We propose a general, fully gate-based quantum algorithm for counterdiabatic driving. The algorithm does not depend on heuristics as in previous variational methods, and exploits regularisation of the adiabatic gauge potential to suppress only the transitions from the eigenstate of interest. This allows for a rigorous quantum gate complexity upper bound in terms of the minimum gap $Δ$ around this eigenstate. We find that, in the worst case, the algorithm requires at most $\tilde O(Δ^{-(3 + o(1))} ε^{-(1 + o(1))})$ quantum gates to achieve a target state fidelity of at least $1 - ε^2$, where $Δ$ is the minimum spectral gap. In certain cases, the gap dependence can be improved to quadratic.
We study a deformation of the counterdiabatic-driving Hamiltonian as a systematic strategy for an adiabatic control of quantum states. Using a unitary transformation, we design a convenient form of the driver Hamiltonian. We apply the method to a particle in a confining potential and discrete systems to find explicit forms of the Hamiltonian and discuss the general properties. The method is derived by using the quantum brachistochrone equation, which shows the existence of a nontrivial dynamical invariant in the deformed system.
Approximate counterdiabatic (CD) protocols are a powerful tool to enhance quantum adiabatic processes that allow to reliably manipulate quantum systems on short time scales. However, implementing CD protocols entails the introduction of additional control fields in the Hamiltonian, often associated with highly non-local multi-body interactions. Here, we introduce a novel variational rotated ansatz (RA) to systematically generate experimentally accessible approximate CD protocols. We numerically benchmark our approach on state preparation and adiabatic quantum computing algorithms, and find tha…
Universal speeded-up adiabatic geometric quantum computation~(SAGQC) is studied in $Λ$-type three-level system with different coupling cases, i.e., time-dependent detuning, large detuning and one-photon resonance couplings, respectively. In these cases, the counterdiabatic driving method is used to speed up the universal quantum computation. These schemes in $Λ$-type three-level system are feasible in experiment because additional unaccessible ground-state-coupling is not needed. Only the shapes and phases of the initial adiabatic classical-field pulse are modified with the aid of effective tw…
Finding the exact counterdiabatic potential is, in principle, particularly demanding. Following recent progresses about variational strategies to approximate the counterdiabatic operator, in this paper we apply this technique to the quantum annealing of the $p$-spin model. In particular, for $ p = 3 $ we find a new form of the counterdiabatic potential originating from a cyclic ansatz, that allows us to have optimal fidelity even for extremely short dynamics, independently of the size of the system. We compare our results with a nested commutator ansatz, recently proposed in P. W. Claeys, M. P…
We propose an efficientmethod to construct shortcuts to adiabaticity through designing a substitute Hamiltonian to try to avoid the defect in which the speed-up protocol' Hamiltonian may involve terms which are difficult to realize in practice. We show that as long as the counterdiabatic coupling terms-even only some of them-have been nullified by the additional Hamiltonian, the corresponding shortcuts to the adiabatic process could be constructed and the adiabatic process would be sped up. As an application example, we apply this method to the popular Landau-Zener model for the realization of…
Quantum coherence and counterdiabatic quantum computing
Facultad de Ciencias, Universidad Nacional Autónoma de México (UNAM)（墨西哥国立自治大学）；Departamento de Física, Universidad de Santiago de Chile (USACH)（智利圣地亚哥大学）；Kipu Quantum（Kipu量子）；Universidad Diego Portales（迭戈·波特莱斯大学）
A method is presented to transfer a system of two-level atoms from a spin coherent state to a maximally spin squeezed Dicke state, relevant for quantum metrology and quantum information processing. The initial state is the ground state of an initial linear Hamiltonian which is gradually turned into a final quadratic Hamiltonian whose ground state is the selected Dicke state. We use compensating operators to suppress diabatic transitions to unwanted states that would occur if the change were not slow. We discuss the possibilities of constructing the compensating operators by sequential applicat…
A scheme for arbitrary quantum state engineering (QSE) in three-state systems is proposed. Firstly, starting from a set of complete orthogonal time-dependent basis with undetermined coefficients, a time-dependent Hamiltonian is derived via Counterdiabatic driving for the purpose of guiding the system to attain an arbitrary target state at a predefined time. Then, on request of the assumed target states, two single-mode driving protocols and a multi-mode driving protocol are proposed as examples to discuss the validity of the QSE scheme. The result of comparison between single-mode driving and …
Counterdiabatic Driving under Variational Frame Dressing
Forschungszentrum Jülich, Institute of Quantum Control (PGI-8)（于利希研究中心，量子控制研究所）；Theoretical Quantum Physics Laboratory, Cluster for Pioneering Research, RIKEN（理化学研究所，先锋研究集群，理论量子物理实验室）；Quantum Information Physics Theory Research Team, Quantum Computing Center, RIKEN（理化学研究所，量子计算中心，量子信息物理理论研究组）；Physics Department, The University of Michigan（密歇根大学，物理系）；Institute for Theoretical Physics, University of Cologne（科隆大学，理论物理研究所）
The application of adiabatic protocols in quantum technologies is severely limited by environmental sources of noise and decoherence. Shortcuts to adiabaticity by counterdiabatic driving constitute a powerful alternative that speed up time-evolution while mimicking adiabatic dynamics. Here we present the first experimental implementation of counterdiabatic driving in a continuous variable system, a shortcut to the adiabatic transport of a trapped ion in the phase space. The resulting dynamics is equivalent to a "fast-motion video" of the adiabatic trajectory. The robustness of this protocol is…
Counterdiabatic driving (CD) exploits auxiliary control fields to tailor the nonequilibrium dynamics of a quantum system, making possible the suppression of dissipated work in finite-time thermodynamics and the engineering of optimal thermal machines with no friction. We show that while the mean work done by the auxiliary controls vanishes, CD leads to a broadening of the work distribution. We derive a fundamental inequality that relates nonequilibrium work fluctuations to the operation time and quantifies the thermodynamic cost of CD in both critical and noncritical systems.
The system undergoes adiabatic evolution when its population in the instantaneous eigenbasis of its time-dependent Hamiltonian changes only negligibly. Realization of such dynamics requires slow-enough changes of the parameters of the Hamiltonian, a task that can be hard to achieve near quantum critical points. A powerful alternative is provided by the counterdiabatic modification of the Hamiltonian allowing for an arbitrarily quick implementation of the adiabatic dynamics. Such a counterdiabatic driving protocol has been recently proposed for the quantum Ising model [A. del Campo et al., Phys…
We present Counterdiabatic Reverse Annealing, a novel quantum annealing protocol that extends the range of application of reverse annealing to the previously inaccessible short-time domain. This is achieved by exploiting approximate counterdiabatic driving expanded in low-order nested commutators. In this work, we offer a comparative study of the performance of this new technique to that of unassisted reverse annealing in terms of metrics such as the ground-state fidelity and the time to solution. We provide a quantitative measure of the energetic cost of counterdiabatic reverse annealing and …
TECNALIA, Basque Research and Technology Alliance (BRTA)（泰克纳利亚，巴斯克研究与技术联盟）；University of the Basque Country UPV/EHU（巴斯克大学）；Forschungszentrum Jülich（于利希研究中心）；Institute for Theoretical Physics, University of Cologne（科隆大学理论物理研究所）；CSIC（西班牙国家研究委员会）；Instituto de Ciencia de Materiales de Madrid (ICMM), CSIC（马德里材料科学研究所）
We discuss dynamics of periodically-driven open quantum systems. The time evolution of the quantum state is described by the quantum master equation and the form of the dissipator is chosen so that the instantaneous stationary state is given by the Gibbs distribution. We find that the correlation between the population part and the coherence part of the density operator is induced by an adiabatic gauge potential. Although the introduction of the counterdiabatic term eliminates the correlation, additional correlations prevent a convergence to the Gibbs distribution. We study the performance of …
Measurement-free Preparation of Surface-Code States with Digital-Analog Counterdiabatic Drivings
Intelligent Data Analysis Laboratory (IDAL), Departament d’Enginyeria Electrònica, ETSE-UV, Universitat de València（瓦伦西亚大学电子工程系智能数据分析实验室）；Kipu Quantum（基普量子）
Unitary processes allow for the transfer of work to and from Hamiltonian systems. However, to achieve nonzero power for the practical extraction of work, these processes must be performed within a finite time, which inevitably induces excitations in the system. We show that depending on the time scale of the process and the physical realization of the external driving employed, the use of counterdiabatic quantum driving to extract more work is not always effective. We also show that by virtue of the two-time energy measurement definition of quantum work, the cost of counterdiabatic driving can…
Symmetric $C_Z$ gate for ultracold neutral atoms based on counterdiabatic driving at Rydberg excitation
Rzhanov Institute of Semiconductor Physics SB RAS（拉扎诺夫半导体物理研究所西伯利亚分院）；Novosibirsk State University（新西伯利亚国立大学）；Novosibirsk State Technical University（新西伯利亚国立技术大学）；Institute of Laser Physics SB RAS（激光物理研究所西伯利亚分院）；Division of Precision Measurement Physics, Wuhan Institute of Physics and Mathematics, Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences（中国科学院精密测量科学与技术创新研究院武汉物理与数学研究所精密测量物理研究室）
Counterdiabatic (CD) protocols enable fast driving of quantum states by invoking an auxiliary adiabatic gauge potential (AGP) that suppresses transitions to excited states throughout the driving process. Usually, the full spectrum of the original unassisted Hamiltonian is a prerequisite for constructing the exact AGP, which implies that CD protocols are extremely difficult for many-body systems. Here, we apply a variational CD protocol recently proposed by P. W. Claeys et al. [Phys. Rev. Lett. 123, 090602 (2019)] to a two-component fermionic Hubbard model in one spatial dimension. This protoco…
We introduce a shortcut to the adiabatic gate teleportation model of quantum computation. More specifically, we determine fast local counterdiabatic Hamiltonians able to implement teleportation as a universal computational primitive. In this scenario, we provide the counterdiabatic driving for arbitrary n-qubit gates, which allows to achieve universality through a variety of gate sets. Remarkably, our approach maps the superadiabatic Hamiltonian for an arbitrary n-qubit gate teleportation into the implementation of a rotated superadiabatic dynamics of an n-qubit state teleportation. This resul…
The quantum approximate optimization algorithm (QAOA) has proved to be an effective classical-quantum algorithm serving multiple purposes, from solving combinatorial optimization problems to finding the ground state of many-body quantum systems. Since QAOA is an ansatz-dependent algorithm, there is always a need to design ansatz for better optimization. To this end, we propose a digitized version of QAOA enhanced via the use of shortcuts to adiabaticity. Specifically, we use a counterdiabatic (CD) driving term to design a better ansatz, along with the Hamiltonian and mixing terms, enhancing th…
Adiabatic protocols are employed across a variety of quantum technologies, from implementing state preparation and individual operations that are building blocks of larger devices, to higher-level protocols in quantum annealing and adiabatic quantum computation. The problem of speeding up these processes has garnered a large amount of interest, resulting in a menagerie of approaches, most notably quantum optimal control and shortcuts to adiabaticity. The two approaches are complementary: optimal control manipulates control fields to steer the dynamics in the minimum allowed time while shortcut…
Weighted Nested Commutators for Scalable Counterdiabatic State Preparation
Instituto de Ciencia de Materiales de Madrid ICMM-CSIC（马德里材料科学研究所）；Departamento de Física Teórica de la Materia Condensada, Universidad Autónoma de Madrid（马德里自治大学凝聚态物理理论系）；Joint Quantum Institute and Joint Center for Quantum Information and Computer Science, NIST/University of Maryland（马里兰大学/美国国家标准与技术研究院联合量子研究所和联合量子信息与计算科学中心）
Coherent control of complex many-body systems is critical to the development of useful quantum devices. Fast perfect state transfer can be exactly achieved through additional counterdiabatic fields. We show that the additional energetic overhead associated with implementing counterdiabatic driving can be reduced while still maintaining high target state fidelities. This is achieved by implementing control fields only during the impulse regime, as identified by the Kibble-Zurek mechanism. We demonstrate that this strategy successfully suppresses most of the defects that would be generated due t…
Fighting Exponentially Small Gaps by Counterdiabatic Driving
University of Luxembourg（卢森堡大学）；Max Planck Institute for the Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）；Donostia International Physics Center（圣塞巴斯蒂安国际物理中心）
Utilizing counterdiabatic (CD) driving - aiming at suppression of diabatic transition - in digitized adiabatic evolution have garnered immense interest in quantum protocols and algorithms. However, improving the approximate CD terms with a nested commutator ansatz is a challenging task. In this work, we propose a technique of finding optimal coefficients of the CD terms using a variational quantum circuit. By classical optimizations routines, the parameters of this circuit are optimized to provide the coefficients corresponding to the CD terms. Then their improved performance is exemplified in…
Counterdiabatic (CD) driving presents a way of generating adiabatic dynamics at arbitrary pace, where excitations due to non-adiabaticity are exactly compensated by adding an auxiliary driving term to the Hamiltonian. While this CD term is theoretically known and given by the adiabatic gauge potential, obtaining and implementing this potential in many-body systems is a formidable task, requiring knowledge of the spectral properties of the instantaneous Hamiltonians and control of highly nonlocal multibody interactions. We show how an approximate gauge potential can be systematically built up a…
