A. Dementsov
One mechanism of decoherence of anyon qubit due to interaction with edge states is considered. The calculations are made at low temperature in Markovian and "short-time" approximation. Two approximations are compared.
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Noise-induced decoherence-free zones for anyons
该研究建立任意子系统的随机 Lindblad 框架，揭示相关矩阵本征结构如何形成无退相干子空间，并证明平衡两格点模型中最优保护角恒为 $θ^\star=π/2$。
Decoherence through Ancilla Anyon Reservoirs
本文通过辅助任意子体库研究拓扑序临界边界的退相干，将其映射为带层间线缺陷的双层临界伊辛模型，并揭示了不同任意子缺陷的相关性、边缘性及边界Rényi熵的对数标度行为。
Anyons, quasiparticles living in two-dimensional spaces with exotic exchange statistics, can serve as the fundamental units for fault-tolerant quantum computation. However, experimentally demonstrating anyonic statistics is a challenge due to the technical limitations of current experimental platforms. Here, we take a state perpetration approach to mimic anyons in the Kitaev lattice model using a 7-qubit nuclear magnetic resonance quantum simulator. Anyons are created by dynamically preparing the ground and excited states of the 7-qubit Kitaev lattice model, and are subsequently braided along …
Proposals to measure non-Abelian anyons in a superconductor by quantum interference of vortices suffer from the predominantly classical dynamics of the normal core of an Abrikosov vortex. We show how to avoid this obstruction using coreless Josephson vortices, for which the quantum dynamics has been demonstrated experimentally. The interferometer is a flux qubit in a Josephson junction circuit, which can nondestructively read out a topological qubit stored in a pair of anyons --- even though the Josephson vortices themselves are not anyons. The flux qubit does not couple to intra-vortex excita…
Statistical Mechanics and Symmetries of Non-Abelian Anyon Proliferation: From Deformation to Decoherence
通过统计力学模型和蒙特卡洛模拟，研究非阿贝尔任意子增殖导致拓扑序失稳的机制，发现两个非阿贝尔任意子物种的增殖会寄生凝聚共享的阿贝尔融合结果，破坏拓扑序。
The anyonic excitations of topological two-body color code model are used to implement a set of gates. Because of two-body interactions, the model can be simulated in optical lattices. The excitations have nontrivial mutual statistics, and are coupled to nontrivial gauge fields. The underlying lattice structure provides various opportunities for encoding the states of a logical qubit in anyonic states. The interactions make the transition between different anyonic states, so being logical operation in the computational bases of the encoded qubit. Two-qubit gates can be performed in a topologic…
We investigate decoherence channels that are modelled as a sequence of collisions of a quantum system (e.g., a qubit) with particles (e.g., qubits) of the environment. We show that collisions induce decoherence when a bi-partite interaction between the system qubit and an environment (reservoir) qubit is described by the controlled-U unitary transformation (gate). We characterize decoherence channels and in the case of a qubit we specify the most general decoherence channel and derive a corresponding master equation. Finally, we analyze entanglement that is generated during the process of deco…
Engineering complex non-Abelian anyon models with simple physical systems is crucial for topological quantum computation. Unfortunately, the simplest systems are typically restricted to Majorana zero modes (Ising anyons). Here we go beyond this barrier, showing that the $\mathbb{Z}_4$ parafermion model of non-Abelian anyons can be realized on a qubit lattice. Our system additionally contains the Abelian $D(\mathbb{Z}_4)$ anyons as low-energetic excitations. We show that braiding of these parafermions with each other and with the $D(\mathbb{Z}_4)$ anyons allows the entire $d=4$ Clifford group t…
This paper has been withdrawn by the author.
We study the relation between the sudden death and revival of the entanglement of two qubits in a common squeezed reservoir, and the normal decoherence, by getting closer to the Decoherence Free Subspace and calculating the effect on the death and revival times.
Anyons are exotic quasiparticles living in two dimensions that do not fit into the usual categories of fermions and bosons, but obey a new form of fractional statistics. Following a recent proposal [Phys. Rev. Lett. 98, 150404 (2007)], we present an experimental demonstration of the fractional statistics of anyons in the Kitaev spin lattice model using a photonic quantum simulator. We dynamically create the ground state and excited states (which are six-qubit graph states) of the Kitaev model Hamiltonian, and implement the anyonic braiding and fusion operations by single-qubit rotations. A pha…
Topological quantum computation is an implementation of a quantum computer in a way that radically reduces decoherence. Topological qubits are encoded in the topological evolution of two-dimensional quasi-particles called anyons and universal set of quantum gates can be constructed by braiding these anyons yielding to a topologically protected circuit model. In the present study we remind the basics of this emerging quantum computation scheme and illustrate how a topological qubit built with three Fibonacci anyons might be adopted to achieve leakage free braiding gate by exchanging the anyons …
When the nonlinearity of nanomechanical resonator is not negligible, the quantum decoherence of charge qubit is studied analytically. Using nonlinear Jaynes-Cummings model, one explores the possibility of being quantum data bus for nonlinear nanomechanical resonator, the nonlinearity destroys the dynamical quantum information-storage and maintains the revival of quantum coherence of charge qubit. With the calculation of decoherence factor, we demonstrate the influence of the nonlinearity of nanomechanical resonator on engineered decoherence of charge qubit.
In this paper we investigate the short-time decoherence of single Josephson charge qubit (JCQ). The measure of decoherence is chosen as the maximum norm of the deviation density operator. It is shown that when the temperature low enough (for example T=30mK), within the elementary gate-operation time tau{g}~12.7ps, the decoherence is smaller than 0.0001 at present setup of JCQ. The Josephson charge qubit is suitable to take the blocks for quantum computations according to the DiVincenzo low decoherence criterion.
At first, we generally investigate the short-time decoherence of a qubit nonlinearly coupling with a bath. The measure of the decoherence is chosen as the maximum norm of the deviation density operator. Then we concretely investigate the Josephson charge qubit (JCQ) model. It is shown that at the temperature T=30mK, the loss of fidelity (due to decoherence) of the JCQ is bigger than the DiVincenzo low decoherence criterion. The decoherence will decrease with the decrease of the experimental temperature. When the temperature decreases to T=0.3mK the DiVincenzo low decoherence criterion can be s…
In this paper we investigate decoherence times of a double quantum dot (DQD) charge qubit due to it coupling with acoustic phonon baths. We individually consider the acoustic piezoelectric as well as deformation coupling phonon baths in the qubit environment. The decoherence times are calculated with two kinds of methods. One of them is based on the qusiadiabatic propagator path integral (QUAPI) and the other is based on Bloch equations, and two kinds of results are compared. It is shown that the theoretical decoherence times of the DQD charge qubit are shorter than the experimental reported r…
Case Study of Decoherence Times of Transmon Qubit
本研究探讨了transmon qubit的拓扑结构，并通过数值方法计算了由噪声、磁通及临界电流噪声引起的退相干时间，以应对超导量子计算机中退相干时间过短的瓶颈。
Using the numerical path integral method we investigate the decoherence and relaxation of qubits in spin-boson (SB) and spin-intermediate harmonic oscillator (IHO)-bath (SIB) models. The cases that the environment baths with low and medium frequencies are investigated. It is shown that the qubits in SB and SIB models have the same decoherence and relaxation as the baths with low frequencies. However, the qubits in the two models have different decoherence and relaxation as the baths with medium frequencies. The decoherence and relaxation of the qubit in SIB model can be modulated through chang…
Anyons have exotic statistical properties, fractional statistics, differing from Bosons and Fermions. They can be created as excitations of some Hamiltonian models. Here we present an experimental demonstration of anyonic fractional statistics by simulating a version of the Kitaev spin lattice model proposed by Han et al[Phys. Rev.Lett. 98, 150404 (2007)] using an NMR quantum information processor. We use a 7-qubit system to prepare a 6-qubit pseudopure state to implement the ground state preparation and realize anyonic manipulations, including creation, braiding and anyon fusion. A $π/2\times…
We study a model of dephasing (decoherence) in a two-state quantum system (qubit) coupled to a bath of harmonic oscillators. An exact analytic solution for the reduced dynamics of a two-state system in this model has been obtained previously for factorizing initial states of the combined system. We show that the model admits exact solutions for a large class of correlated initial states which are typical in the theory of quantum measurements. We derive exact expressions for the off-diagonal elements of the qubit density matrix, which hold for an arbitrary strength of coupling between the qubit…
We analyze robustness of decoherence-free (DF) subspace in charge qubits when there are a local structure and non-uniformity that violate collective decoherence measurement condition. We solve master equations of up to four charge qubits and a detector as two serially coupled quantum point contacts (QPC) with an island structure. We show that robustness of DF states is strongly affected by local structure as well as by non-uniformities of qubits.
Consistent Simulation of Fibonacci Anyon Braiding within a Qubit Quasicrystal Inflation Code
提出基于一维准晶体膨胀码（QIC）的框架模拟斐波那契任意子编织，推导出局部3量子比特门$B_{gate}$，大幅降低电路深度，并在IBM量子处理器上验证了算法可行性。
Using the numerical path integral method we investigate the decoherence and relaxation of qubits coupled to an Ohmic bath directly and via an intermediate harmonic oscillator (IHO). Here, we suppose the oscillation frequencies of the bath modes are higher than the IHO's. When we choose suitable parameters the qubits in the two models may have almost same decoherence and relaxation times. However, the decoherence and relaxation times of the qubit in the qubit-IHO-bath model can be modulated through changing the coupling coefficients of the qubit-IHO and IHO-bath and the oscillation frequency of…
We study the suppression of noise-induced phase decoherence in a single atomic qubit by employing pulse sequences. The atomic qubit is composed of a single neutral atom in a far-detuned optical dipole trap and the phase decoherence may originate from the laser intensity and beam pointing fluctuations as well as magnetic field fluctuations. We show that suitable pulse sequences may prolongate the qubit coherence time substantially as comparing to the conventional spin echo pulse.
Phases of Floquet code under local decoherence
本文研究了Floquet码在局部退相干下的相位特性，推导了相关模型并提出诊断方法，揭示了其在阈值下的稳健性及相变行为。
Fibonacci anyons are non-Abelian particles for which braiding is universal for quantum computation. Reichardt has shown how to systematically generate nontrivial braids for three Fibonacci anyons which yield unitary operations with off-diagonal matrix elements that can be made arbitrarily small in a particular natural basis through a simple and efficient iterative procedure. This procedure does not require brute force search, the Solovay-Kitaev method, or any other numerical technique, but the phases of the resulting diagonal matrix elements cannot be directly controlled. We show that despite …
Non-adiabatic holonomic quantum gate in decoherence-free subspaces is of greatly practical importance due to its built-in fault tolerance, coherence stabilization virtues, and short run-time. Here we propose some compact schemes to implement two- and three-qubit controlled unitary quantum gates and Fredkin gate. For the controlled unitary quantum gates, the unitary operator acting on the target qubit is an arbitrary single-qubit gate operation. The controlled quantum gates can be directly implemented using non-adiabatic holonomy in decoherence-free subspaces and the required resource for the d…
It is known that a quantum system with finite degrees of freedom can simulate a composite of a system and an environment if the state of the hypothetical environment is randomized by external manipulation. We show theoretically that any phase decoherence phenomena of a single qubit can be simulated with a two-qubit system and demonstrate experimentally two examples: one is phase decoherence of a single qubit in a transmission line, and the other is that in a quantum memory. We perform NMR experiments employing a two-spin molecule and clearly measure decoherence for both cases. We also prove ex…
We propose a quantum-information processor that consists of decoherence-free logical qubits encoded into arrays of dipole-coupled qubits. High-fidelity single-qubit operations are performed deterministically within a decoherence-free subsystem without leakage via global addressing of bichromatic laser fields. Two-qubit operations are realized locally with four physical qubits, and between separated logical qubits using linear optics. We show how to prepare cluster states using this method. We include all non-nearest-neighbor effects in our calculations, and we assume the qubits are not located…
We investigate the decay of entanglement, due to decoherence, of multi-qubit systems that are initially prepared in highly (in some cases maximally) entangled states. We assume that during the decoherence processes each qubit of the system interacts with its own, independent environment. We determine, for systems with a small number of qubits and for various decoherence channels, the initial states exhibiting the most robust entanglement. We also consider a restricted version of this robustness optimization problem, only involving states equivalent under local unitary transformations to the |G…
In this paper we investigate decoherence time of superconducting Josephson charge qubit (JCQ). Two kinds of methods, iterative tensor multiplication (ITM) method derived from the qusiadiabatic propagator path integral (QUAPI) and Bloch equations method are used. Using the non-Markovian ITM method we correct the decoherence time predicted by Bloch equations method. By comparing the exact theoretical result with the experimental data we suggest that the Ohmic noise plays the central role to the decoherence of the JCQ.
A theory of dynamical control by modulation for optimal decoherence reduction is developed. It is based on the non-Markovian Euler-Lagrange equation for the energy-constrained field that minimizes the average dephasing rate of a qubit for any given dephasing spectrum.
We study the time evolution of a qubit linearly coupled with a quantum environment under a sequence of short pi pulses. Our attention is focused on the case where qubit-environment interactions induce the decoherence with population decay. We assume that the environment consists of a set of bosonic excitations. The time evolution of the reduced density matrix for the qubit is calculated in the presence of periodic short pi pulses. We confirm that the decoherence is suppressed if the pulse interval is shorter than the correlation time for qubit-environment interactions.
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.
In this paper we investigate a open two-qubit model whose dynamics is not exactly solvable. When the initial state is the maximum entangled state, as the exactly solvable open two-qubit model [D. Tolkunov and V. Privman, Phys. Rev. A 71, 060308(R) (2005)], the decay of entanglement of formation of the model, expressed by concurrence is also governed by the product of suppression factors describing decoherence of the subsystems (qubits). However, if the initial state is not the maximum entangled state, its concurrence will decrease faster than the product of the suppression factors describing d…
In this paper we study the decoherence and purity of a driven solid-state qubit in the Ohmic bath by using the method based on the master equation. At first, instead of solving the master equation we investigate the coefficients of the equation which describe the shift in frequency, diffusive, decoherence, and so on. It is shown that one of the coefficients (we called it decoherence coefficient) is crucial to the decoherence of the qubit in the model. Then we investigate the evolution of the purity of the state in the model. From the analysis of the purity we see that the decoherence time of t…
We study one-way quantum deficit of two-qubit $X$ states systematically from analytical derivations. An effective approach to compute one-way quantum deficit of two-qubit $X$ states has been provided. Analytical results are presented as for detailed examples. Moreover, we demonstrate the decoherence of one-way quantum deficit under phase damping channel.
Different from the previous works on generating entangled states, this work is focused on how to transfer the prepared entangled states onto memory qubits for protecting them against decoherence. We here consider a physical system consisting of $n$ operation qubits and $2n$ memory qubits placed in a cavity or coupled to a resonator. A method is presented for transferring $n$-qubit Greenberger-Horne-Zeilinger (GHZ) entangled states from the operation qubits (i.e., information processing cells) onto the memory qubits (i.e., information memory elements with long decoherence time). The transferred…
We analyze decoherence of a quantum register in the absence of non-local operations i.e. of $n$ non-interacting qubits coupled to an environment. The problem is solved in terms of a sum rule which implies linear scaling in the number of qubits. Each term involves a single qubit and its entanglement with the remaining ones. Two conditions are essential: first decoherence must be small and second the coupling of different qubits must be uncorrelated in the interaction picture. We apply the result to a random matrix model, and illustrate its reach considering a GHZ state coupled to a spin bath.
Decoherence may significantly affect the polarization state of optical pulses propagating in dispersive media because of the unavoidable presence of more than a single frequency in the envelope of the pulse. Here we report on the suppression of polarization decoherence in a ring cavity obtained by properly retooling for photonic qubits the ``bang-bang'' protection technique already employed for nuclear spins and nuclear-quadrupole qubits. Our results show that bang-bang control can be profitably extended to quantum information processes involving flying polarization qubits.
We study non-perturbatively the time evolution of a qubit subject to amplitude-damping noise. We show that at strong coupling the qubit decoherence can be quenched owing to large environment feedbacks, such that the qubit can evolve coherently even in the long-time limit. As an application, we show that for a quantum channel that consists of two independent qubits subject to uncorrelated local amplitude-damping noises, it can maintain at strong coupling finite entanglement and better than classical teleportation fidelity at long times.
We study quantum teleportation between two different types of optical qubits using hybrid entanglement as a quantum channel under decoherence effects. One type of qubit employs the vacuum and single photon states for the basis, called a single-rail single-photon qubit, and the other utilizes coherent states of opposite phases. We find that teleportation from a single-rail single-photon qubit to a coherent state qubit is better than the opposite direction in terms of fidelity and success probability. We compare our results with those using a different type of hybrid entanglement between a polar…
In this paper we investigate the short-time decoherence from Ohmic and 1/f noise of single Josephson charge qubit (JCQ). At first, we use the short-time approximation to obtain the dynamics of the open JCQ. Then we calculate the decoherence the measure of which is chosen as the maximum norm of the deviation density operator. It is shown that the decoherence from 1/f noise plays the central role. The total decoherence from Ohmic and 1/f noise is serious at present experiential conditions according to the DiVincenzo criterion.
The thesis is contributed to the study of the decoherence dynamics of dissipative qubit systems. We reveal the profound impact of the formation of a bound state between the qubit and its local environment on the decoherence dynamics of qubit system in non-Markovian regime. We find that the decoherence can be suppressed greatly under the non-Markovian dynamics when the bound state is formed. Consequently, the entanglement can be partially preserved in the steady state. A criterion on this decoherence/disentanglement suppression is given explicitly. It can give a useful guideline on the decohere…
We propose a geometric phase gate in a decoherence-free subspace with trapped ions. The quantum information is encoded in the Zeeman sublevels of the ground-state and two physical qubits to make up one logical qubit with ultra long coherence time. Single- and two-qubit operations together with the transport and splitting of linear ion crystals allow for a robust and decoherence-free scalable quantum processor. For the ease of the phase gate realization we employ one Raman laser field on four ions simultaneously, i.e. no tight focus for addressing. The decoherence-free subspace is left neither …
We summarize our results on decoherence for short- to intermediate-time dynamics of an externally controlled two-state quantum system - a qubit - interacting with thermal bosonic environment. The developed approximation schemes are illustrated for an adiabatic model with time-dependent gate control, and for a model with rotating-wave gate function.
We investigate the time evolution of entanglement for bipartite systems of arbitrary dimensions under the influence of decoherence. For qubits, we determine the precise entanglement decay rates under different system-environment couplings, including finite temperature effects. For qudits, we show how to obtain upper bounds for the decay rates and also present exact solutions for various classes of states.
Photons in cavities have been already used for the realization of simple quantum gates [Q.A. Turchette, Phys. Rev. Lett. 75,4710 (1995)]. We present a method for combatting decoherence in this case.
Quantum decoherence happens when the system interacts with the environment. Quantum correlation behaviours in the two-qubit spin squeezing model are studied under the influence of intrinsic decoherence. Quantitative results were determined, which depend on parameters of the physical system by checking different quantifiers of quantum correlation such as entanglement, local quantum uncertainty, trace distance discord and uncertainty-induced quantum nonlocality. We show that the entanglement suffers from intrinsic decoherence and exhibits sudden death, whereas the other measures are more robust …
Quantum properties of the probes used to estimate a classical parameter can be used to attain accuracies that beat the standard quantum limit. When qubits are used to construct a quantum probe, it is known that initializing $n$ qubits in an entangled "cat state," rather than in a separable state, can improve the measurement uncertainty by a factor of $1/\sqrt{n}$. We investigate how the measurement uncertainty is affected when the individual qubits in a probe are subjected to decoherence. In the face of such decoherence, we regard the rate $R$ at which qubits can be generated and the total dur…
In the viewpoint of quasi normal modes, we describe a novel decoherence mechanism of charge qubit of Josephson Junctions (JJ) in a lossy micro-cavity, which can appear in the realistic experiment for quantum computation based on JJ qubit. We show that the nonlinear coupling of a charge qubit to quantum cavity field can result in an additional dissipation of resonant mode due to its effective interaction between those non-resonant modes and a resonant mode, which is induced by the charge qubit itself. We calculate the characterized time of the novel decoherence by making use of the system plus …
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.
We investigate the decoherence in a $\mathcal{PT}$-symmetric qubit coupled with a bosonic bath. Using cannonical transformations, we map the non-Hermitian Hamiltonian representing the$\mathcal{PT}$-symmetric qubit to a spin boson model. Identifying the parameter α that demarcates the hermiticity and non-hermiticity in the model, we show that the qubit does not decohere at the transition from real eigen spectrum to complex eigen spectrum. Using a general class of spectral densities, the strong suppression of decoherence is observed due to both vaccum and thermal fluctuations of the bath, and in…
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…
The decoherence of two initially entangled qubits in a non-Markovian reservoir has been investigated exactly without Born Markovian approximation and rotating-wave approximation(RWA). The non-perturbative quantum master equation is derived and its exact solution is obtained. The decoherence behaviors of two qubits, initially entangled in Bell states, has been investigated in three different cases of parameters. The results show that the counter-rotating wave terms have great influence on the decoherence behavior, and there are differences between the exact solution of the Hamiltonian with RWA …
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.
We study the entanglement of the superconducting charge qubit with the quantized electromagnetic field in a microwave cavity. It can be controlled dynamically by a classical external field threading the SQUID within the charge qubit. Utilizing the controllable quantum entanglement, we can demonstrate the dynamic process of the quantum storage of information carried by charge qubit. On the other hand, based on this engineered quantum entanglement, we can also demonstrate a progressive decoherence of charge qubit with quantum jump due to the coupling with the cavity field in quasi-classical stat…
It is commonly stated that decoherence in open quantum systems is due to growing entanglement with an environment. In practice, however, surprisingly often decoherence may equally well be described by random unitary dynamics without invoking a quantum environment at all. For a single qubit, for instance, pure decoherence (or phase damping) is always of random unitary type. Here, we construct a simple example of true quantum decoherence of two qubits: we present a feasible phase damping channel of which we show that it cannot be understood in terms of random unitary dynamics. We give a very int…
In this article we develop, step by step, the framework for universal dynamical control of two-level systems (TLS) or qubits experiencing amplitude- or phase-noise (AN or PN) due to coupling to a thermal bath. A comprehensive arsenal of modulation schemes is introduced and applied to either AN or PN, resulting in completely analogous formulae for the decoherence rates, thus underscoring the unified nature of this universal formalism. We then address the extension of this formalism to multipartite decoherence control, where symmetries are exploited to overcome decoherence.
We examine the influence of environmental interactions on simple quantum systems by obtaining the exact reduced dynamics of a qubit coupled to a one-dimensional spin bath. In contrast to previous studies, both the qubit-bath coupling and the nearest neighbor intrabath couplings are taken as the spin-flip XX-type. We first study the Rabi oscillations of a single qubit with the spin bath prepared in a spin coherent state, finding that nonresonance and finite intrabath interactions have significant effects on the qubit dynamics. Next, we discuss the bath-induced decoherence of the qubit when the …
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