We study the decoherence of a quantum computer in an environment which is inherently correlated in time and space. We first derive the nonunitary time evolution of the computer and environment in the presence of a stabilizer error correction code, providing a general way to quantify decoherence for a quantum computer. The general theory is then applied to the spin-boson model. Our results demonstrate that effects of long-range correlations can be systematically reduced by small changes in the error correction codes.
We introduce a general formalism to describe the effects of Markovian noise which is spatially correlated, typically decaying over some finite correlation length. For any system of interest, this formalism describes spatial correlations without the necessity to choose a particular microscopic model for the environment. We present a method of mapping the equations to Lindblad form and discuss functional forms for homogeneous spatial correlation functions. We also discuss two example microscopic models for the environment which exhibit non-trivial spatial-temporal correlation functions.
It is shown that the noise process in quantum computation can be described by spatially correlated decoherence and dissipation. We demonstrate that the conventional quantum error correcting codes correcting for single-qubit errors are applicable for reducing spatially correlated noise.
We investigate decoherence-free evolution (DFE) of quantum discord (QD) for two initially-correlated qubits in two finite-temperature reservoirs using an exactly solvable model. We study QD dynamics of the two qubits coupled to two independent Ohmic reservoirs when the two qubits are initially prepared in X-type quantum states. It is found that reservoir temperature significantly affects the DFE dynamics. We show that it is possible to control the DFE and to prolong the DFE time by choosing suitable parameters of the two-qubit system and reservoirs.
By use of a generalized Bloch vector construction, we study the decoherence of a system composed of two interacting qubits in a general noisy environment. In particular, we investigate the effects of correlations in the noise acting on distinct qubits. Our treatment of the two-qubit system by use of the generalized Bloch vector leads to tractable analytic equations for the dynamics of the 4-level Bloch vector and allows for the application of geometrical concepts from the well known 2-level Bloch sphere. We find that in the presence of correlated or anticorrelated noise, the rate of decoherenc…
The problem of dipole-dipole decoherence of nuclear spins is considered for strongly entangled spin cluster. Our results show that its dynamics can be described as the decoherence due to interaction with a composite bath consisting of fully correlated and uncorrelated parts. The correlated term causes the slower decay of coherence at larger times. The decoherence rate scales up as a square root of the number of spins giving the linear scaling of the resulting error. Our theory is consistent with recent experiment reported in decoherence of correlated spin clusters.
We show that errors are not generated correlatedly provided that quantum bits do not directly interact with (or couple to) each other. Generally, this no-qubits-interaction condition is assumed except for the case where two-qubit gate operation is being performed. In particular, the no-qubits-interaction condition is satisfied in the collective decoherence models. Thus, errors are not correlated in the collective decoherence. Consequently, we can say that current quantum error correcting codes which correct single-qubit-errors will work in most cases including the collective decoherence.
We have studied decoherence in a system where two Josephson-junction flux qubits share a part of their superconducting loops and are inductively coupled. By tuning the flux bias condition, we control the sensitivities of the energy levels to flux noises in each qubit. The dephasing rate of the first excited state is enhanced or suppressed depending on the amplitudes and the signs of the sensitivities. We have quantified the $1/f$ flux noises and their correlations and found that the dominant contribution is by local fluctuations.
Quantum error correction is a solution to preserve the fidelity of quantum information encoded in physical systems subject to noise. However, unfavorable correlated errors could be induced even for non-interacting qubits through the environment (bath), when they are "packed" together. The question is, to what extent can we treat the noise induced by the bath as independent? In the context of the spin-boson model, we show that, under some reasonable constraints, the independent noise approximation could be valid. On the other hand, in the strongly correlated limit, we show how the method of dec…
Quantum technologies have shown immeasurable potential to effectively solve several information processing tasks such as prime number factorization, unstructured database search or complex macromolecule simulation. As a result of such capability to solve certain problems that are not classically tractable, quantum machines have the potential revolutionize the modern world via applications such as drug design, process optimization, unbreakable communications or machine learning. However, quantum information is prone to suffer from errors caused by the so-called decoherence, which describes the …
In this work, we studied the relaxation dynamics of coherences of different order present in a system of two coupled nuclear spins. We used a previously designed model for intrinsic noise present in such systems which considers the Lindblad master equation for Markovian relaxation. We experimentally created zero-, single- and double- quantum coherences in several two-spin systems and performed a complete state tomography and computed state fidelity. We experimentally measured the decay of zero- and double- quantum coherences in these systems. The experimental data fitted well to a model that c…
Certain physical aspects of quantum error correction are discussed for a quantum computer (n-qubit register) in contact with a decohering environment. Under rather plausible assumptions upon the form of the computer-environment interaction, the efficiency of a general correcting procedure is evaluated as a function of the spontaneous-decay duration and the rank of errors covered by the procedure. It is proved that the probability of errors can be made arbitrarily small by enhancing the correction method, provided the decohering interaction is represented by a bounded operator.
We identify different schemes to enhance the violation of Leggett-Garg inequalities in open many-body systems. Considering a nonequilibrium archetypical setup of quantum transport, we show that particle interactions control the direction and amplitude of maximal violation and that in the strongly-interacting and strongly-driven regime bulk dephasing enhances the violation. Through an analytical study of a minimal model, we unravel the basic ingredients to explain this decoherence-enhanced quantumness, illustrating that such an effect emerges in a wide variety of systems.
We investigate the influence of environmental noise on spin networks and spin chains. In addition to the common model of an independent bath for each spin in the system we also consider noise with a finite spatial correlation length. We present the emergence of new dynamics and decoherence-free subspaces with increasing correlation length for both dephasing and dissipating environments. This leads to relaxation blocking of one spin by uncoupled surrounding spins. We then consider perfect state transfer through a spin chain in the presence of decoherence and discuss the dependence of the transf…
Reflection of a microscopic particle from a mesoscopic/macroscopic `mirror' generates two-body correlated interference from the incident and reflected particle substates and their associated mirror substates. The microscopic momentum exchanged generates two mirror substates which interfere to produce fringes which do not vanish as the mirror mass increases. The small displacement between these mirror states can yield negligible environmental decoherence times. Mirror coherence lengths impose constraints on the extent of this interference, which are mitigated using interference of the two-body …
The dynamics of a dimer coupled to two different environments each in a spin star configuration under the influence of decoherence is studied. The exact analytical expression for the transition probability in the dimer system is obtained for different situations, i.e., independent and correlated environments. In all cases considered, it is shown that there exist well-defined ranges of parameters for which decoherent interaction with the environment assists energy transfer in the dimer system. In particular, we find that correlated environments can assist energy transfer more efficiently than s…
We study the effect of continuous quantum error correction in the case where each qubit in a codeword is subject to a general Hamiltonian interaction with an independent bath. We first consider the scheme in the case of a trivial single-qubit code, which provides useful insights into the workings of continuous error correction and the difference between Markovian and non-Markovian decoherence. We then study the model of a bit-flip code with each qubit coupled to an independent bath qubit and subject to continuous correction, and find its solution. We show that for sufficiently large error-corr…
We considered the interaction of semiconductor quantum register with noisy environment leading to various types of qubit errors. We analysed both phase and amplitude decays during the process of electron-phonon interaction. The performance of quantum error correction codes (QECC) which will be inevitably used in full scale quantum information processors was studied in realistic conditions in semiconductor nanostructures. As a hardware basis for quantum bit we chose the quantum spatial states of single electron in semiconductor coupled double quantum dot system. The modified 5- and 9-qubit quan…
We show that multidimensional Zeno effect combined with non-holonomic control allows to efficiently protect quantum systems from decoherence by a method similar to classical coding. Contrary to the conventional approach, our method is applicable to arbitrary error-inducing Hamiltonians and general quantum systems. We also propose algorithms of finding encoding that approaches the Hamming upper bound along with methods of practical realizations of the encodings. Two new codes protecting 2 information qubits out of 7 and 4 information qubits out of 9 against a single error with arbitrarily small…
We discuss the effect of correlated noise on the robustness of quantum coherent phenomena. First we consider a simple, toy model to illustrate the effect of such correlations on the decoherence process. Then we show how decoherence rates can be suppressed using a Parrondo-like effect. Finally, we report the results of many-body calculations in which an experimentally-measurable quantum coherence phenomenon is significantly enhanced by non-Markovian dynamics arising from the noise source.
We study the three-player Prisoner's Dilemma game under the effect of decoherence and correlated noise. It is seen that the quantum player is always better off over the classical players. It is also seen that the game's Nash equilibrium does not change in the presence of correlated noise in contradiction to the effect of decoherence in multiplayer case. Furthermore, it is shown that for maximum correlation the game does not behave as a noiseless game and the quantum player is still better off for all values of the decoherence parameter p which is not possible in the two-player case. In additio…
A major problem facing the realisation of scalable solid-state quantum computing is that of overcoming decoherence - the process whereby phase information encoded in a qubit is lost as the qubit interacts with its environment. Due to the vast number of environmental degrees of freedom, it is challenging to accurately calculate decoherence times $T_2$, especially when the qubit and environment are highly correlated. Hybrid or mixed electron-nuclear spin qubits, such as donors in silicon, possess 'optimal working points' (OWPs) which are sweet-spots for reduced decoherence in magnetic fields. An…
Relaxation effects impose fundamental limitations on our ability to coherently control quantum mechanical phenomena. In this letter, we establish physical limits on how closely can a quantum mechanical system be steered to a desired target state in the presence of relaxation. In particular, we explicitly compute the maximum coherence or polarization that can be transferred between coupled nuclear spins in the presence of very general decoherence mechanisms that include cross-correlated relaxation. We give analytical expressions for the control laws (pulse sequences) which achieve these physica…
In this paper we study the dissipative effects and decoherence induced on a particle moving at constant speed in front of a dielectric plate in quantum vacuum, developing a Closed-Time-Path (CTP) integral formulation in order to account for the corrections to these phenomena generated by finite temperatures. We compute the frictional force of the moving particle and find that it contains two different contributions: a pure quantum term due to quantum fluctuations (even present at vanishing temperatures) and a temperature dependent component generated by thermal fluctuations (bigger contributio…
Correlated decoherence and thermometry with mobile impurities in a 1D Fermi gas
School of Physics, Trinity College Dublin（都柏林三一学院物理学院）；Quantum Systems Unit, OIST Graduate University（冲绳科学技术大学院大学量子系统单元）；Department of Physics, King’s College London（伦敦国王学院物理系）
The effect of entanglement and correlated noise in a four-player quantum Minority game is investigated. Different time correlated quantum memory channels are considered to analyze the Nash equilibrium payoff of the 1st player. It is seen that the Nash equilibrium payoff is substantially enhanced due to the presence of correlated noise. The behaviour of damping channels (amplitude damping and phase damping) is approximately similar. However, bit-phase flip channel heavily influences the minority game as compared to other channels in the presence of correlated noise. On the other hand, phase fli…
In metrological tasks, employing entanglement can quantitatively improve the precision of parameter estimation. However, susceptibility of the entanglement to decoherence fades this capability in the realistic metrology and limits ultimate quantum improvement. One of the most destructive decoherence-type noise is uncorrelated Markovian noise which commutes with the parameter-encoding Hamiltonian and is modelled as a semigroup dynamics, for which the quantum improvement is constrained to a constant factor. It has been shown [Phys. Rev. Lett. \textbf{109}, 233601 (2012)] that when the noisy time…
We propose a solid-state experiment to study the process of continuous quantum measurement of a qubit state. The experiment would verify that an individual qubit stays coherent during the process of measurement (in contrast to the gradual decoherence of the ensemble-averaged density matrix) thus confirming the possibility of the qubit purification by continuous measurement. The experiment can be realized using quantum dots, single-electron transistors, or SQUIDs.
Based on the quantum technique of weak measurement, we propose a scheme to protect the entanglement from correlated amplitude damping decoherence. In contrast to the results of memoryless amplitude damping channel, we show that the memory effects play a significant role in the suppression of entanglement sudden death and protection of entanglement under severe decoherence. Moreover, we find that the initial entanglement could be drastically amplified by the combination of weak measurement and quantum measurement reversal even under the correlated amplitude damping channel. The underlying mecha…
We construct generally applicable short-time perturbative expansions for some fidelities, such as the input-output fidelity, the entanglement fidelity, and the average fidelity. Successive terms of these expansions yield characteristic times for the damping of the fidelities involving successive powers of the Hamiltonian. The second-order results, which represent the damping rates of the fidelities, are extensively discussed. As an interesting application of these expansions, we use them to study the spatially-correlated dissipation of quantum bits. Spatial correlations in the dissipation are …
Two initially correlated coherent states, each interacting with its own independent dissipative environment exhibit a sudden transition from classical to quantum decoherence. This change in the dynamics is a turning point in the decoherence, in the sense that depending on the average number of photons of each cavity, decoherence can even be suppressed. Indeed, the quantum state is time-independent for a time span in the mesoscopic regime, revealing a decoherence-free subspace. Furthermore, the absence of decoherence is manifested in the apparition of a metastable pointer state basis.
We consider quantum error correction of quantum-noise that is created by a local interaction of qubits with a common bosonic bath. The possible exchange of bath bosons between qubits gives rise to spatial and temporal correlations in the noise. We find that these kind of noise correlations have a strong negative impact on quantum error correction.
We analytically derive a decoherence model for orbital angular momentum states of a photon in a multimode optical fiber and show that rate of decoherence scales exponentially with $l^2$, where $l$ is the azimuthal mode order.~We also show numerically that for large values of $l$ the orbital angular momentum photon state completely dephases.~However for lower values of $l$ the decoherence can be minimized by using dynamical decoupling to allow for qudit high-bandwidth quantum communication and similar applications. \end{abstract}
We investigate the impact of loss (amplitude damping) and decoherence (phase damping) on the performance of a simple quantum computer which solves the one-bit Deutsch problem. The components of this machine are beamsplitters and nonlinear optical Kerr cells, but errors primarily originate from the latter. We develop models to describe the effect of these errors on a quantum optical Fredkin gate. The results are used to analyze possible error correction strategies in a complete quantum computer. We find that errors due to loss can be avoided perfectly by appropriate design techniques, while dec…
Decoherence is the process by which quantum systems interact and become correlated with their external environments; quantum trajectories are a powerful technique by which decohering systems can be resolved into stochastic evolutions, conditioned on different possible ``measurements'' of the environment. By calling on recently-developed tools from quantum information theory, we can analyze simplified models of decoherence, explicitly quantifying the flow of information and randomness between the system, the environment, and potential observers.
There exists the well known approximate expression describing the large time behaviour of matrix elements of the evolution operator in quantum theory: <U(t)>=exp(at)+... This expression plays the crucial role in considerations of problems of quantum decoherence, radiation, decay, scattering theory, stochastic limit, derivation of master and kinetic equations etc. This expression was obtained in the Weisskopf-Wigner approximation and in the van Hove (stochastic) limit. We derive the exact general formula which includes the higher order corrections to the above approximate expression: <U(t)>=exp…
We show that the decoherence, which in the long run destroys quantum features of a system, can be used to reveal the entanglement in a two-qubit system. To this end, we consider a criterion that formally resembles the Clauser-Horne-Shimony-Holt (CHSH) inequality. In our case the local observables are set by the coupling of each qubit to the environmental noise, controlled with the dynamical decoupling method. We demonstrate that the constructed inequality is an entanglement criterion---it can only be violated by non-separable initial two-qubit states, provided that the local noises are correla…
The long-time maintenance of quantum coherence is crucial for its practical applications. We explore decoherence process of a multiqubit system passing through a correlated channel (phase flip, bit flip, bit-phase flip, and depolarizing). The results show that the decay of coherence was evidently delayed when the consecutive actions of the channel on the sequence of qubits has some classical correlations. In particular, the relative entropy of coherence for a system with large number of qubits is more robust than that with small number of qubits. We also provide an explanation for the delayed …
In the framework of nuclear magnetic resonance, we consider the general problem of the coherent control of a spin coupled to a bath by means of composite or continuous pulses of duration $τ_\mathrm{p}$. We show explicity that it is possible to design the pulse in order to achieve a decoupling of the spin from the bath up to the third order in $τ_\mathrm{p}$. The evolution of the system is separated in the evolution of the spin under the action of the pulse and of the bath times correction terms. We derive the correction terms for a general time dependent axis of rotation and for a general coup…
We numerically study coherent errors in surface codes on planar graphs, focusing on noise of the form of $Z$- or $X$-rotations of individual qubits. We find that, similarly to the case of incoherent bit- and phase-flips, a trade-off between resilience against coherent $X$- and $Z$-rotations can be made via the connectivity of the graph. However, our results indicate that, unlike in the incoherent case, the error-correction thresholds for the various graphs do not approach a universal bound. We also study the distribution of final states after error correction. We show that graphs fall into thr…
"Decoherence of quantum superpositions through coupling to engineered reservoirs" is the topic of a recent article by Myatt et al. [Nature {\underline{403}}, 269 (2000)] which has attracted much interest because of its relevance to current research in fundamental quantum theory, quantum computation, teleportation, entanglement and the quantum-classical interface. However, the preponderance of theoretical work on decoherence does not consider the effect of an {\underline{external field}}. Here, we present an analysis of such an effect in the case of the random delta-correlated force discussed b…
The decoherence matrix studied by Gudder and Sorkin (2011) can be considered as a map from the set of all the pairs of $n$-length paths to complex numbers, which is induced by the discrete-time quantum walk. The decoherence matrix is one of the decoherence functionals which present their historical quantum measure theory. In this paper, we compute the von Neumann entropy of the decoherence matrix. To do so, we use the result that the eigensystem of the decoherence matrix can be expressed by a corresponding correlated random walk.
It is shown how possible corrections to ordinary quantum mechanics described by the Lindblad equation might be detected by exploiting the great precision of atomic clocks.
Dynamically corrected gates were recently introduced [Khodjasteh and Viola, Phys. Rev. Lett. 102, 080501 (2009)] as a tool to achieve decoherence-protected quantum gates based on open-loop Hamiltonian engineering. Here, we further expand the framework of dynamical quantum error correction, with emphasis on elucidating under what conditions decoherence suppression can be ensured while performing a generic target quantum gate, using only available bounded-strength control resources. Explicit constructions for physically relevant error models are detailed, including arbitrary linear decoherence a…
Bodies in relative motion, spatially separated in vacuum, experience a tiny friction force known as quantum friction. This force has eluded experimental detection so far due to its small magnitude and short range. Herein, we give quantitative details so as to track traces of the quantum friction by measuring coherences in the atom. We notice that the environmentally induced decoherence can be decomposed into contributions of different signature: corrections induced by the electromagnetic vacuum in presence of the dielectric sheet and those induced by the motion of the particle. In this directi…
The interaction of two--level atoms with a common heat bath leads to an effective interaction between the atoms, such that with time the internal degrees of the atoms become correlated or even entangled. If part of the atoms remain unobserved this creates additional indirect decoherence for the selected atoms, on top of the direct decoherence due to the interaction with the heat bath. I show that indirect decoherence can drastically increase and even dominate the decoherence for sufficiently large times. I investigate indirect decoherence through thermal black body radiation quantitatively for…
Using a numerical simulation of the evolution of a qubit interacting with the environment we show that quantum error detection and correction can work effectively even when the recovery procedure introduces errors.
Decoherence-free subspaces (DFSs) shield quantum information from errors induced by the interaction with an uncontrollable environment. Here we study a model of correlated errors forming an Abelian subgroup (stabilizer) of the Pauli group (the group of tensor products of Pauli matrices). Unlike previous studies of DFSs, this type of errors does not involve any spatial symmetry assumptions on the system-environment interaction. We solve the problem of universal, fault-tolerant quantum computation on the associated class of DFSs.
Environmental noise can hinder the metrological capabilities of entangled states. While the use of entanglement allows for Heisenberg-limited resolution, the largest permitted by quantum mechanics, deviations from strictly unitary dynamics quickly restore the standard scaling dictated by the central limit theorem. Product and maximally entangled states become asymptotically equivalent when the noisy evolution is both local and strictly Markovian. However, temporal correlations in the noise have been shown to lift this equivalence while fully (spatially) correlated noise allows for the identifi…
Quantum systems in mixed states can be unentangled and yet still correlated in a way that is not possible for classical systems. These correlations can be quantified by the quantum discord and might provide a resource for certain mixed-state quantum information processing tasks. Here we report on the generation of discordant states of two trapped atomic ions via Markovian decoherence processes. While entanglement is strictly non-increasing under such operations, discord can be generated in various forms. Firstly we show that, starting from two classically correlated qubits, it is possible to g…
