coherence transfers with a systematic numerical study where we obtain strong evidence that a certain analytically-motivated family of restricted controls is sufficient for time-optimality. In the case of a linear thr…
Dynamical decoupling (DD) is a technique for preserving the coherence of quantum mechanical states in the presence of a noisy environment. It uses sequences of inversion pulses to suppress the environmental perturbations by periodically refocusing them. It has been shown that different sequences of inversion pulses show vastly different performance, in particular also concerning the correction of experimental pulse imperfections. Here, we investigate specifically the role of time-reversal symmetry in the building-blocks of the pulse sequence. We show that using time symmetric building blocks o…
Dynamical decoupling (DD) is a promising tool for preserving the quantum states of qubits. However, small imperfections in the control pulses can seriously affect the fidelity of decoupling, and qualitatively change the evolution of the controlled system at long times. Using both analytical and numerical tools, we theoretically investigate the effect of the pulse errors accumulation for two aperiodic DD sequences, the Uhrig's DD UDD) protocol [G. S. Uhrig, Phys. Rev. Lett. {\bf 98}, 100504 (2007)], and the Quadratic DD (QDD) protocol [J. R. West, B. H. Fong and D. A. Lidar, Phys. Rev. Lett {\b…
We propose and demonstrate a quantum control scheme for hybrid quantum registers that can reduce the operation time, and therefore the effects of relaxation, compared to existing implementations. It combines resonant excitation pulses with periods of free precession under the internal Hamiltonian of the qubit system. We use this scheme to implement quantum gates like controlled-NOT operations on electronic and nuclear spins of the nitrogen-vacancy center in diamond. As a specific application, we transfer population between electronic and nuclear spin qubits and use it to measure the Rabi oscil…
We minimize the stray electric field in a linear Paul trap quickly and accurately, by applying interferometry pulse sequences to a trapped ion optical qubit. The interferometry sequences are sensitive to the change of ion equilibrium position when the trap stiffness is changed, and we use this to determine the stray electric field. The simplest pulse sequence is a two-pulse Ramsey sequence, and longer sequences with multiple pulses offer a higher precision. The methods allow the stray field strength to be minimized beyond state-of-the-art levels, with only modest experimental requirements. Usi…
Composite pulses are an efficient tool for robust quantum control. In this work, we derive the form of the composite pulse sequence to implement robust single-qubit gates in a three-level system, where two low-energy levels act as a qubit. The composite pulses can efficiently cancel the systematic errors up to a certain order. We find that the three-pulse sequence cannot completely eliminate the first order of systematic errors, but still availably makes the fidelity resistant to variations in a specific direction. When employing more pulses in the sequence ($N>3$), the fidelity can be insensi…
We consider the problem of pulsed biexciton preparation in a quantum dot and show that a pulse-sequence with a simple on-off-on modulation can achieve complete preparation of the target state faster than the commonly used constant and hyperbolic secant pulses. The durations of the pulses composing the sequence are obtained from the solution of a transcendental equation. Furthermore, using numerical optimal control, we demonstrate that for a wide range of values of the maximum pulse amplitude, the proposed pulse-sequence prepares the biexciton state in the numerically obtained minimum time, for…
We investigate the prospects of creating broad rotational wave packets by means of molecular interaction with long sequences of intense femtosecond pulses. Using state-resolved rotational Raman spectroscopy of oxygen, subject to a sequence of more than 20 laser pulses with peak intensities exceeding $10^{13}$ W/cm$^{2}$ per pulse, we show that the centrifugal distortion is the main obstacle on the way to reaching high rotational states. We demonstrate that the timing of the pulses can be optimized to partially mitigate the centrifugal limit. The cumulative effect of a long pulse sequence resul…
