Parity-time (PT) symmetric non-Hermitian Hamiltonians bring about many novel features and interesting applications such as quantum gates faster than those in Hermitian systems, and topological state transfer. The performance of evolutions under $\mathcal{PT}$-symmetric Hamiltonians is degraded by the inevitable noise and errors due to system-environment interaction and experimental imperfections. In contrast to Hermitian Hamiltonians, the fluctuations in dissipative beams that are utilized to generate non-Hermitian contributions in the PT-symmetric Hamiltonians cause additional errors. Here we achieve the protection of PT-symmetric Hamiltonians against noise acting along the qubit's quantization axis by combining quantum evolutions with dynamical decoupling sequences. We demonstrate the performance of our method by numerical simulations. Realistic noise sources and parameters are chosen including: constant detuning error, time-varying detuning noise and dissipative-beam noise. The fidelities of the protected evolutions are well above the unprotected ones under all the above situations. Our work paves the way for further studies and applications of non-Hermitian $\mathcal{PT}$-symmetric physics in noisy quantum systems.
We show that continuous dynamical decoupling can protect a two-qubit entangled state from sudden death at finite temperature due to uncorrelated dephasing, bit flipping, and dissipation. We consider a situation where an entangled state shared between two non-interacting qubits is initially prepared and left evolve under the environmental perturbations and the protection of external fields. To illustrate the protection of the entanglement, we solve numerically a master equation in the Born approximation, considering independent boson fields at the same temperature coupled to the different error…
Hybrid systems consisting of different types of qubits are promising for building quantum computers if they combine useful properties of their constituent qubits. However, they also pose additional challenges if one type of qubits is more susceptible to environmental noise than the others. Dynamical decoupling can help to protect such systems by reducing the decoherence due to the environmental noise, but the protection must be designed such that it does not interfere with the control fields driving the logical operations. Here, we test such a protection scheme on a quantum register consisting…
In this letter, we investigate the effects of non-Hermitian driving on quantum coherence in a bipartite system. The results that the dynamical localization destroyed by the Hermitian interaction revives are an evidence of the restoration of quantum coherence by non-Hermitian driving. Besides, the entanglement between the two subsystems also decays with the boosting of non-hermitian driving strength, which provides another evidence that non-Hermitian driving will protect quantum coherence. The physics behind this phenomenon is the domination of the quasieigenstate with maximum imaginary value o…
We experimentally demonstrate the efficacy of a three-layer nested Uhrig dynamical decoupling (NUDD) sequence to preserve arbitrary quantum states in a two-dimensional subspace of the four-dimensional two-qubit Hilbert space, on an NMR quantum information processor. The effect of the state preservation is studied first on four known states, including two product states and two maximally entangled Bell states. Next, to evaluate the preservation capacity of the NUDD scheme, we apply it to eight randomly generated states in the subspace. Although, the preservation of different states varies, the …
We embarked upon the task of experimental protection of different classes of tripartite entangled states, namely the maximally entangled GHZ and W states and the ${\rm W \bar{W}}$ state, using dynamical decoupling. The states were created on a three-qubit NMR quantum information processor and allowed to evolve in the naturally noisy NMR environment. Tripartite entanglement was monitored at each time instant during state evolution, using negativity as an entanglement measure. It was found that the W state is most robust while the GHZ-type states are most fragile against the natural decoherence …
Based on a theorem we establish on dynamical decoupling of time-dependent systems, we present a scheme of nested Uhrig dynamical decoupling (NUDD) to protect multi-qubit systems in generic quantum baths to arbitrary decoupling orders, using only single-qubit operations. The number of control pulses in NUDD increases polynomially with the decoupling order. For general multi-level systems, this scheme can preserve a set of unitary Hermitian system operators which mutually either commute or anti-commute, and hence all operators in the Lie algebra generated from this set of operators, generating a…
We show that dissipative quantum state preparation processes can be protected against qubit dephasing by interlacing the state preparation control with dynamical decoupling (DD) control consisting of a sequence of short $π$-pulses. The inhomogeneous broadening can be suppressed to second order of the pulse interval, and the protection efficiency is nearly independent of the pulse sequence but determined by the average interval between pulses. The DD protection is numerically tested and found to be efficient against inhomogeneous dephasing on two exemplary dissipative state preparation schemes …
Non-Hermitian degeneracies are classified as defective and nondefective exceptional points~(EP). While in defective EPs, both eigenvalues and eigenenergies coalesce, nondefective EPs are characterized merely by the occurrence of degeneracies in their eigenvalues. It is also known that all degeneracies are either symmetry-protected or accidental. In this paper, I prove that anti-unitary symmetries protect all nondefective twofold EPs. By developing a 2D non-Hermitian tight-binding model, I have demonstrated that these symmetries are composite of various symmetry operations such as discrete or s…
The interaction of a discrete state coupled to a continuum is a longstanding problem of major interest in different areas of quantum and classical physics. In Hermitian models, several dynamical decoupling schemes have been suggested, in which the discrete-continuum interaction can be substantially reduced and even suppressed. In this work we consider a discrete state interacting with a continuum via a time-dependent {\em non-Hermitian} coupling with finite (albeit arbitrarily long) duration, and show rather generally that for a wide class of coupling temporal shapes, in which the real and ima…
We consider protecting a Hadamard operation from independent dephasing, bit flipping, and dissipation. These environment-induced errors are represented by three uncorrelated reservoirs of thermalized bosons and we show that the protection is achievable through continuous dynamical decoupling. We find that, to decouple the Hadamard evolution from the environmental influence, we need a control field of higher frequency if the boson spectral density is super-ohmic than if it is ohmic. We also study the relevance of bit flipping and dissipation to the gate fidelity when it is protected from dephas…
Topological phenomena in non-Hermitian systems have recently become a subject of great interest in the photonics and condensed-matter communities. In particular, the possibility of observing topologically-protected edge states in non-Hermitian lattices has sparked an intensive search for systems where this kind of states are sustained. Here, we present the first study on the emergence of topological edge states in two-dimensional Haldane lattices exhibiting balanced gain and loss. In line with recent studies on other Chern insulator models, we show that edge states can be observed in the so-ca…
Dynamical decoupling can enforce a symmetry on the dynamics of an open quantum system. Here we develop an efficient dynamical-decoupling-based strategy to create the decoherence-free subspaces (DFSs) for a set of qubits by optimally transferring the states of these qubits. We design to transfer the state of each qubit to all of the other qubits in an optimal and efficient manner, so as to produce an effective collective-type noise for all qubits. This collective pseudo-noise is essentially derived from arbitrarily independent real baths and needs only nearest-neighbor state transfers for its i…
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…
We consider topological protection mechanisms in dissipative quantum systems in the presence of quenched disorder, with the intent to prolong coherence times of qubits. The physical setting is a network of qubits and dissipative cavities whose coupling parameters are tunable, such that topological edge states can be stabilized. The evolution of a fiducial qubit is entirely determined by a non-Hermitian Hamiltonian which thus emerges from a bona-fide physical process. It is shown how even in the presence of disorder winding numbers can be defined and evaluated in real space, as long as certain …
One dimensional topological insulators are characterized by edge states with exponentially small energies. According to one generalization of topological phases to non-Hermitian systems, a finite system in a non-trivial topological phase displays surface states with exponentially long life times. In this work we explore the possibility of exploiting such non-Hermitian topological phases to enhance the quantum coherence of a fiducial qubit embedded in a dissipative environment. We first show that a network of qubits interacting with lossy cavities can be represented, in a suitable super-one-par…
Spectra of bulk or edges in topological insulators are often made complex by non-Hermiticity. Here, we show that symmetry protection enables entirely real spectra for both bulk and edges even in non-Hermitian topological insulators. In particular, we demonstrate entirely real spectra without non-Hermitian skin effects due to a combination of pseudo-Hermiticity and Kramers degeneracy. This protection relies on nonspatial fundamental symmetry and has stability against disorder. As an illustrative example, we investigate a non-Hermitian extension of the Bernevig-Hughes-Zhang model. The helical ed…
We propose a technique that allows to simultaneously perform universal control of the evolution operator and compensate for the first order contribution of an arbitrary Hermitian constant noise. We show that, at least, a three-valued Hamiltonian is needed in order to protect the system against any such noise. This technique is illystrated by an explicit algorithm for a control sequence that is applied to numerically design a safe two-qubit gate.
One of the biggest challenges for implementing quantum devices is the requirement to perform accurate quantum gates. The destructive effects of interactions with the environment present some of the most difficult obstacles that must be overcome for precise quantum control. In this work we implement a proof of principle experiment of quantum gates protected against a fluctuating environment using dynamical decoupling techniques. We show that decoherence can be reduced during the application of quantum gates. High fidelity quantum gates can be achieved even if the gate time exceeds the decoheren…
Future quantum technologies rely heavily on good protection of quantum entanglement against environment-induced decoherence. A recent study showed that an extension of Uhrig's dynamical decoupling (UDD) sequence can (in theory) lock an arbitrary but known two-qubit entangled state to the $N$th order using a sequence of $N$ control pulses [Mukhtar et al., Phys. Rev. A 81, 012331 (2010)]. By nesting three layers of explicitly constructed UDD sequences, here we first consider the protection of unknown two-qubit states as superposition of two known basis states, without making assumptions of the s…
This thesis deals with the generation, estimation and preservation of novel quantum states of two and three qubits, on an NMR quantum information processor. Using the maximum likelihood ansatz, we have developed a method for state estimation such that the reconstructed density matrix does not have negative eigenvalues and the errors are within the space of valid density operators. Due to interactions with the environment, unwanted changes occur in the system, leading to decoherence. Controlling decoherence is one of the biggest challenges to be overcome to build quantum computers. We have used…
We study dynamical decoupling in a multi-qubit setting, where it is combined with quantum logic gates. This is illustrated in terms of computation using Heisenberg interactions only, where global decoupling pulses commute with the computation. We derive a rigorous error bound on the trace distance or fidelity between the desired computational state and the actual time-evolved state, for a system subject to coupling to a bounded-strength bath. The bound is expressed in terms of the operator norm of the effective Hamiltonian generating the evolution in the presence of decoupling and logic operat…
A recently developed theory for eliminating decoherence and design constraints in quantum computers, ``encoded recoupling and decoupling'', is shown to be fully compatible with a promising proposal for an architecture enabling scalable ion-trap quantum computation [D. Kielpinski et al., Nature 417, 709 (2002)]. Logical qubits are encoded into pairs of ions. Logic gates are implemented using the Sorensen-Molmer (SM) scheme applied to pairs of ions at a time. The encoding offers continuous protection against collective dephasing. Decoupling pulses, that are also implemented using the SM scheme d…
Active protection of quantum states is an essential prerequisite for the implementation of quantum computing. Dynamical decoupling (DD) is a promising approach that applies sequences of control pulses to the system in order to reduce the adverse effect of system-environment interactions. Since every hardware device has finite precision, the errors of the DD control pulses can themselves destroy the stored information rather than protect it. We experimentally compare the performance of different DD sequences in the presence of an environment that was chosen such that all relevant DD sequences c…
We consider one system in which the terminal dots of a one-dimensional quantum-dot chain couple equally to the left and right leads and study the influence of $\mathcal{PT}$-symmetric complex potentials on the quantum transport process. It is found that in the case of the Hermitian Hamiltonian, remarkable decoupling and antiresonance phenomena have an opportunity to co-occur in the transport process. For the chains with odd(even) dots, all their even(odd)-numbered molecular states decouple from the leads. Meanwhile, antiresonance occurs at the positions of the even(odd)-numbered eigenenergies …
We experimentally emulate, in a controlled fashion, the non-Markovian dynamics of a pure dephasing spin-boson model at zero temperature. Specifically, we use a randomized set of external radio-frequency fields to engineer a desired noise power-spectrum to effectively realize a non-Markovian environment for a single NMR qubit. The information backflow, characteristic to the non-Markovianity, is captured in the nonmonotonicity of the decoherence function and von Neumann entropy of the system. Using such emulated non-Markovian environments, we experimentally study the efficiency of the Carr-Purce…
We study the occurrence of errors in a continuously decoupled two-qubit state during a $\sqrt{SWAP}$ quantum operation under decoherence. We consider a realization of this quantum gate based on the Heisenberg exchange interaction, which alone suffices for achieving universal quantum computation. Furthermore, we introduce a continuous-dynamical-decoupling scheme that commutes with the Heisenberg Hamiltonian to protect it from the amplitude damping and dephasing errors caused by the system-environment interaction. We consider two error-protection settings. One protects the qubits from both ampli…
A quantum memory interacts with its environment and loses information via decoherence as well as incoherence. A robust quantum control that prepares, preserves, and manipulates nonclassical correlations even in the presence of environmental influence is of paramount importance in quantum information processing. A well-known technique to suppress decoherence, namely Dynamical Decoupling (DD), consists of a sequence of rapid flips applied to the system in order to refocus the system-environment interactions. In this work, we integrate DD with quantum gates using optimal control techniques to rea…
The inevitable dissipative interaction of an entangled quantum system with its environment causes degradation in quantum correlations present in the system. This can lead to a finite-time disappearance of entanglement, which is known as entanglement sudden death (ESD). Here, we consider an initially entangled qubit-qutrit system and a dissipative noise which leads to ESD, and propose a set of local unitary operations, which when applied on the qubit, qutrit, or both subsystems during the decoherence process, cause ESD to be hastened, delayed, or avoided altogether, depending on its time of app…
Aperiodic dynamical decoupling (DD) sequences of $π$ pulses are of great interest to decoherence control and have been recently extended from single-qubit to two-qubit systems. If the environmental noise power spectrum is made available, then one may further optimize aperiodic DD sequences to reach higher efficiency of decoherence suppression than known universal schemes. This possibility is investigated in this work for the protection of two-qubit states, using an exactly solvable pure dephasing model including both local and nonlocal noise. The performance of optimized DD sequences in protec…
Quantum information requires protection from the adverse affects of decoherence and noise. This review provides an introduction to the theory of decoherence-free subspaces, noiseless subsystems, and dynamical decoupling. It addresses quantum information preservation as well protected computation.
In the propagation of optical pulses through dispersive media, the frequency degree of freedom acts as an effective decohering environment on the polarization state of the pulse. Here we discuss the application of open-loop dynamical-decoupling techniques for suppressing such a polarization decoherence in one-way communication channels. We describe in detail the experimental proof of principle of the "bang-bang" protection technique recently applied to flying qubits in [Damodarakurup et al., Phys. Rev. Lett. 103, 040502]. Bang-bang operations are implemented through appropriately oriented wave…
Cavity-mediated coherence protection and one-axis twisting for spins in solids
California Institute of Technology（加州理工学院）；Chimie ParisTech, PSL University, CNRS, Institut de Recherche de Chimie Paris（巴黎化学学院，巴黎文理研究大学，法国国家科学研究中心，巴黎化学研究院）
We study the suppression of qubit dephasing through Uhrig dynamical decoupling (UDD) in nontrivial environments modeled within the spin-boson formalism. In particular, we address the case of (i) a qubit coupled to a bosonic bath with power-law spectral density, and (ii) a qubit coupled to a single harmonic oscillator that dissipates energy into a bosonic bath, which embodies an example of a structured bath for the qubit. We then model the influence of random time jitter in the UDD protocol by sorting pulse-application times from Gaussian distributions centered at appropriate values dictated by…
We present a strategy for producing multi-qubit gates that promise high fidelity with minimal tuning requirements. Our strategy combines gap protection from the adiabatic theorem with dynamical decoupling in a complementary manner. To avoid degenerate states and maximize the benefit of the gap protection, the scheme is best suited when there are two different kinds of qubits (not mutually resonant). Furthermore, we require a robust operating point in control space where the qubits interact with little sensitivity to noise. This allows us to circumvent a No-Go theorem that prevents block-box dy…
We propose a scheme to achieve the analogous interface-state laser by dint of the interface between the two intermediate-resonator-coupled non-Hermitian resonator chains. We find that, after introducing the couplings between the two resonator chains and the intermediate resonator at the interface, the photons of the system mainly gather into the three resonators near the intermediate resonator. The phenomenon of the photon gathering towards the certain resonators is expected to construct the photon storage and even the laser generator. We reveal that the phenomenon is induced via the joint eff…
Stable and phase-locked emission in an extended topological supermode of coupled laser arrays, based on concepts of non-Hermitian and topological photonics, is theoretically suggested. We consider a non-Hermitian Su-Schrieffer-Heeger chain of coupled microring resonators and show that application of a synthetic imaginary gauge field via auxiliary passive microrings leads to all supermodes of the chain, except one, to become edge states. The only extended supermode, that retains some topological protection, can stably oscillate suppressing all other non-topological edge supermodes. Numerical si…
The protection of qubit coherence is an essential task in order to build a practical quantum computer able to manipulate, store and read quantum information with a high degree of fidelity. Recently, it has been proposed to increase the operation time of a qubit by means of strong pulses to achieve a dynamical decoupling of the qubit from its environment. We propose and demonstrate a simple and highly efficient alternative pulse protocol based on Floquet modes, which increases the decoherence time in a number of materials with different spin Hamiltonians and environments. We demonstrate the reg…
We investigate the nonlinear scattering dynamics in interacting atomic Bose-Einstein condensates under non-Hermitian dissipative conditions. We show that by carefully engineering a momentum-dependent atomic loss profile one can achieve matter-wave amplification through four wave mixing in a one-dimensional quasi free-space setup - a process that is forbidden in the counterpart Hermitian systems due to energy mismatch. Additionally, we show that similar effects lead to rich nonlinear dynamics in higher dimensions. Finally, we propose a physical realization for selectively tailoring the momentum…
A quantum memory or information processing device is subject to disturbance from its surrounding environment or inevitable leakage due to its contact with other systems. To tackle these problems, several control protocols have been proposed for quantum memory or storage. Among them, the fast-signal control or dynamical decoupling based on external pulse sequences provides a prevailing strategy aimed at suppressing decoherence and preventing the target systems from the leakage or diffusion process. In this paper, we review the applications of this protocol in protecting quantum memory under the…
Quantum correlation quantified by quantum discord has been demonstrated experimentally as important physical resources in quantum computation and communication for some cases even without the presence of entanglement. However, since the interaction between the quantum system and the noisy environment is inevitable, it is essential to protect quantum correlation from lost in the environment and to characterize its dynamical behavior in the real open systems. Here we showed experimentally in the solid-state P:Si system the existence of a stable interval for the quantum correlation in the beginni…
Tuning topological phases and exceptional points in a non-Hermitian Rice Mele model beyond nearest neighbors
Donostia International Physics Center (DIPC)（圣塞巴斯蒂安国际物理中心）；Chemistry Faculty (UPV/EHU)（巴斯克地区理工大学化学学院）；IKERBASQUE, Basque Foundation for Science（伊克拉巴斯基奎巴斯克科学基金会）；Wrocław University of Science and Technology（弗罗茨瓦夫科技大学）
High-fidelity quantum entanglement is a key resource for quantum communication and distributed quantum computing, enabling quantum state teleportation, dense coding, and quantum encryption. Any sources of decoherence in the communication channel however degrade entanglement fidelity, thereby increasing the error rates of entangled state protocols. Entanglement purification provides a method to alleviate these non-idealities, by distilling impure states into higher-fidelity entangled states. Here we demonstrate the entanglement purification of Bell pairs shared between two remote superconductin…
We study an interacting one-dimensional gas of spin-1/2 fermions with two-body losses. The dynamical phase diagram that characterises the approach to the stationary state displays a wide quantum-Zeno region, identified by a peculiar behaviour of the lowest eigenvalues of the associated non-Hermitian Hamiltonian. We characterise the universal dynamics of this Zeno regime using an approximation scheme based on a effective decoupling of charge and spin degrees of freedom, where the latter effectively evolve in a non-Markovian way according to a non-Hermitian Heisenberg Hamiltonian. We present det…
