Evolution Of Quantum System Research Articles

Robustness of quantum correlation in quantum energy teleportation

In this article, we explore a feedback-control protocol in different quantum field theories (QFTs) to study the quantum correlation in nonunitary evolution of quantum systems. Traditional studies on QFTs focus on quantum entanglement of pure states under the unitary evolution, however, we examine quantum correlation in mixed states using quantum energy teleportation (QET), which is an energy transfer protocol by utilizing ground state entanglement, and introduce quantum discord as a measure. QET involves a midcircuit measurement, which disrupts pure state entanglement. Despite this, our analysis demonstrates that quantum discord maintains the correlation throughout the QET process. We conducted numerical analyses with benchmark models including the Nambu-Jona-Lasinio (NJL) model, revealing that quantum discord consistently acts as an order parameter for phase transitions. The model is extended in a way that it has both the chiral chemical potential and the chemical potential, which are useful to study the phase structures mimicking the chiral imbalance between left- and right- quarks coupled to the chirality density operator. In all cases we studied, the quantum discord behaved as an order parameter of the phase transition. Published by the American Physical Society 2024

Evolution of Quantum Systems with a Discrete Energy Spectrum in an Adiabatically Varying External Field

We introduce a new approach for describing nonstationary quantum systems with a discrete energy spectrum. The essence of this approach is that we describe the evolution of a quantum system in a time-dependent basis. In a sense, this approach is similar to the description of the system in the interaction representation. However, the time dependence of the basic states of the representation is determined not by the evolution operator with a time-independent Hamiltonian but by the eigenstates of the time-dependent Hamiltonian defined at the current time. The time dependence of the basic states of the representation leads to the appearance of an additional term in the Schrödinger equation, which in the case of slowly changing parameters of the Hamiltonian can be considered as a small perturbation. The adiabatic representation is suitable in cases where it is impossible to apply the standard interaction representation. The application of the adiabatic representation is illustrated by the example of two spins connected by a magnetic dipole–dipole interaction in a slowly varying external magnetic field.

Ab-initio variational wave functions for the time-dependent many-electron Schrödinger equation

Understanding the real-time evolution of many-electron quantum systems is essential for studying dynamical properties in condensed matter, quantum chemistry, and complex materials, yet it poses a significant theoretical and computational challenge. Our work introduces a variational approach for fermionic time-dependent wave functions, surpassing mean-field approximations by accurately capturing many-body correlations. We employ time-dependent Jastrow factors and backflow transformations, enhanced through neural networks parameterizations. To compute the optimal time-dependent parameters, we employ the time-dependent variational Monte Carlo technique and introduce a new method based on Taylor-root expansions of the propagator, enhancing the accuracy of our simulations. The approach is demonstrated in three distinct systems. In all cases, we show clear signatures of many-body correlations in the dynamics. The results showcase the ability of our variational approach to accurately describe the time evolution, providing insight into quantum dynamical effects in interacting electronic systems, beyond the capabilities of mean-field.

Measurement and Feed Forward Induced Entanglement Negativity Transition.

We study the interplay between measurement-induced dynamics and conditional unitary evolution in quantum systems. We numerically and analytically investigate commuting random measurement and feed forward (MFF) processes and find a sharp transition in their ability to generate entanglement negativity as the number of MFF channels varies. We also establish a direct connection between these findings and transitions induced by random dephasing from an environment with broken time-reversal symmetry. In one variant of the problem, we employ free probability theory to rigorously prove the transition's existence. Furthermore, these MFF processes have dynamic circuit representations that can be experimentally explored on current quantum computing platforms.

Adiabatic Time Evolution of Highly Excited States

Adiabatic time evolution of quantum systems is a widely used tool with applications ranging from state preparation through simplifications of computations and topological transformations to optimization and quantum computing. Adiabatic time evolution generally works well for gapped ground states, but not for thermal states in the middle of the spectrum that lack a protecting energy gap. Here we show that quantum many-body scars—a particular type of highly excited states—are suitable for adiabatic time evolution despite the absence of a protecting energy gap. Considering two rather different models, namely a one-dimensional model constructed from tensor networks and a two-dimensional fractional quantum Hall model with anyons, we find that the quantum scars perform similarly to gapped ground states with respect to adiabatic dynamics when the required final adiabatic fidelity is around 0.99. The maximum speed at which the scar state of the one-dimensional model can be adiabatically transformed decreases as a power law with system size, as opposed to exponentially for both generic thermal and disorder-driven localized states. At constant and very low ramp speed, we find that the deviation of the fidelity from unity scales linearly with ramp speed for scar states, but quadratically for gapped ground states. The gapped ground states hence perform better when the required adiabatic fidelities are very high, such as 0.9999 and above. We identify two mechanisms for leakage out of the scar state and use them to explain our results. While manipulating a single, isolated ground state is common in quantum applications, adiabatic evolution of scar states provides the flexibility to manipulate an entire tower of ground-state-like states simultaneously in a single system. Published by the American Physical Society 2024

Number of steady states of quantum evolutions

We prove sharp universal upper bounds on the number of linearly independent steady and asymptotic states of discrete- and continuous-time Markovian evolutions of open quantum systems. We show that the bounds depend only on the dimension of the system and not on the details of the dynamics. A comparison with similar bounds deriving from a recent spectral conjecture for Markovian evolutions is also provided.

Near-term distributed quantum computation using mean-field corrections and auxiliary qubits

Distributed quantum computation is often proposed to increase the scalability of quantum hardware, as it reduces cooperative noise and requisite connectivity by sharing quantum information between distant quantum devices. However, such exchange of quantum information itself poses unique engineering challenges, requiring high gate fidelity and costly non-local operations. To mitigate this, we propose near-term distributed quantum computing, focusing on approximate approaches that involve limited information transfer and conservative entanglement production. We first devise an approximate distributed computing scheme for the time evolution of quantum systems split across any combination of classical and quantum devices. Our procedure harnesses mean-field corrections and auxiliary qubits to link two or more devices classically, optimally encoding the auxiliary qubits to both minimize short-time evolution error and extend the approximate scheme’s performance to longer evolution times. We then expand the scheme to include limited quantum information transfer through selective qubit shuffling or teleportation, broadening our method’s applicability and boosting its performance. Finally, we build upon these concepts to produce an approximate circuit-cutting technique for the fragmented pre-training of variational quantum algorithms. To characterize our technique, we introduce a non-linear perturbation theory that discerns the critical role of our mean-field corrections in optimization and may be suitable for analyzing other non-linear quantum techniques. This fragmented pre-training is remarkably successful, reducing algorithmic error by orders of magnitude while requiring fewer iterations.

Weak second-order quantum state diffusion unraveling of the Lindblad master equation

Simulating mixed-state evolution in open quantum systems is crucial for various chemical physics, quantum optics, and computer science applications. These simulations typically follow the Lindblad master equation dynamics. An alternative approach known as quantum state diffusion unraveling is based on the trajectories of pure states generated by random wave functions, which evolve according to a nonlinear Itô–Schrödinger equation (ISE). This study introduces weak first-order and second-order solvers for the ISE based on directly applying the Itô–Taylor expansion with exact derivatives in the interaction picture. We tested the method on free and driven Morse oscillators coupled to a thermal environment and found that both orders allowed practical estimation with a few dozen iterations. The variance was relatively small compared to the linear unraveling and did not grow with time. The second-order solver delivers a much higher accuracy and stability with bigger time steps than the first-order scheme, with a small additional workload. However, the second-order algorithm has quadratic complexity with the number of Lindblad operators as opposed to the linear complexity of the first-order algorithm.

Liouvillian exceptional points of an open driven two-level system.

We study the applicability of the Liouvillian exceptional points (LEPs) approach to nanoscale open quantum systems. A generic model of the driven two-level system in a thermal environment is analyzed within the nonequilibrium Green's function (NEGF) and Bloch quantum master equation formulations. We derive the latter starting from the exact NEGF Dyson equations and highlight the qualitative limitations of the LEP treatment by examining the approximations employed in its derivation. We find that the non-Markov character of evolution in open quantum systems does not allow for the introduction of the concept of exceptional points for a description of their dynamics. Theoretical analysis is illustrated with numerical simulations.

On the origin of black hole paradoxes

Black hole firewall paradox is an inconsistency between four postulates in black hole physics: (1) the unitary evolution in quantum systems, (2) application of the semi-classical field theory in low curvature backgrounds, (3) statistical mechanical origin of the black hole entropy, and (4) the equivalence principle in the version of no drama for free-falling observers in the vicinity of the horizon. Based on the existence of the Hawking radiation for the static observers standing outside a Schwarzschild black hole, we show a direct contradiction between the postulates (2) and (4). If there is not a way out of this new problem, it implies the necessity of relaxing one of these two assumptions for resolving the black hole firewall paradox.

SimuQ: A Framework for Programming Quantum Hamiltonian Simulation with Analog Compilation

Quantum Hamiltonian simulation, which simulates the evolution of quantum systems and probes quantum phenomena, is one of the most promising applications of quantum computing. Recent experimental results suggest that Hamiltonian-oriented analog quantum simulation would be advantageous over circuit-oriented digital quantum simulation in the Noisy Intermediate-Scale Quantum (NISQ) machine era. However, programming analog quantum simulators is much more challenging due to the lack of a unified interface between hardware and software. In this paper, we design and implement SimuQ, the first framework for quantum Hamiltonian simulation that supports Hamiltonian programming and pulse-level compilation to heterogeneous analog quantum simulators. Specifically, in SimuQ, front-end users specify the target quantum system with Hamiltonian Modeling Language, and the Hamiltonian-level programmability of analog quantum simulators is specified through a new abstraction called the abstract analog instruction set (AAIS) and programmed in AAIS Specification Language by hardware providers. Through a solver-based compilation, SimuQ generates executable pulse schedules for real devices to simulate the evolution of desired quantum systems, which is demonstrated on superconducting (IBM), neutral-atom (QuEra), and trapped-ion (IonQ) quantum devices. Moreover, we demonstrate the advantages of exposing the Hamiltonian-level programmability of devices with native operations or interaction-based gates and establish a small benchmark of quantum simulation to evaluate SimuQ's compiler with the above analog quantum simulators.

The classification of rebit quantum channels

The classification of qubit channels is known since 2002. However, that of rebit channels has never been studied so far, maybe because of the scarcity of concrete rebit examples. In this paper we point out that the strategy used to classify qubit channels cannot be pursued in the rebit case and we propose an alternative which allows us to complete the rebit channel classification. This mathematical result has not only a purely abstract interest: as we shall briefly mention, it may have applications in the analysis of local properties and temporal evolution of real quantum systems and also in a recent color vision model based on quantum information.

Operator size distribution in large N quantum mechanics of Majorana fermions

Under the Heisenberg evolution in chaotic quantum systems, initially simple operators evolve into complicated ones and ultimately cover the whole operator space. We study the growth of the operator “size” in this process, which is related to the out-of-time-order correlator (OTOC). We derive the full time evolution of the size distribution in large N quantum mechanics of Majorana fermions. As examples, we apply the formalism to the Brownian SYK model (infinite temperature) and the large q SYK model (finite temperature).

Exact Markovian evolution of quantum systems with several degrees of freedom: Phase space representations

Exact Markovian evolution of quantum systems with several degrees of freedom: Phase space representations

A possibilistic no-go theorem on the Wigner’s friend paradox

The famous ‘Wigner’s friend’ paradox highlights the difficulty of modelling the evolution of quantum systems under measurement in situations where observers themselves are considered to be subject to the laws of quantum mechanics. In recent years, variations of the original Wigner’s friend paradox have been recognized as fruitful arenas for probing the foundations of quantum theory. In particular (Bong et al 2020 Nat. Phys. 16 1199) demonstrated a contradiction between a set of intuitive assumptions called ‘Local Friendliness’ (LF) and certain quantum phenomena on an extended version of the Wigner’s friend paradox. The LF assumptions can be understood as the conjunction of two independent assumptions: Absoluteness of Observed Events requires that any event observed by any observer has an absolute, rather than relative, value; Local Agency is the assumption that an intervention cannot be correlated with relevant events outside its future light cone. These assumptions are weaker than the assumptions that lead to Bell’s theorem, and thus while the LF result may be considered to be conceptually comparable to Bell’s result, its implications are even deeper. The proof of the LF no-go theorem, however, relies on probability theory, and a fundamental question remained whether or not LF is an inherently statistical concept. Here we present a probability-free version of the LF theorem, building upon Hardy’s no-go theorem for local hidden variables. The argument is phrased in the language of possibilities, which we make formal by using a modal logical approach. It relies on a weaker version of Local Agency, which we call ‘Possibilistic Local Agency’: the assumption that an intervention cannot affect the possibilities of events outside its future light cone.

Quantum Time and Quantum Evolution

The problem of quantum time and evolution of quantum systems, where time is not a parameter, is considered. In our model, following some earlier works, time is represented by a quantum operator. In this paper, similarly to the position operators in the Schrödinger representation of quantum mechanics, this operator is a multiplication-type operator. It can be also represented by an appropriate positive operator-valued measure (POVM) which together with the 3D position operators/measures provide a quantum observable giving a position in the quantum spacetime. The quantum evolution itself is a stochastic process based on Lüder’s projection postulate. In fact, it is a generalization of the unitary evolution. This allows to treat time and generally the spacetime position as a quantum observable, in a consistent and observer-independent way.

Bayesian quantum parameter estimation with Gaussian states and homodyne measurements in a dissipative environment

The deterioration of precision caused by quantum decoherence in dissipative environments is a longstanding problem in the development of quantum metrology. Therefore, it is significant to effectively analyze the evolution of quantum systems under dissipative environments and quantitatively estimate the parameters given a certain probe. Here, we propose a continuous-variable (CV) quantum metrology scheme within the Bayesian paradigm to estimate phase shift, loss coefficient and temperature of a dissipative environment. Through numerical evaluation and concrete analysis, we investigate the achievable precision of Bayesian quantum parameter estimation with Gaussian states and homodyne measurements, and the influence of different parameters on the estimation process. More interestingly, the scheme can be applied in more practical scenarios where not enough measurements are obtained and the frequentist analysis is not well defined.

Variational Hamiltonian simulation for translational invariant systems via classical pre-processing

The simulation of time evolution of large quantum systems is a classically challenging and in general intractable task, making it a promising application for quantum computation. A Trotter–Suzuki approximation yields an implementation thereof, where a higher approximation accuracy can be traded for an increased gate count. In this work, we introduce a variational algorithm which uses solutions of classical optimizations to predict efficient quantum circuits for time evolution of translationally invariant quantum systems. Our strategy can improve upon the Trotter–Suzuki accuracy by several orders of magnitude. It translates into a reduction in gate count and hence gain in overall fidelity at the same algorithmic accuracy. This is important in noisy intermediate scale quantum-applications where the fidelity of the output state decays exponentially with the number of gates. The performance advantage of our classical assisted strategy can be extended to open boundaries with translational symmetry in the bulk. We can extrapolate our method to beyond classically simulatable system sizes, maintaining its total fidelity advantage over a Trotter–Suzuki approximation making it an interesting candidate for beyond classical time evolution.

Dynamics of Quantum Networks in Noisy Environments.

Noise exists inherently in realistic quantum systems and affects the evolution of quantum systems. We investigate the dynamics of quantum networks in noisy environments by using the fidelity of the quantum evolved states and the classical percolation theory. We propose an analytical framework that allows us to characterize the stability of quantum networks in terms of quantum noises and network topologies. The calculation results of the framework determine the maximal time that quantum networks with different network topologies can maintain the ability to communicate under noise. We demonstrate the results of the framework through examples of specific graphs under amplitude damping and phase damping noises. We further consider the capacity of the quantum network in a noisy environment according to the proposed framework. The analytical framework helps us better understand the evolution time of a quantum network and provides a reference for designing large quantum networks.

Operator formalism for the propagation of paraxial electromagnetic fields

The operator formalism of the time evolution of quantum systems is applied to describe the propagation of light beams in homogeneous and inhomogeneous media, which are governed by the paraxial wave equation. This approach allowed us to address the important case of a Gaussian beam propagating in homogeneous and isotropic space, along with the depiction of relevant beam parameters, such as the beam waist, curvature radius and Gouy phase. By using this method, we show that a special class of operators can be used to generate arbitrary families of Gaussian beams when applied to the fundamental Gaussian mode. We exemplify with the reproduction of the well-known higher-order modes of the Hermite- and Laguerre–Gaussian beams, as well as with the generation of a new family of Gaussian modes, whose propagation properties could also be described. The present method provides a new venue to investigate physical phenomena in the realm of paraxial wave optics.