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 argue that superradiance (collective emission) due to radiative coupling of qubit states results in non-local noise, and thus introduces an error source that cannot be corrected using current models of fault-tolerant quantum computation.
The symmetric collective states of an atomic spin ensemble (i.e., many-body states that are invariant under particle exchange) are not preserved by decoherence that acts identically but individually on members of the ensemble. We develop a class of collective states in an ensemble of N spin-1/2 particles that is invariant under symmetric local decoherence and find that the dimension of the Hilbert space spanned by these collective states scales only as N^2. We then investigate the open system dynamics of experimentally relevant non-classical collective atomic states, including Schroedinger cat…
We discuss the structure of decoherence-free subsystems for a bosonic channel affected by collective depolarization. A single use of the channel is defined as a transmission of a pair of bosonic modes. Collective depolarization consists in a random linear U(2) transformation of the respective mode operators, which is assumed to be identical for $N$ consecutive uses of the channel. We derive a recursion formula that characterizes the dimensionality of available decoherence-free subsystems in such a setting.
The information in quantum computers is often stored in identical two-level systems (spins or pseudo-spins) that are separated by a distance shorter than the characteristic wavelength of a reservoir which is responsible for decoherence. In such a case, the collective spin-reservoir interaction, rather than an individual spin-reservoir interaction, may determine the decoherence characteristics. We use computational basis states, symmetrized spin states and spin coherent states to study collective decoherence in the implementation of various quantum algorithms. A simple method of implementing qu…
The influence of decoherence on the fidelity of quantum memories for photonic qubits based on dark-state polaritons in atomic ensembles is discussed. It is shown that despite the large entanglement of the collective storage states corresponding to single photons or nonclassical states of light the sensitivity to decoherence does not scale with the number of atoms. This is due to the existence of equivalence classes of storage states corresponding to states with the same number of dark-state polariton excitations but arbitrary excitations in other polariton modes. Several decoherence processes …
We investigate the decoherence of a superposition of symmetric collective internal states of an atomic ensemble due to inhomogeneous coupling to external control fields. For asymptotically large system, we find the characteristic decoherence rate scales as $\sqrt{N}$ with $N$ being the total number of atoms. Our results shed new light on attempts for quantum information processing and storage with atomic ensembles.
We investigate the influence of critical phenomena on two distinct physical processes: the center-of-mass decoherence of a single emitter, and the collective radiation of two emitters. We address these different physical mechanisms with an unified formalism relying on standard perturbation theory. We decompose the decoherence and the collective emission rates as a sum of two contributions, accounting for the spontaneous emission and for interference effects respectively. The former is enhanced by the Purcell effect when the material is in the vicinity of the emitter(s). The latter, associated …
We propose schemes that are efficient when each pair of qubits undergoes some imperfect collective decoherence with different baths. In the proposed scheme, each pair of qubits is first encoded in a decoherence-free subspace composed of two qubits. Leakage out of the encoding space generated by the imperfection is reduced by the quantum Zeno effect. Phase errors in the encoded bits generated by the imperfection are reduced by concatenation of the decoherence-free subspace with either a three-qubit quantum error correcting code that corrects only phase errors or a two-qubit quantum error detect…
Quantum decoherence has been studied using nuclear magnetic resonance(NMR). By choosing one qubit to simulate environment, we examine the decoherence behavior of two quantum systems: a one qubit system and a two qubit system. The experimental results show agreements with the theoretical predictions. Our experiment schemes can be generalized to the case that the environment is composed of multiple qubits.
The longitudinal coupling of a system to the bath usually induces the pure dephasing of the system. In this paper, we study the collective dephasing induced dissipation and decoherence in a coupled-qubit system with a common bath. It is shown that, compared with the case of the same system with independent baths, the interference between the dephasing processes of different qubits induced by the common bath significantly changes the dissipation of the system. For the system of two coupled qubits, the interference leads to a faster decoherence in the non-single-excitation subspaces and a slower…
This study deals with the further development of nuclear spin model of scalable quantum register, which presents the one-dimensional chain of the magnetic atoms with nuclear spins 1/2, substituting the basic atoms in the plate of nuclear spin-free easy-axis 3D antiferromagnet. The decoherence rates of one qubit state and entanglement state of two removed qubits and longitudinal relaxation rates are caused by the interaction of nuclear spins-qubits with virtual spin waves in antiferromagnet ground state were calculated. It was considered also one qubit adiabatic decoherence, is caused by the in…
We report on the application of a dynamic decoherence control pulse sequence on a nuclear quadrupole transition in $Pr^{3+}:Y_2SiO_5$ . Process tomography is used to analyse the effect of the pulse sequence. The pulse sequence was found to increase the decoherence time of the transition to over 30 seconds. Although the decoherence time was significantly increased, the population terms were found to rapidly decay on the application of the pulse sequence. The increase of this decay rate is attributed to inhomogeneity in the ensemble. Methods to circumvent this limit are discussed.
Decoherence-free subspaces (DFS) in systems of dipole-dipole interacting multi-level atoms are investigated theoretically. It is shown that the collective state space of two dipole-dipole interacting four-level atoms contains a four-dimensional DFS. We describe a method that allows to populate the antisymmetric states of the DFS by means of a laser field, without the need of a field gradient between the two atoms. We identify these antisymmetric states as long-lived entangled states. Further, we show that any single-qubit operation between two states of the DFS can be induced by means of a mic…
We study the generation of spin-squeezing in arrays of long-lived dipoles subject to collective emission, coherent drive, elastic interactions, and spontaneous emission. Counter-intuitively, it is found that the introduction of spontaneous emission leads to an enhancement of the achievable spin-squeezing, relative to that which emerges in the steady-state of the purely collective dynamics for the same model parameters. This behavior is connected to the dynamical self-tuning of the system through a dissipative phase transition that is present in the collective system alone. Our findings will be…
We theoretically study the decoherence and the dynamical decoupling control of nitrogen-vacancy center electron spins in high-purity diamond, where the hyperfine interaction with $^{13}$C nuclear spins is the dominating decoherence mechanism. The decoherence is formulated as the entanglement between the electron spin and the nuclear spins, which is induced by nuclear spin bath evolution conditioned on the electron spin state. The nuclear spin bath evolution is driven by elementary processes such as single spin precession and pairwise flip-flops. The importance of different elementary processes…
We propose a simple technique for the generation of arbitrary-sized Dicke states in a chain of trapped ions. The method uses global addressing of the entire chain by two pairs of delayed but partially overlapping laser pulses to engineer a collective adiabatic passage along a multi-ion dark state. Our technique, which is a many-particle generalization of stimulated Raman adiabatic passage (STIRAP), is decoherence-free with respect to spontaneous emission and robust against moderate fluctuations in the experimental parameters. Furthermore, because the process is very rapid, the effects of heati…
We propose easy implementable protocols for robust quantum key distribution with the collective dephasing channel or collective rotating channel. In these protocols, Bob only takes passive photon detection to measure the polarization qubits in the random bases. The source for the protocol with collective rotating channel is made by type 2 spontaneous parametric down conversion with random unitary rotation and phase shifter, no quantum disentangler is required. A simple proof for unconditionally security is shown.
By choosing H nucleus in Carbon-13 labelled trichloroethylene as one qubit environment, and two C nuclei as a two-qubit system, we have simulated quantum decoherence when the system lies in an entangled state using nuclear magnetic resonance (NMR). Decoupling technique is used to trace over the environment degrees of freedom. Experimental results show agreements with the theoretical predictions. Our experiment scheme can be generalized to the case that environment is composed of multiple qubits.
We consider decoherence of quantum registers, which consist of the qubits sited approximately periodically in space. The sites of the qubits are permitted to have a small random variance. We derive the explicit conditions under which the qubits can be assumed decohering independently. In other circumstances, the qubits are decohered cooperatively. We describe two kinds of collective decoherence. In each case, a scheme is proposed for reducing the collective decoherence. The schemes operate by encoding the input states of the qubits into some ''subdecoherent'' states.
We propose a novel architecture for scalable quantum computation based on quantum actuated decoherence-free (DF) qubits. Each qubit is encoded by the DF subspace of a nuclear spin pair and has long coherence time. A nitrogen-vacancy center in diamond is chosen as the quantum actuator to realize initialization, readout and universal control of DF qubits with fidelities higher than 99%. It reduces the challenge of classical interfaces from controlling and observing complex quantum systems down to a simple quantum actuator. Our scheme also provides a novel way to handle complex quantum systems.
The dynamical evolution of a quantum register of arbitrary length coupled to an environment of arbitrary coherence length is predicted within a relevant model of decoherence. The results are reported for quantum bits (qubits) coupling individually to different environments (`independent decoherence') and qubits interacting collectively with the same reservoir (`collective decoherence'). In both cases, explicit decoherence functions are derived for any number of qubits. The decay of the coherences of the register is shown to strongly depend on the input states: we show that this sensitivity is …
Many-body correlations can yield key insights into the nature of interacting systems; however, detecting them is often very challenging in many-particle physics, especially in nanoscale systems. Here, taking a phosphorus donor electron spin in a natural-abundance 29Si nuclear spin bath as our model system, we discover both theoretically and experimentally that many-body correlations in nanoscale nuclear spin baths produce identifiable signatures in the decoherence of the central spin under multiple-pulse dynamical decoupling control. We find that when the number of decoupling -pulses is odd, c…
We consider the decoherence of a single localized electron spin due to its coupling to the lattice nuclear spin bath in a semiconductor quantum computer architecture. In the presence of an external magnetic field and at low temperatures, the dominant decoherence mechanism is the spectral diffusion of the electron spin resonance frequency due to the temporally fluctuating random magnetic field associated with the dipolar interaction induced flip-flops of nuclear spin pairs. The electron spin dephasing due to this random magnetic field depends intricately on the quantum dynamics of the nuclear s…
The nuclear spin of a phosphorus atom in silicon has been used as a quantum bit in various quantum-information experiments. It has been proposed that this nuclear-spin qubit can be efficiently controlled by an ac electric field, when embedded in a two electron dot-donor setup subject to intrinsic or artificial spin-orbit interaction. Exposing the qubit to control electric fields in that setup exposes it to electric noise as well. In this work, we describe the effect of electric noise mechanisms, such as phonons and $1/f$ charge noise, and estimate the corresponding decoherence time scales of t…
We study how the decoherence of macroscopic objects is induced intrisinically by relativistic effect. With the degree of freedom of center of mass (CM) characterizing the collective quantum state of a macroscopic object (MO), it is found that a MO consisting of N particles can decohere with time scale no more than sqrt(N). Here, the special relativity can induce the coupling of the collective motion mode and the relative motion modes in an order of 1/c2, which intrinsically results in the above minimum decoherence.
Spin ensemble based hybrid quantum systems suffer from a significant degree of decoherence resulting from the inhomogeneous broadening of the spin transition frequencies in the ensemble. We demonstrate that this strongly restrictive drawback can be overcome simply by burning two narrow spectral holes in the spin spectral density at judiciously chosen frequencies. Using this procedure we find an increase of the coherence time by more than an order of magnitude as compared to the case without hole burning. Our findings pave the way for the practical use of these hybrid quantum systems for the pr…
Scaling theory of decoherence in Dicke superradiance
TU Darmstadt（达姆施塔特工业大学）；Friedrich-Alexander-Universität Erlangen-Nürnberg（埃尔朗根-纽伦堡大学）；Max Planck Institute for the Science of Light（马克斯·普朗克光科学研究所）；CNRS and Université de Strasbourg（法国国家科学研究中心与斯特拉斯堡大学）
We analyze the dynamics of entanglement due to decoherence in a system of two identical fermions with spin $3/2$ interacting with a global bosonic environment. We resort to an appropriate measure of the so-called fermionic entanglement to quantify the fermionic correlations, and compare its dynamics with that of a pair of distinguishable qubits immersed in the same environment. According to the system's initial state, three types of qualitatively different dynamics are identified: i) \textit{invariant regime}, corresponding to initial states that belong to a decoherence free subspace (DFS), wh…
We consider interactions that generate a universal set of quantum gates on logical qubits encoded in a collective-dephasing-free subspace, and discuss their implementations with trapped ions. This allows for the removal of the by-far largest source of decoherence in current trapped-ion experiments, collective dephasing. In addition, an explicit parametrization of all two-body Hamiltonians able to generate such gates without the system's state ever exiting the protected subspace is provided.
The realization of a network of quantum registers is an outstanding challenge in quantum science and technology. We experimentally investigate a network node that consists of a single nitrogen-vacancy (NV) center electronic spin hyperfine-coupled to nearby nuclear spins. We demonstrate individual control and readout of five nuclear spin qubits within one node. We then characterize the storage of quantum superpositions in individual nuclear spins under repeated application of a probabilistic optical inter-node entangling protocol. We find that the storage fidelity is limited by dephasing during…
The coherent behavior of the single electron and single nuclear spins of a defect center in diamond and a 13C nucleus in its vicinity, respectively, are investigated. The energy levels associated with the hyperfine coupling of the electron spin of the defect center to the 13C nuclear spin are analyzed. Methods of magnetic resonance together with optical readout of single defect centers have been applied in order to observe the coherent dynamics of the electron and nuclear spins. Long coherence times, in the order of microseconds for electron spins and tens of microseconds for nuclear spins, re…
We propose a method to adiabatically control an atomic ensemble using a decoherence-free subspace (DFS) within a dissipative cavity. We can engineer a specific eigenstate of the system's Lindblad jump operators by injecting a field into the cavity which deconstructively interferes with the emission amplitude of the ensemble. In contrast to previous adiabatic DFS proposals, our scheme creates a DFS in the presence of collective decoherence. We therefore have the ability to engineer states that have high multi-particle entanglements which may be exploited for quantum information science or metro…
Control of electron spin decoherence in contact with a mesoscopic bath of many interacting nuclear spins in an InAs quantum dot is studied by solving the coupled quantum dynamics. The nuclear spin bath, because of its bifurcated evolution predicated on the electron spin up or down state, measures the which-state information of the electron spin and hence diminishes its coherence. The many-body dynamics of nuclear spin bath is solved with a pair-correlation approximation. In the relevant timescale, nuclear pair-wise flip-flops, as elementary excitations in the mesoscopic bath, can be mapped int…
We develop in the weak coupling approximation a quasi-non-Markovian master equation and study the phenomenon of decoherence during the operation of a controlled-not (CNOT) quantum gate in a quantum computer model formed by a linear chain of three nuclear spins system with second neighbor Ising interaction between them. We compare with the behavior of the Markovian counterpart for temperature different from zero (thermalization) and at zero temperature for low and high dissipation rates. At low dissipation there is a very small difference between Markovian and quasi no-Markovian at any temperat…
The coupled-channels density-matrix technique for nuclear reaction dynamics, which is based on the Liouville-von Neumann equation with Lindblad dissipative terms, is developed with the inclusion of full angular momentum couplings. It allows a quantitative study of the role and importance of quantum decoherence in nuclear scattering. Formulae of asymptotic observables that can reveal effects of quantum decoherence are given. A method for extracting energy-resolved scattering information from the time-dependent density matrix is introduced. As an example, model calculations are carried out for t…
We study the quantum dynamics of a single qubit coupled to a bath of interacting spins as a model for decoherence in solid state quantum memories. The spin bath is described by the Lipkin-Meshkov-Glick model and the bath spins are subjected to a transverse magnetic field. We investigate the qubit interacting via either an Ising- or an XY-type coupling term to subsets of bath spins of differing size. The large degree of symmetry of the bath allows us to find parameter regimes where the initial qubit state is revived at well defined times after the qubit preparation. These times may become indep…
We study single- and multi-quantum transitions of the nuclear spins of ionized arsenic donors in silicon and find quadrupolar effects on the coherence times, which we link to fluctuating electrical field gradients present after the application of light and bias voltage pulses. To determine the coherence times of superpositions of all orders in the 4-dimensional Hilbert space, we use a phase-cycling technique and find that, when electrical effects were allowed to decay, these times scale as expected for a field-like decoherence mechanism such as the interaction with surrounding $^{29}$Si nuclea…
Solid-state quantum registers are exceptional for storing quantum information at room temperature with long coherence time. Nevertheless, practical applications toward quantum supremacy require even longer coherence time to allow for more complex algorithms. In this work we propose a quantum register that lies in a decoherence-free subspace to be implemented with color centers in diamond. The quantum information is encoded in two logical states composed of two nearby nuclear spins, while an electron spin is used as ancilla for initialization and control. Moreover, by tuning an off-axis magneti…
We study a model describing competition of interactions between $N$ two-level systems (TLSs) against decoherence. We apply it to analyze dye molecules in an optical microcavity, where molecular vibrations provide a local source for decoherence. Most interesting is the case when decoherence strongly affects each individual TLS, e.g. via broadening of emission lines as well as vibrational satellites, however its influence is strongly suppressed for large $N$ due to the interactions between TLSs. In this interaction dominated regime we find unique signatures in the emission spectrum, including st…
We present an optical device which is capable of heralding a variety of DFS states which protect against collective noise. Specifically, it can prepare all three basis states which span a DFS qutrit as well as an arbitrarily encoded DFS qubit state. We also discuss an interferometric technique for determining the amplitudes associated with an arbitrary encoding. The heralded state may find use in coherent optical systems which exhibit collective correlations.
Time-dependent density-matrix propagation is used to demonstrate, in a schematic model of an open quantum system, that the complex potential approach and the Lindblad dissipative dynamics are \emph{not} equivalent. While the former preserves coherence, it is destroyed in the Lindblad dissipative dynamics. Quantum decoherence is the key aspect that makes the difference between the two approaches, indicating that the complex potential model is inadequate for a consistent description of open quantum-system dynamics. It is suggested that quantum decoherence should always be explicitly included whe…
Hybrid qubit systems combining electronic spins with nearby ("proximate") nuclear spin registers offer a promising avenue towards quantum information processing, with even multi-spin error correction protocols recently demonstrated in diamond. However, for the important platform offered by spins of donor atoms in cryogenically-cooled silicon,decoherence mechanisms of $^{29}$Si proximate nuclear spins are not yet well understood.The reason is partly because proximate spins lie within a so-called "frozen core" region where the donor electronic hyperfine interaction strongly suppresses nuclear dy…
We propose a model for spectral diffusion of localized spins in semiconductors due to the dipolar fluctuations of lattice nuclear spins. Each nuclear spin flip-flop is assumed to be independent, the rate for this process being calculated by a method of moments. Our calculated spin decoherence time $T_{M}=0.64$ ms for donor electron spins in Si:P is a factor of two longer than spin echo decay measurements. For $^{31}$P nuclear spins we show that spectral diffusion is well into the motional narrowing regime. The calculation for GaAs quantum dots gives $T_{M}=10-50$ $μ$s depending on the quantum …
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.
It is discussed the decoherence problems in ensemble large-scale solid state NMR quantum computer based on the array of P donor atoms having nuclear spin I = 1/2. It is considered here, as main mechanisms of decoherence for low temperature (< 0.1 K), the adiabatic processes of random modulation of qubit resonance frequency determined by secular part of nuclear spin interaction with electron spin of the basic atoms, with impurity paramagnetic atoms and also with nuclear spins of impurity diamagnetic atoms. It was made estimations of allowed concentrations of magnetic impurities and of spin temp…
In this paper, we study the electron spin decoherence of single defects in silicon carbide (SiC) nuclear spin bath. We find that, although the natural abundance of $^{29}\rm{Si}$ ($p_{\rm{Si}}=4.7\%$) is about 4 times larger than that of $^{13}{\rm C}$ ($p_{\rm{C}}=1.1\%$), the electron spin coherence time of defect centers in SiC nuclear spin bath in strong magnetic field ($B>300~\rm{Gauss}$) is longer than that of nitrogen-vacancy (NV) centers in $^{13}{\rm C}$ nuclear spin bath in diamond. The reason for this counter-intuitive result is the suppression of heteronuclear-spin flip-flop proces…
Decoherence of electron spins in nanoscale systems is important to quantum technologies such as quantum information processing and magnetometry. It is also an ideal model problem for studying the crossover between quantum and classical phenomena. At low temperatures or in light-element materials where the spin-orbit coupling is weak, the phonon scattering in nanostructures is less important and the fluctuations of nuclear spins become the dominant decoherence mechanism for electron spins. Since 1950s, semiclassical noise theories have been developed for understanding electron spin decoherence.…
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…
Collective decoherence is possible if the departure between quantum bits is smaller than the effective wave length of the noise field. Collectivity in the decoherence helps us to devise more efficient quantum codes. We present a class of optimal quantum codes for preventing collective amplitude damping to a reservoir at zero temperature. It is shown that two qubits are enough to protect one bit quantum information, and approximately $L+ 1/2 \log_2((πL)/2)$ qubits are enough to protect $L$ qubit information when $L$ is large. For preventing collective amplitude damping, these codes are much mor…
Recent work has proposed that the interaction between ordinary matter and a stochastic gravitational background can lead to the decoherence of large aggregates of ordinary matter. In this work we point out that these arguments can be carried over to a stochastic neutrino background but with the Planck scale of the gravitational decoherence replaced by the weak scale. This implies that it might be possible to observe such neutrino induced decoherence on a small, microscopic system rather than a macroscopic system as is the case for gravitationally induced decoherence. In particular we suggest t…
An operator sum representation is derived for a decoherence-free subspace (DFS) and used to (i) show that DFSs are the class of quantum error correcting codes (QECCs) with fixed, unitary recovery operators, and (ii) find explicit representations for the Kraus operators of collective decoherence. We demonstrate how this can be used to construct a concatenated DFS-QECC code which protects against collective decoherence perturbed by independent decoherence. The code yields an error threshold which depends only on the perturbing independent decoherence rate.
We demonstrate that for an ensemble of qudits, subjected to collective decoherence in the form of perfectly correlated random SU(d) unitaries, quantum superpositions stored in the decoherence free subspace are fully immune against the removal of one particle. This provides a feasible scheme to protect quantum information encoded in the polarization state of a sequence of photons against both collective depolarization and one photon loss, and can be demonstrated with photon quadruplets using currently available technology.
We study the dynamics of entanglement in spin gases. A spin gas consists of a (large) number of interacting particles whose random motion is described classically while their internal degrees of freedom are described quantum-mechanically. We determine the entanglement that occurs naturally in such systems for specific types of quantum interactions. At the same time, these systems provide microscopic models for non--Markovian decoherence: the interaction of a group of particles with other particles belonging to a background gas are treated exactly, and differences between collective and non--co…
Phosphorus-doped silicon single crystals with 0.19 % <= f <= 99.2 %, where f is the concentration of 29^Si isotopes, are measured at 8 K using a pulsed electron spin resonance technique, thereby the effect of environmental 29^Si nuclear spins on the donor electron spin is systematically studied. The linewidth as a function of f shows a good agreement with theoretical analysis. We also report the phase memory time T_M of the donor electron spin dependent on both f and the crystal axis relative to the external magnetic field.
We analyze the interplay of chaos, entanglement and decoherence in a system of qubits whose collective behaviour is that of a quantum kicked top. The dynamical entanglement between a single qubit and the rest can be calculated from the mean of the collective spin operators. This allows the possibility of efficiently measuring entanglement dynamics in an experimental setting. We consider a deeply quantum regime and show that signatures of chaos are present in the dynamical entanglement for parameters accessible in an experiment that we propose using cold atoms. The evolution of the entanglement…
