Quadratic and Higher-Order Unconstrained Binary Optimization of Railway Dispatching Problem for Quantum Computing

The consequences of disruptions in railway traffic are the primary cause of passengers' dissatisfaction. Hence, appropriate dispatching decisions are necessary (e.g., by assigning the order of trains), given the numerous restrictions of traffic nature. The latter is perceived as an NP-hard problem. This paper outlines QUBO (quadratic unconstrained binary optimization) and HOBO (higher-order binary optimization) representations for dispatching problems of railway traffic management. Specifically, we consider minimal span between trains, minimal stay on stations, station/track occupation, and rolling stock circulation. The main result is the hybrid algorithm to deal with disturbances in rail traffic on single-, double- and multi-track lines; the demonstrative model illustrates the issue briefly. This algorithm can solve railway dispatching problems using the quantum annealer or any other QUBO-based optimization device

Quantum Accelerated Causal Tomography: Circuit Considerations Towards Applications

In this research we study quantum computing algorithms for accelerating causal inference. Specifically, we investigate the formulation of causal hypothesis testing presented in [\textit{Nat Commun} 10, 1472 (2019)]. The theoretical description is constructed as a scalable quantum gate-based algorithm on qiskit. We present the circuit construction of the oracle embedding the causal hypothesis and assess the associated gate complexities. Our experiments on a simulator platform validates the predicted speedup. We discuss applications of this framework for causal inference use cases in bioinformatics and artificial general intelligence.Comment: 9 pages, 5 figure

Visualizing Quantum Circuit Probability -- estimating computational action for quantum program synthesis

This research applies concepts from algorithmic probability to Boolean and quantum combinatorial logic circuits. A tutorial-style introduction to states and various notions of the complexity of states are presented. 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.Comment: 17 page

Filling an empty lattice by local injection of quantum particles

We study the quantum dynamics of filling an empty lattice of size $L$, by connecting it locally with an equilibrium thermal bath that injects non-interacting bosons or fermions. We adopt four different approaches, namely (i) direct exact numerics, (ii) Redfield equation, (iii) Lindblad equation, and (iv) quantum Langevin equation -- which are unique in their ways for solving the time dynamics and the steady-state. Our setup offers a simplistic platform to understand fundamental aspects of dynamics and approach to thermalization. The quantities of interest that we consider are the spatial density profile and the total number of bosons/fermions in the lattice. The spatial spread is ballistic in nature and the local occupation eventually settles down owing to equilibration. The ballistic spread of local density admits a universal scaling form. We show that this universality is only seen when the condition of detailed balance is satisfied by the baths. The difference between bosons and fermions shows up in the early time growth rate and the saturation values of the profile. The techniques developed here are applicable to systems in arbitrary dimensions and for arbitrary geometries.Comment: 18 pages, 10 figure

Enhancing variational quantum state diagonalization using reinforcement learning techniques

The development of variational quantum algorithms is 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 the variational diagonalization method, which constitutes an important algorithmic subroutine, and it can be used directly for working 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. To achieve this, we utilize a novel encoding method that can be used to tackle the problem of circuit depth optimization using a reinforcement learning approach. We demonstrate that our approach provides a solid approximation to the diagonalization task while using a small number of gates. The circuits proposed by the reinforcement learning methods are shallower than the standard variational quantum state diagonalization algorithm, and thus can be used in situations where the depth of quantum circuits is limited by the hardware capabilities.Comment: 17 pages with 13 figures, some minor, important improvements, code available at https://github.com/iitis/RL_for_VQSD_ansatz_optimizatio

SeqL+: Secure Scan-Obfuscation with Theoretical and Empirical Validation

Existing logic-locking attacks are known to successfully decrypt a functionally correct key of a locked combinational circuit. Extensions of these attacks to real-world Intellectual Properties (IPs, which are sequential circuits) have been demonstrated through the scan-chain by selectively initializing the combinational logic and analyzing the responses. In this paper, we propose SeqL+ to mitigate a broad class of such attacks. The key idea is to lock selective functional-input/scan-output pairs of flip-flops without feedback to cause attackers to decrypt an incorrect key, and to scramble flip-flops with feedback to increase key length without introducing further vulnerabilities. We conduct a formal study of the scan-locking and scan-scrambling problems and demonstrate automating our proposed defense on any given IP. This study reveals the first formulation and complexity analysis of Boolean Satisfiability (SAT)-based attack on scan-scrambling. We formulate the attack as a conjunctive normal form (CNF) using a worst-case O(n^3) reduction in terms of scramble-graph size n, making SAT-based attack applicable and show that scramble equivalence classes are equi-sized and of cardinality 1. In order to defeat SAT-based attack, we propose an iterative swapping-based scan-cell scrambling algorithm that has linear implementation time-complexity and exponential SAT-decryption time-complexity in terms of a user-configurable cost constraint. We empirically validate that SeqL+ hides functionally correct keys from the attacker, thereby increasing the likelihood of the decrypted key being functionally incorrect. When tested on pipelined combinational benchmarks (ISCAS, MCNC), sequential benchmarks (ITC), and a fully-fledged RISC-V CPU, SeqL+ gave 100% resilience to a broad range of state-of-the-art attacks including SAT [1], Double-DIP [2], HackTest [3], SMT [4], FALL [5], Shift-and-Leak [6], Multi-cycle [7], Scan-flushing [8], and Removal [9] attacks

Transparency and enhancement in fast and slow light in qq-deformed optomechanical system

Nonclassical phenomena can be enhanced by introducing $q$-deformation in optomechanical systems. This motivated us to investigate 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. Our 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 $0<q<0.5$, the optomechanical system results in gain. Moreover for a fixed deformation of cavities, by tuning the tunnelling strength and optomechanical coupling, one can observe a delay and advancement in probe filed in the order of \textit{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, indicating a class of \textit{anyon} models. Our 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.Comment: 25 pages, 15 figures, accepted for publication in Annalen der Physi