We analyse dissipation in quantum computation and its destructive impact on efficiency of quantum algorithms. Using a general model of decoherence, we study the time evolution of a quantum register of arbitrary length coupled with an environment of arbitrary coherence length. We discuss relations between decoherence and computational complexity and show that the quantum factorization algorithm must be modified in order to be regarded as efficient and realistic.
A method is described for calculating the heat generated in a quantum computer due to loss of quantum phase information. Amazingly enough, this heat generation can take place at zero temperature. and may explain why it is impossible to extract energy from vacuum fluctuations. Implications for optical computers and quantum cosmology are also briefly discussed.
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…
As revealed by discussions of principle on energy dissipation by computers, logic imposes constraints on physical systems designed for a logical function. We define a notion of logical dissipation for a finite automaton. We discuss the constraints associated with physical implementation of automata and exhibit the role played by modularity for testability. As a result, practical computers, which are necessarily modular, dissipate proportionally to computation time.
In this paper, we propose an approach to accelerate the dissipation dynamics for quantum state generation with Lyapunov control. The strategy is to add target-state-related coherent control fields into the dissipation process to intuitively improve the evolution speed. By applying the current approach, without losing the advantages of dissipation dynamics, the target stationary states can be generated in a much shorter time as compared to that via traditional dissipation dynamics. As a result, the current approach containing the advantages of coherent unitary dynamics and dissipation dynamics …
We show that at least 2kTln2 of heat dissipation per qubit occurs in measurement-based quantum computation according to Landauer's principle. This result is derived by using only the fundamental fact that quantum physics respects the no-signaling principle.
The effects of dissipation on a holonomic quantum computation scheme are analyzed within the quantum-jump approach. We extend to the non-Abelian case the refocusing strategies formerly introduced for (Abelian) geometric computation. We show how double loop symmetrization schemes allow one to get rid of the unwanted influence of dissipation in the no-jump trajectory.
Effects on the spectra of the quantum bouncer due to dissipation are given when a linear or quadratic dissipation is taken into account. Classical constant of motions and Hamiltonians are deduced for these systems and their quantized eigenvalues are estimated through perturbation theory. we found some differences when we compare the eigenvalues of these two quantities.
We investigate the influence of dissipation and decoherence on quantum Darwinism by generalizing Zurek's original qubit model of decoherence and the establishment of pointer states (Zurek, Nature Physics 5, 181 - 188 (2009)). Our model allows for repeated multiple qubit-qubit couplings between system and environment which are described by randomly applied two-qubit quantum operations inducing entanglement, dissipation and dephasing. The resulting stationary qubit states of system and environment are investigated. They exhibit the intricate influence of entanglement generation, dissipation and …
In this paper an extended scalability condition is proposed to achieve the ground-state stability for a class of multipartite quantum systems which may involve two-body interactions, and an explicit procedure to construct the dissipation control is presented. Moreover, we show that dissipation control can be used for automatic error correction in addition to stabilization. We demonstrate the stabilization and error correction of three-qubit repetition code states using dissipation control.
Quantum information processing is in real systems often limited by dissipation, stemming from remaining uncontrolled interaction with microscopic degrees of freedom. Given recent experimental progress, we consider weak dissipation, resulting in a small error probability per operation. Here, we find a simple formula for the fidelity reduction of any desired quantum operation. Interestingly, this reduction is independent of the specific operation; it depends only on the operation time and the dissipation. Using our formula, we investigate the situation where dissipation in different parts of the…
We study the connection between dissipation and reality in macroscopic quantum systems. We present the following scenario; if we consider the dynamics of a `partial' wave function, the dissipation is represented as a nonlocal term and it causes destructive interference to suppress the quantum fluctuation. Using the variational method, we confirm that this dissipation term is a reasonable extension of the standard (Schrödinger) description for isolated systems, from which we also derive the classical action. Consequently, in macroscopic systems, the states whose time-integrated dissipation take…
We introduce and study the adiabatic dynamics of free-fermion models subject to a local Lindblad bath and in the presence of a time-dependent Hamiltonian. The merit of these models is that they can be solved exactly, and will help us to study the interplay between non-adiabatic transitions and dissipation in many-body quantum systems. After the adiabatic evolution, we evaluate the excess energy (average value of the Hamiltonian) as a measure of the deviation from reaching the target final ground state. We compute the excess energy in a variety of different situations, where the nature of the b…
We investigate quantum control of the dissipation of entanglement under environmental decoherence. We show by means of a simple two-qubit model that standard control methods - coherent or open-loop control - will not in general prevent entanglement loss. However, we propose a control method utilising a Wiseman-Milburn feedback/measurement control scheme which will effectively negate environmental entanglement dissipation.
The quantum statistical dynamics of a position coordinate x coupled to a reservoir requires theoretically two copies of the position coordinate within the reduced density matrix description. One coordinate moves forward in time while the other coordinate moves backward in time. It is shown that quantum dissipation induces, in the plane of the forward and backward motions, a noncommutative geometry. The noncommutative geometric plane is a consequence of a quantum dissipation induced phase interference which is closely analogous to the Aharanov-Bohm effect.
We report on a systematic geometric procedure, built up on solutions designed in the absence of dissipation, to mitigate the effects of dissipation in the control of open quantum systems. Our method addresses a standard class of open quantum systems modeled by non-Hermitian Hamiltonians. It provides the analytical expression of the extra magnetic field to be superimposed to the driving field in order to compensate the geometric distortion induced by dissipation, and produces an exact geometric optimization of fast population transfer. Interestingly, it also preserves the robustness properties …
Dissipation can be used as a resource to control and simulate quantum systems. We discuss a modular model based on fast dissipation capable of performing universal quantum computation, and simulating arbitrary Lindbladian dynamics. The model consists of a network of elementary dissipation-generated modules and it is in principle scalable. In particular, we demonstrate the ability to dissipatively prepare all single qubit gates, and the CNOT gate; prerequisites for universal quantum computing. We also show a way to implement a type of quantum memory in a dissipative environment, whereby we can …
We propose a new kind of individual attack, based on randomly selected dissipation, on Bennett-Brassard 1984 protocol of practical quantum key distribution (QKD) system with lossy and noisy quantum channel. Since an adversary with super quantum channel can disguise loss and errors induced by his attack as that of the system, he can obtain innegligible amount of information for a practical QKD system, without being detected by legal participants.
The energy loss due to a quadratic velocity dependent force on a quantum particle bouncing on a perfectly reflecting surface is obtained for a full cycle of motion. We approach this problem by means of a new effective phenomenological Hamiltonian which corresponds to the actual energy of the system and obtained the correction to the eigenvalues of the energy in first order quantum perturbation theory for the case of weak dissipation.
We propose a realistic scheme to determine the quantum state of a single mode cavity field even after it has started to decay due to the coupling with an environment. Although dissipation destroys quantum coherences, we show that at zero temperature enough information about the initial state remains, in an observable quantity, to allow the reconstruction of its Wigner function.
We analyze truncation of coherent states up to a single-photon Fock state by applying linear quantum scissors, utilizing the projection synthesis in a linear optical system, and nonlinear quantum scissors, implemented by periodically driven cavity with a Kerr medium. Dissipation effects on optical truncation are studied in the Langevin and master equation approaches. Formulas for the fidelity of lossy quantum scissors are found.
We derive a quantum limit to the sensitivity of laser interferometric gravitational-wave detectors from optical-loss-induced dissipation, analogous to the sensitivity limit from the mechanical dissipation. It applies universally to different interferometer configurations, and cannot be surpassed unless the optical property is improved. This result provides an answer to the long-standing question of how far we can push the detector sensitivity given the state-of-the-art optics.
Quantum transmissions of a free particle passing through a rectangular potential barrier with dissipation are studied using a path decomposition technique. Dissipative processes strongly suppress the transmission probability at resonance just above the barrier resulting in an unexpected reduction of the mean traversal time through the potential barrier.
We examine temperature cooling of optical chaotic light in a quantum dissipation channel with the damping parameter k.The way we do it is by introducing its thermal vacuum state which can expose entangling effect between the system and the reservoir. The temperature cooling formula is derived, which depends on the parameter k, by adjusting k one can control temperature.
The principal obstacle to quantum information processing with many qubits is decoherence. One source of decoherence is spontaneous emission which causes loss of energy and information. Inability to control system parameters with high precision is another possible source of error. As a solution we propose quantum computing experiments using dissipation based on an environment-induced quantum Zeno effect. As an example we present a simple scheme for quantum gate implementations with cold trapped ions in the presence of cooling.
Decoherence can be provided by a dissipative environment as described by the Caldeira-Leggett equation. This equation is foundational to the theory of quantum dissipation. However, no experimental test has been performed that measures for one physical system both the dissipation and the decoherence. Anglin and Zurek predicted that a resistive surface could provide such a dissipative environment for a free electron wave passing close to it. We propose that the electron wave's coherence and energy loss can be measured simultaneously by using Kapitza-Dirac scattering for varying light intensity.
A general theory of thermal magnetic fluctuations near conductive materials is developed; such fluctuations are the magnetic analog of Johnson noise. For realistic experiments in quantum computing and magnetic resonance force microscopy, the predicted relaxation can be rapid enough that substantial experimental care should be taken to minimize it. The same Hamiltonian matrix elements that govern fluctuation and dissipation are shown to also govern entanglement and renormalization, and a specific example of a fluctuation-dissipation-entanglement theorem is constructed.
We present a quantum Monte Carlo method for solving the evolution of an open quantum system. In our approach, the density operator evolution is unraveled in the frequency domain. Significant advantages of this approach arise when the frequency of each dissipative event conveys information about the state of the system.
We implement the normal ordering technique to study the quantum dissipation of a single mode harmonic oscillator system. The dynamic evolution of the system is investigated for a reasonable initial state by solving the Schrödinger equation directly through the normal ordering technique. The decoherence process of the system for the cases $T=0K$ and $T\neq0K$ is investigated as an application.
We propose a new approach to the implementation of quantum gates in which decoherence during the gate operations is strongly reduced. This is achieved by making use of an environment induced quantum Zeno effect that confines the dynamics effectively to a decoherence-free subspace.
In their constructions of system of quantum stochastic differential equations, mathematicians and/or several physicists interpret that the function of random force operator is to preserve the canonical commutation relation in time, i.e., to secure the unitarity of time evolution generator even for dissipative systems. If this is the case, it means physically that the origin of dissipation is attributed to quantum non-commutativity ({\it quantumness}). The mechanism that the mathematician's approaches rest on will be investigated from the unified view point of Non-Equilibrium Thermo Field Dynam…
Stark-chirped rapid adiabatic passage (SCRAP) is an important technique used for coherent quantum controls. In this paper we investigate how the practically-existing dissipation of the system influences on the efficiency of the passage, and thus the fidelities of the SCRAP-based quantum gates. With flux-biased Josephson qubits as a specifical example, our results show clearly that the efficiency of the logic gates implemented by SCRAP are robust against the weak dissipation. The influence due to the non-adiabtic transitions between the adiabatic passages is comparatively significantly small. T…
By a generalization of the Hopfield model, we construct a microscopic Lagrangian describing a dielectric medium with dispersion and dissipation. This facilitates a well-defined and unambiguous $\textit{ab initio}$ treatment of quantum electrodynamics in such media, even in time-dependent backgrounds. As an example, we calculate the number of photons created by switching on and off dissipation in dependence on the temporal switching function. This effect may be stronger than quantum radiation produced by variations of the refractive index $Δn(t)$ since the latter are typically very small and yi…
We study the relaxation of a quantum system towards the thermal equilibrium using tools developed within the context of quantum information theory. We consider a model in which the system is a qubit, and reaches equilibrium after several successive two-qubit interactions (thermalizing machines) with qubits of a reservoir. We characterize completely the family of thermalizing machines. The model shows a tight link between dissipation, fluctuations, and the maximal entanglement that can be generated by the machines. The interplay of quantum and classical information processes that give rise to p…
We invoke an efficient search algorithms as a key challenge in multi-qubit quantum systems. An original algorithm called dynamical quantum search algorithm from which Grover algorithm is obtained at a specified time is presented. This algorithm is distinguished by accuracy in obtaining high probability of finding any marked state in a shorter time than Grover algorithm time. The algorithm performance can be improved with respect to the different values of the controlled phase. A new technique is used to generate the dynamical quantum gates in the presence of dissipation effect that helps in im…
Quantum state transfer from an information-carrying qubit to a receiving qubit is ubiquitous for quantum information technology. In a closed quantum system, this task requires precisely-timed control of coherent qubit-qubit interactions that are intrinsically reciprocal. Here, breaking reciprocity by tailoring dissipation in an open system, we show that it is possible to autonomously transfer a quantum state between stationary qubits without time-dependent control. We present the general requirements for this directional transfer process, and show that the minimum system dimension for transfer…
We derive and analyze the Born-Markov master equation for a quantum harmonic oscillator interacting with a bath of independent two-level systems. This hitherto virtually unexplored model plays a fundamental role as one of the four "canonical" system-environment models for decoherence and dissipation. To investigate the influence of further couplings of the environmental spins to a dissipative bath, we also derive the master equation for a harmonic oscillator interacting with a single spin coupled to a bosonic bath. Our models are experimentally motivated by quantum-electromechanical systems an…
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 …
We study the information dynamics in a network of spin-$1/2$ particles when edges representing $XY$ interactions are randomly added to a disconnected graph accordingly to a probability distribution characterized by a "weighting" parameter. In this way we model dissipation of information initially localized in single or two qubits all over the network. We then show the dependence of this phenomenon from weighting parameter and size of the network.
Simulating the Dynamics of Markovian Quantum Processes by Quantum Collision Models on Quantum Computers
RIKEN Center for Computational Science（理化学研究所计算科学中心）；Q-CTRL；RIKEN Center for Quantum Computing（理化学研究所量子计算中心）；RIKEN Pioneering Research Institute（理化学研究所先导研究本部）；RIKEN Center for Emergent Matter Science（理化学研究所新兴物质科学中心）
Arrays of weakly-coupled quantum systems can be made to compute by subjecting them to a sequence of electromagnetic pulses of well-defined frequency and length. Such pulsed arrays are true quantum computers: bits can be placed in superpositions of 0 and 1, logical operations take place coherently, and dissipation is required only for error correction. Programming such computers is accomplished by selecting the proper sequence of pulses.
We introduce a scheme to perform dissipation-assisted quantum information processing in ion traps considering realistic decoherence rates, for example, due to motional heating. By means of continuous sympathetic cooling, we overcome the trap heating, and show that the damped vibrational excitations can still be exploited to mediate coherent interactions as well as collective dissipative effects. We describe how to control their relative strength experimentally, allowing for protocols of coherent or dissipative generation of entanglement. This scheme can be scaled to larger ion registers for co…
An error prevention procedure based on two-particle encoding is proposed for protecting an arbitrary unknown quantum state from dissipation, such as phase damping and amplitude damping. The schemes, which exhibits manifestation of the quantum Zeno effect, is effective whether quantum bits are decohered independently or cooperatively. We derive the working condition of the scheme and argue that this procedure has feasible practical implementation.
Optomechanical devices have been cooled to ground-state and genuine quantum features, as well as long-predicted nonlinear phenomena, have been observed. When packing close enough more than one optomechanical unit in the same substrate the question arises as to whether collective or independent dissipation channels are the correct description of the system. Here we explore the effects arising when introducing dissipative couplings between mechanical degrees of freedom. We investigate synchronization, entanglement and cooling, finding that collective dissipation can drive synchronization even in…
We study the dissipative dynamics of a single quantum harmonic oscillator subjected to a parametric driving with in an effective Hamiltonian approach. Using Liouville von Neumann approach, we show that the time evolution of a parametrically driven dissipative quantum oscillator has a strong connection with the classical damped Mathieu equation. Based on the numerical analysis of the Monodromy matrix, we demonstrate that the dynamical instability generated by the parametric driving are reduced by the effect of dissipation. Further, we obtain a closed relationship between the localization of the…
The quantum thermodynamic behavior of small systems is investigated in presence of finite quantum dissipation. We consider the archetype cases of a damped harmonic oscillator and a free quantum Brownian particle. A main finding is that quantum dissipation helps to ensure the validity of the Third Law. For the quantum oscillator, finite damping replaces the zero-coupling result of an exponential suppression of the specific heat at low temperatures by a power-law behavior. Rather intriguing is the behavior of the free quantum Brownian particle. In this case, quantum dissipation is able to restor…
Stabilization of quantum manifolds is at the heart of error-protected quantum information storage and manipulation. Nonlinear driven-dissipative processes achieve such stabilization in a hardware efficient manner. Josephson circuits with parametric pump drives implement these nonlinear interactions. In this article, we propose a scheme to engineer a four-photon drive and dissipation on a harmonic oscillator by cascading experimentally demonstrated two-photon processes. This would stabilize a four-dimensional degenerate manifold in a superconducting resonator. We analyze the performance of the …
The principal obstacle to quantum information processing with many qubits is decoherence. One source of decoherence is spontaneous emission which causes loss of energy and information. Inability to control system parameters with high precision is another possible source of error. Strategies aimed at overcoming one kind of error typically increase sensitivity to others. As a solution we propose quantum computing with dissipation-assisted quantum gates. These can be run relatively fast while achieving fidelities close to one. The success rate of each gate operation can, at least in principle, be…
The dissipation effect in a hybrid system is studied in this Letter. The hybrid system is a compound of a classical magnetic particle and a quantum single spin. Two cases are considered. In the first case, we investigate the effect of the dissipative quantum subsystem on the motion of its classical partner. Whereas in the second case we show how the dynamics of the quantum single spin are affected by the dissipation of the classical particle. Extension to general dissipative hybrid systems is discussed.
Quantum coherence conservation is shown to be achieved by a very high rate of dissipation of an environmental system coupled with a principal system. This effect is not in the list of previously-known strategies of noise suppression, such as Zeno effect, dynamical decoupling, quantum error correction code, and decoherence free subspace. An analytical solution is found for a simplified model of a single qubit coupled with an environmental single qubit dissipating rapidly. We also show examples of coherence conservation in a spin-boson linear coupling model with a numerical evaluation.
The fluctuation-dissipation relation is usually formulated for a system interacting with a heat bath at finite temperature in the context of linear response theory, where only small deviations from the mean are considered. We show that for an open quantum system interacting with a non-equilibrium environment, where temperature is no longer a valid notion, a fluctuation-dissipation inequality exists. Clearly stated, quantum fluctuations are bounded below by quantum dissipation, whereas classically the fluctuations can be made to vanish. The lower bound of this inequality is exactly satisfied by…
We theoretically investigate the escape rate occurring via quantum tunneling in a system affected by tailored dissipation. Specifically, we study the environmental assisted quantum tunneling of the superconducting phase in a current-biased Josephson junction. We consider Ohmic resistors inducing dissipation both in the phase and in the charge of the quantum circuit. We find that the charge dissipation leads to an enhancement of the quantum escape rate. This effect appears already in the low Ohmic regime and also occurs in the presence of phase dissipation that favors localization. Inserting re…
