We examine the adiabatic dynamics of a quantum system coupled to a noisy classical control field. A stochastic phase shift is shown to arise in the off-diagonal elements of the system's density matrix which can cause decoherence. We derive the condition for onset of decoherence, and identify the noise properties that drive decoherence. We show how this decoherence mechansim causes: (1) a dephasing of the observable consequences of the adiabatic geometric phase; and (2) the loss of computational efficiency of the Shor algorithm when run on a sufficiently noisy geometric quantum computer.
A non-adiabatic nuclear wavepacket dynamics simulation of the H$_2$O$^+$ de-excitation process is performed based on electronic structure calculations using the variational quantum eigensolver. The adiabatic potential energy surfaces and non-adiabatic coupling vectors are computed with algorithms for noisy intermediate-scale quantum devices, and time propagation is simulated with conventional methods for classical computers. The results of non-adiabatic transition dynamics from the $\tilde{B}$ state to $\tilde{A}$ state reproduce the trend reported in previous studies, which suggests that this…
Projective Quantum Eigensolver via Adiabatically Decoupled Subsystem Evolution: a Resource Efficient Approach to Molecular Energetics in Noisy Quantum Computers
Quantum computation by the adiabatic theorem requires a slowly varying Hamiltonian with respect to the spectral gap. We show that the Landau-Zener-Stückelberg oscillation phenomenon, that naturally occurs in quantum two level systems under non-adiabatic periodic drive, can be exploited to find the ground state of an N dimensional Grover Hamiltonian. The total runtime of this method is $O(\sqrt{2^n})$ which is equal to the computational time of the Grover algorithm in the quantum circuit model. An additional periodic drive can suppress a large subset of Hamiltonian control errors using coherent…
Shortcuts to adiabaticity are well-known methods for controlling the quantum dynamics beyond the adiabatic criteria, where counter-diabatic (CD) driving provides a promising means to speed up quantum many-body systems. In this work, we show the applicability of CD driving to enhance the digitized adiabatic quantum computing paradigm in terms of fidelity and total simulation time. We study the state evolution of an Ising spin chain using the digitized version of the standard CD driving and its variants derived from the variational approach. We apply this technique in the preparation of Bell and…
We review methods to shuttle quantum particles fast and robustly. Ideal robustness amounts to the invariance of the desired transport results with respect to deviations, noisy or otherwise, from the nominal driving protocol for the control parameters; this can include environmental perturbations. "Fast" is defined with respect to adiabatic transport times. Special attention is paid to shortcut-to-adiabaticity protocols that achieve, in faster-than-adiabatic times, the same results of slow adiabatic driving.
Adiabatic braiding of Majorana zero modes can be used for topologically protected quantum information processing. While extremely robust to many environmental perturbations, these systems are vulnerable to noise with high-frequency components. Ironically, slower processes needed for adiabaticity allow more noise-induced excitations to accumulate, resulting in an antiadiabatic behavior that limits the precision of Majorana gates if some noise is present. In a recent publication [Phys. Rev. B 96, 075158 (2017)], fast optimal protocols were proposed as a shortcut for implementing the same unitary…
Adiabatic evolution is a common strategy for manipulating quantum states and has been employed in diverse fields such as quantum simulation, computation and annealing. However, adiabatic evolution is inherently slow and therefore susceptible to decoherence. Existing methods for speeding up adiabatic evolution require complex many-body operators or are difficult to construct for multi-level systems. Using the tools of Floquet engineering, we design a scheme for high-fidelity quantum state manipulation, utilizing only the interactions available in the original Hamiltonian. We apply this approach…
Quantum annealing is explored as a resource for quantum information beyond solution of classical combinatorial problems. Envisaged as a generator of robust interferometric probes, we examine a Hamiltonian of $N>> 1$ uniformly-coupled spins subject to a transverse magnetic field. The discrete many-body problem is mapped onto dynamics of a single one-dimensional particle in a continuous potential. This reveals all the qualitative features of the ground state beyond typical mean-field or large classical spin models. It illustrates explicitly a graceful warping from an entangled unimodal to bi-mod…
Adiabatic quantum algorithms solve computational problems by slowly evolving a trivial state to the desired solution. On an ideal quantum computer, the solution quality improves monotonically with increasing circuit depth. By contrast, increasing the depth in current noisy computers introduces more noise and eventually deteriorates any computational advantage. What is the optimal circuit depth that provides the best solution? Here, we address this question by investigating an adiabatic circuit that interpolates between the paramagnetic and ferromagnetic ground states of the one-dimensional qua…
Quantum integer factorization is a potential quantum computing solution that may revolutionize cryptography. Nevertheless, a scalable and efficient quantum algorithm for noisy intermediate-scale quantum computers looks far-fetched. We propose an alternative factorization method, within the digitized-adiabatic quantum computing paradigm, by digitizing an adiabatic quantum factorization algorithm enhanced by shortcuts to adiabaticity techniques. We find that this fast factorization algorithm is suitable for available gate-based quantum computers. We test our quantum algorithm in an IBM quantum c…
Precise and efficient control of quantum systems is essential to perform quantum information processing tasks. In terms of adiabatic speedup via leakage elimination operator approach, for a closed system, the ideal pulse control conditions have been theoretically derived by P-Q partitioning technique. However, it is a challenge to design the corresponding control pulses for an open system, which requires to tackle noisy environments. In this paper, we apply the stochastic search procedures to an open qutrit system and successfully obtain the optimal control pulses for significant adiabatic spe…
We study adiabatic reverse annealing (ARA) in an open system. In the closed system (unitary) setting, this annealing protocol allows avoidance of first-order quantum phase transitions of selected models, resulting in an exponential speedup compared with standard quantum annealing, provided that the initial state of the algorithm is close in Hamming distance to the target one. Here, we show that decoherence can significantly modify this conclusion: by resorting to the adiabatic master equation approach, we simulate the dynamics of the ferromagnetic $p$-spin model with $p=3$ under independent an…
We show that a thermally isolated system driven across a quantum phase transition by a noisy control field exhibits anti-Kibble-Zurek behavior, whereby slower driving results in higher excitations. We characterize the density of excitations as a function of the ramping rate and the noise strength. The optimal driving time to minimize excitations is shown to scale as a universal power law of the noise strength. Our findings reveal the limitations of adiabatic protocols such as quantum annealing and demonstrate the universality of the optimal ramping rate.
Kibble-Zurek mechanism (KZM) is a universal framework which could in principle describe phase transition phenomenon in any system with required symmetry properties. However, a conflicting observation termed anti-KZ behavior has been reported in the study of ferroelectric phase transition, in which slower driving results in more topological defects [S. M. Griffin, et al. Phys. Rev. X. 2, 041022 (2012)]. Although this research is significant, its experimental simulations have been scarce until now. In this work, we experimentally demonstrate anti-KZ behavior under noisy control field in three ki…
Quantum information processing is likely to have far-reaching impact in the field of artificial intelligence. While the race to build an error-corrected quantum computer is ongoing, noisy, intermediate-scale quantum (NISQ) devices provide an immediate platform for exploring a possible quantum advantage through hybrid quantum--classical machine learning algorithms. One example of such a hybrid algorithm is "quantum kitchen sinks", which builds upon the classical algorithm known as "random kitchen sinks" to leverage a gate model quantum computer for machine learning applications. We propose an a…
The glued-trees problem is the only example known to date for which quantum annealing provides an exponential speedup, albeit by partly using excited state evolution, in an oracular setting. How robust is this speedup to noise on the oracle? To answer this, we construct phenomenological short-range and long-range noise models, and noise models that break or preserve the reflection symmetry of the spectrum. We show that under the long-range noise models an exponential quantum speedup is retained. However, we argue that a classical algorithm with an equivalent long-range noise model also exhibit…
Robustness of non-abelian holonomic quantum gates against parametric noise
本文对一类非阿贝尔完整量子门的鲁棒性进行了数值研究。我们考虑到由于控制场的随机波动的参数噪声驱动的时间相关的哈密顿沿绝热环。所用的性能估计器是无噪声和有噪声完整门之间的状态保真度。我们进行了我们的分析与不同的相关时间，我们发现，有噪声的完整门似乎是接近无噪声的“短”和“长”噪声相关时间。这个结果可以解释为完整算子的几何性质的结果。我们的模拟是通过使用与激子方案有关的参数来实现完整量子计算的[P.Solinas et al.Phys.Rev.B67，121307（2003）]
Benchmark of quantum algorithms for ground state preparation in the presence of noise
Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与技术中心）；Technical University of Munich, TUM School of Natural Sciences, Physics Department（慕尼黑工业大学）；Max-Planck-Institut für Quantenoptik（马克斯·普朗克量子光学研究所）
Determining Hamiltonian ground states and energies is a challenging task with many possible approaches on quantum computers. While variational quantum eigensolvers are popular approaches for near term hardware, adiabatic state preparation is an alternative that does not require noisy optimization of parameters. Beyond adiabatic schedules, QAOA is an important method for optimization problems. In this work we modify QAOA to apply to finding ground states of molecules and empirically evaluate the modified algorithm on several molecules. This modification applies physical insights used in classic…
Hall viscosity of the Laughlin state on noisy quantum computers
Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）；City College of the City University of New York（纽约市立学院）；Western Washington University（西华盛顿大学）；Graduate Center of City University of New York（纽约市立大学研究生中心）
We propose an adiabatic protocol for implementing a controlled-phase gate CZ$_θ$ with continuous $θ$ of neutral atoms through a symmetrical two-photon excitation process via the second resonance line, $6P$ in $^{87}$Rb, with a single-temporal-modulation-coupling of the ground state and intermediate state. Relying on different adiabatic paths, the phase factor $θ$ of CZ$_θ$ gate can be accumulated on the logic qubit state $|11\rangle$ alone by calibrating the shape of the temporal pulse where strict zero amplitudes at the start and end of the pulse are not needed. For a wide range of $θ$, we ca…
Currently, existing quantum annealers have proven themselves as viable technology for the first practical applications in the noisy-intermediate-scale-quantum era. However, to fully exploit their capabilities, a comprehensive characterization of their finite-time excitations is instrumental. To this end, we develop a phase diagram for driven Ising chains, from which the scaling behavior of the excess work can be read off as a function of process duration and system size. "Fast" processes are well described by the Kibble-Zurek mechanism; "slow" processes are governed by effective Landau-Zener d…
We study the adiabatic dynamics of degenerate quantum states induced by loop paths in a control parameter space. The latter correspond to noisy trajectories if the system is weakly coupled to environmental modes. On top of conventional dynamic dephasing, we find a universal non-Abelian geometric dephasing (NAGD) contribution and express it in terms of the non-Abelian Berry connection and curvature. We show that NAGD implies either decay or amplification of coherences as compared to the coherences when only dynamic dephasing is present. The full NAGD matrix structure can be probed through inter…
Quantum annealing (QA) is one of the efficient methods to calculate the ground-state energy of a problem Hamiltonian. In the absence of noise, QA can accurately estimate the ground-state energy if the adiabatic condition is satisfied. However, in actual physical implementation, systems suffer from decoherence. On the other hand, much effort has been paid into the noisy intermediate-scale quantum (NISQ) computation research. For practical NISQ computation, many error mitigation (EM) methods have been devised to remove noise effects. In this paper, we propose a QA strategy combined with the EM m…
Geometric phases and holonomies (their non-commuting generalizations) are a promising resource for the realization of high-fidelity quantum operations in noisy devices, due to their intrinsic fault-tolerance against noise and experimental imperfections. Despite their conceptual appeal and proven fault-tolerance, for a long time their practical use in quantum computing was limited to proof of principle demonstrations. Only in 2012 Sjöqvist et al. formulated a strategy to generate non-Abelian (i.e. holonomic) quantum gates through non-adiabatic transformation. Successful experimental demonstrati…
