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Register a new userTransformation of quantum photonic circuit models by term rewriting
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The development of practical methods for synthesis and verification of complex photonic circuits presents a grand challenge for the nascent field of quantum engineering. Of course, classical electrical engineering provides essential foundations and serves to illustrate the degree of sophistication that can be achieved in automated circuit design. In this paper we explore the utility of term rewriting approaches to the transformation of quantum circuit models, specifically applying rewrite rules for both reduction/verification and robustness analysis of photonic circuits for autonomous quantum error correction. We outline a workflow for quantum photonic circuit analysis that leverages the Modelica framework for multi-domain physical modeling, which parallels a previously described approach based on VHSIC Hardware Description Language (VHDL).
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The goal of quantum circuit transformation is to map a logical circuit to a physical device by inserting additional gates as few as possible in an acceptable amount of time. We present an effective approach called TSA to construct the mapping. It consists of two key steps: one makes use of a combined subgraph isomorphism and completion to initialize some candidate mappings, the other dynamically modifies the mappings by using tabu search-based adjustment. Our experiments show that, compared with state-of-the-art methods GA, SABRE and FiDLS proposed in the literature, TSA can generate mappings with a smaller number of additional gates and it has a better scalability for large-scale circuits.
This paper addresses quantum circuit mapping for Noisy Intermediate-Scale Quantum (NISQ) computers. Since NISQ computers constraint two-qubit operations on limited couplings, an input circuit must be transformed into an equivalent output circuit obeying the constraints. The transformation often requires additional gates that can affect the accuracy of running the circuit. Based upon a previous work of quantum circuit mapping that leverages gate commutation rules, this paper shows algorithms that utilize both transformation and commutation rules. Experiments on a standard benchmark dataset confirm the algorithms with more rules can find even better circuit mappings compared with the previously-known best algorithms.
A silicon quantum photonic circuit was proposed and demonstrated as an integrated quantum light source for telecom band polarization entangled Bell state generation and dynamical manipulation. Biphoton states were firstly generated in four silicon waveguides by spontaneous four wave mixing. They were transformed to polarization entangled Bell states through on-chip quantum interference and quantum superposition, and then coupled to optical fibers. The property of polarization entanglement in generated photon pairs was demonstrated by two-photon interferences under two non-orthogonal polarization bases. The output state could be dynamically switched between two polarization entangled Bell states, which was demonstrated by the experiment of simplified Bell state measurement. The experiment results indicate that its manipulation speed supported a modulation rate of several tens kHz, showing its potential on applications of quantum communication and quantum information processing requiring dynamical quantum entangled Bell state control.
This paper will deal with the modeling-problem of combining thermal subsystems (e.g. a semiconductor module or package with a cooling radiator) making use of reduced models. The subsystem models consist of a set of Foster-type thermal equivalent circuits, which are only behavioral models. A fast al-gorithm is presented for transforming the Foster-type circuits in Cauer-circuits which have physical behavior and therefore allow for the construction of the thermal model of the complete system. Then the set of Cauer-circuits for the complete system is transformed back into Foster-circuits to give a simple mathematical representation and applicability. The transfor-mation algorithms are derived in concise form by use of recur-sive relations. The method is exemplified by modeling and measurements on a single chip IGBT package mounted on a closed water cooled radiator. The thermal impedance of the complete system is constructed from the impedances of the sub-systems, IGBT-package and radiator, and also the impedance of the package can be inferred from the measured impedance of the complete system.
We consider the Szegedy walk on graphs adding infinite length tails to a finite internal graph. We assume that on these tails, the dynamics is given by the free quantum walk. We set the $ell^infty$-category initial state so that the internal graph receives time independent input from the tails, say $boldsymbol{alpha}_{in}$, at every time step. We show that the response of the Szegedy walk to the input, which is the output, say $boldsymbol{beta}_{out}$, from the internal graph to the tails in the long time limit, is drastically changed depending on the reversibility of the underlying random walk. If the underlying random walk is reversible, we have $boldsymbol{beta}_{out}=mathrm{Sz}(boldsymbol{m}_{delta E})boldsymbol{alpha}_{in}$, where the unitary matrix $mathrm{Sz}(boldsymbol{m}_{delta E})$ is the reflection matrix to the unit vector $boldsymbol{m}_{delta E}$ which is determined by the boundary of the internal graph $delta E$. Then the global dynamics so that the internal graph is regarded as one vertex recovers the local dynamics of the Szegedy walk in the long time limit. Moreover if the underlying random walk of the Szegedy walk is reversible, then we obtain that the stationary state is expressed by a linear combination of the reversible measure and the electric current on the electric circuit determined by the internal graph and the random walks reversible measure. On the other hand, if the underlying random walk is not reversible, then the unitary matrix is just a phase flip; that is, $boldsymbol{beta}_{out}=-boldsymbol{alpha}_{in}$, and the stationary state is similar to the current flow but satisfies a different type of the Kirchhoff laws.
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