This work applies concepts from algorithmic probability to Boolean and quantum combinatorial logic circuits. The relations among the statistical, algorithmic, computational, and circuit complexities ...of states are reviewed. Thereafter, the probability of states in the circuit model of computation is defined. Classical and quantum gate sets are compared to select some characteristic sets. The reachability and expressibility in a space-time-bounded setting for these gate sets are enumerated and visualized. These results are studied in terms of computational resources, universality, and quantum behavior. The article suggests how applications like geometric quantum machine learning, novel quantum algorithm synthesis, and quantum artificial general intelligence can benefit by studying circuit probabilities.
Abstract
The variational quantum algorithms are crucial for the application of NISQ computers. Such algorithms require short quantum circuits, which are more amenable to implementation on near-term ...hardware, and many such methods have been developed. One of particular interest is the so-called variational quantum state diagonalization method, which constitutes an important algorithmic subroutine and can be used directly to work with data encoded in quantum states. In particular, it can be applied to discern the features of quantum states, such as entanglement properties of a system, or in quantum machine learning algorithms. In this work, we tackle the problem of designing a very shallow quantum circuit, required in the quantum state diagonalization task, by utilizing reinforcement learning (RL). We use a novel encoding method for the RL-state, a dense reward function, and an
ε
-greedy policy to achieve this. We demonstrate that the circuits proposed by the RL methods are shallower than the standard variational quantum state diagonalization algorithm and thus can be used in situations where hardware capabilities limit the depth of quantum circuits. The methods we propose in the paper can be readily adapted to address a wide range of variational quantum algorithms.
A hybrid quantum optomechanical system is an interface made from coupling between photons, excitons and mechanical oscillations. We use the quantum Langevin approach to study a hybrid optomechanical ...system which contains a single undoped semiconductor quantum well placed inside a cavity as well as one mirror of the optical resonator linear coupled to the cavity fields. A decorrelation method is employed to get a closed set of coupled equations. Furthermore, we have used these solutions to discuss squeezing dynamics for the coupled mode quadratures of the cavity field and the semiconductor quantum well exciton. We have illustrated that squeezing dynamics can be controlled by appropriate choice of physical parameters present in our hybrid optomechanical system.
We investigate a dual membrane active–passive cavity where each mechanical membrane individually quadratically coupled to passive and active cavities via two-phonon process. Due to the fact that in ...the quadratically coupled optomechanical system mean-field approximation fails, hence to analyze the system completely, we switch to a more generalized out of equilibrium approach, namely Keldysh Green’s functional approach. We calculate transmission rate using predetermined full retarded Green’s function, and then numerically examine the effect of the various parameters on the transmission coefficient and discuss the features and physical mechanism behind them in detail. On the basis of the optical responsivity we further extend our study to fast and slow light phenomenon. The results show that our proposed system can not only realize ultra-fast/ultra-slow light under proper choice of cavity parameters but also a realization of the conversion between fast and slow light and vice versa has also been pointed out.
•The optical response is determined by competition between photon-tunneling, two-phonon process, gain effect.•The photon-tunneling adjusts supermode frequency.•The absorption coefficient can exceed 1.•Not only realize fast/slow light but conversion between fast and slow light.
In the field of quantum computing, variational quantum algorithms (VQAs) represent a pivotal category of quantum solutions across a broad spectrum of applications. These algorithms demonstrate ...significant potential for realising quantum computational advantage. A fundamental aspect of VQAs involves formulating expressive and efficient quantum circuits (namely ansatz), and automating the search of such ansatz is known as quantum architecture search (QAS). Recently reinforcement learning (RL) techniques is utilized to automate the search for ansatzes, know as RL-QAS. This study investigates RL-QAS for crafting ansatz tailored to the variational quantum state diagonalisation problem. Our investigation includes a comprehensive analysis of various dimensions, such as the entanglement thresholds of the resultant states, the impact of initial conditions on the performance of RL-agent, the phase transition behaviour of correlation in concurrence bounds, and the discrete contributions of qubits in deducing eigenvalues through conditional entropy metrics. We leverage these insights to devise an entanglement-guided admissible ansatz in QAS to diagonalise random quantum states using optimal resources. Furthermore, the methodologies presented herein offer a generalised framework for constructing reward functions within RL-QAS applicable to variational quantum algorithms.
As consequences of disruptions in railway traffic affect passenger experience and satisfaction, appropriate rerouting and/or rescheduling is necessary. These problems are known to be NP-hard, given ...the numerous restrictions of traffic nature. With the recent advances in quantum technologies, quantum annealing has become an alternative method to solve such optimization problems. To use quantum annealing, the problem needs to be encoded in quadratic unconstrained binary optimization (QUBO) or higher-order binary optimization (HOBO) formulation that can be recast as a QUBO. This paper introduces QUBO and HOBO representations for rescheduling problems of railway traffic management; the latter is a new approach up to our knowledge. This new approach takes into account not only the single-track lines but also the double- and multi-track lines, as well as stations composed of tracks and switches. We consider the conditions of minimal headway between trains, minimal stay on stations, track occupation, and rolling stock circulation. Furthermore, a hybrid quantum-classical procedure is presented that includes rerouting. We demonstrate the proof of concept implementation on the D-Wave Quantum Processing Unit and D-Wave hybrid solver.
Optimization of pre-production vehicle configurations is one of the challenges in the automotive industry. Given a list of tests requiring cars with certain features, it is desirable to find the ...minimum number of cars that cover the tests and obey the configuration rules. In this paper, we model the problem in the framework of satisfiability and solve it utilizing the newly introduced hybrid constrained quadratic model (CQM) solver provided by D-Wave. The problem definition is based on the “Optimizing the Production of Test Vehicles” use-case given in the BMW quantum computing challenge. We formulate a constrained quadratic model for the problem and use a greedy algorithm to configure the cars. We benchmark the results obtained from the CQM solver with the results from the classical solvers like coin-or branch and cut and Gurobi solver. We conclude that the performance of the CQM solver is comparable to the classical solvers in optimizing the number of test vehicles, given the noise-prone quantum hardware. However, the CQM solver takes much more time, which prohibits obtaining useful quantum advantages. As an extension to the problem, we describe how the scheduling of the tests can be incorporated into the model.
In this work, a scalable quantum gate‐based algorithm for accelerating causal inference is introduced. Specifically, the formalism of causal hypothesis testing presented in Nat Commun 10, 1472 (2019) ...is considered. Through the algorithm, the existing definition of error probability is generalized, which is a metric to distinguish between two competing causal hypotheses, to a practical scenario. The results on the Qiskit validate the predicted speedup and show that in the realistic scenario, the error probability depends on the distance between the competing hypotheses. To achieve this, the causal hypotheses are embedded as a circuit construction of the oracle. Furthermore, by assessing the complexity involved in implementing the algorithm's subcomponents, a numerical estimation of the resources required for the algorithm is offered. Finally, applications of this framework for causal inference use cases in bioinformatics and artificial general intelligence are discussed.
It expands the current framework by adjusting error probability based on process distance between the causal hypotheses. This implementation facilitates gate complexity estimation for the quantum algorithm. Stressing the significance of causal inference in machine learning and quantum networks, it anticipates applications in grasping general intelligence limits and bioinformatics.
Nonclassical phenomena can be enhanced by introducing q‐deformation in optomechanical systems. This motivates investigation of the optical response in a q‐deformed linearly coupled optomechanical ...system. The system consists of two deformed cavities that are linearly coupled to the motion of mechanical mirrors, and the cavities are coupled to each other by transmission strength parameter. This study shows that compared to non‐deformed cases, the deformed system exhibits more rapid phase transition at the positions of transparency windows, causing stronger and enhanced fast and slow light phenomena. Moreover, in the region 0<q<0.5$0<q<0.5$, the optomechanical system results in gain. Additionally, for a fixed deformation of cavities, by tuning the tunneling strength and optomechanical coupling, one can observe a delay and advancement in probe field in the order of milliseconds and even above milliseconds for fine‐tuning of the coupling parameters. Finally, the bridge between mathematical and physical models is built by assuming the deformation to be a primitive root of unity, which indicates a class of anyon models. These results demonstrate that q‐deformation provides a novel method for manipulating and significantly enhancing optical phenomena not only in arbitrarily deformed optomechanical systems but also in anyon models.
This work investigates the effect of nonlinearity raised due to the introduction of q‐deformation in an optomechanical system. As a part of the investigation, the transmission, phase, and the corresponding ground delay are studied. It is found that the fast and slow light phenomena in the deformed system are enhanced compared to non‐deformed and can even go above milliseconds.
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