اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدBeating the House: Fast Simulation of Dissipative Quantum Systems with Ensemble Rank Truncation
68
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We introduce a new technique for the simulation of dissipative quantum systems. This method is composed of an approximate decomposition of the Lindblad equation into a Kraus map, from which one can define an ensemble of wavefunctions. Using principal component analysis, this ensemble can be truncated to a manageable size without sacrificing numerical accuracy. We term this method emph{Ensemble Rank Truncation} (ERT), and find that in the regime of weak coupling, this method is able to outperform existing wavefunction Monte-Carlo methods by an order of magnitude in both accuracy and speed. We also explore the possibility of combining ERT with approximate techniques for simulating large systems (such as Matrix Product States (MPS)), and show that in many cases this approach will be more efficient than directly expressing the density matrix in its MPS form. We expect the ERT technique to be of practical interest when simulating dissipative systems for quantum information, metrology and thermodynamics.
قيم البحث
اقرأ أيضاً
The controls enacting logical operations on quantum systems are described by time-dependent Hamiltonians that often include rapid oscillations. In order to accurately capture the resulting time dynamics in numerical simulations, a very small integrat
ion time step is required, which can severely impact the simulation run-time. Here, we introduce a semi-analytic method based on the Dyson expansion that allows us to time-evolve driven quantum systems much faster than standard numerical integrators. This solver, which we name Dysolve, efficiently captures the effect of the highly oscillatory terms in the system Hamiltonian, significantly reducing the simulations run time as well as its sensitivity to the time-step size. Furthermore, this solver provides the exact derivative of the time-evolution operator with respect to the drive amplitudes. This key feature allows for optimal control in the limit of strong drives and goes beyond common pulse-optimization approaches that rely on rotating-wave approximations. As an illustration of our method, we show results of the optimization of a two-qubit gate using transmon qubits in the circuit QED architecture.
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 of protocols originally optimized against noise. Its extension to two interacting spins restores a fidelity close to unity for the fast generation of Bell state in the presence of dissipation.
It is challenged only recently that the precision attainable in any measurement of a physical parameter is fundamentally limited by the quantum Cram{e}r-Rao Bound (QCRB). Here, targeting at measuring parameters in strongly dissipative systems, we pro
pose an innovative measurement scheme called {it dissipative adiabatic measurement} and theoretically show that it can beat the QCRB. Unlike projective measurements, our measurement scheme, though consuming more time, does not collapse the measured state and, more importantly, yields the expectation value of an observable as its measurement outcome, which is directly connected to the parameter of interest. Such a direct connection {allows to extract} the value of the parameter from the measurement outcomes in a straightforward manner, with no fundamental limitation on precision in principle. Our findings not only provide a marked insight into quantum metrology but also are highly useful in dissipative quantum information processing.
The interplay of Anderson localisation and decoherence results in intricate dynamics but is notoriously difficult to simulate on classical computers. We develop the framework for a quantum simulation of such an open quantum system making use of time-
varying randomised gradients, and show that even an implementation with limited experimental resources results in accurate simulations.
We discuss topology in dissipative quantum systems from the perspective of quantum trajectories. The latter emerge in the unraveling of Markovian quantum master equations and/or in continuous quantum measurements. Ensemble-averaging quantum trajector
ies at the occurrence of quantum jumps, i.e., the jumptimes, gives rise to a discrete, deterministic evolution which is highly sensitive to the presence of dark states. We show for a broad family of translation-invariant collapse models that the set of dark state-inducing Hamiltonians imposes a nontrivial topological structure on the space of Hamiltonians, which is also reflected by the corresponding jumptime dynamics. The topological character of the latter can then be observed, for instance, in the transport behavior, exposing an infinite hierarchy of topological phase transitions. We develop our theory for one- and two-dimensional two-band Hamiltonians, and show that the topological behavior is directly manifest for chiral, PT, or time reversal-symmetric Hamiltonians.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
