Similarity of Computations Across Domains Does Not Imply Shared Implementation: The Case of Language Comprehension

Understanding language requires applying cognitive operations (e.g., memory retrieval, prediction, structure building) that are relevant across many cognitive domains to specialized knowledge structures (e.g., a particular language’s lexicon and syntax). Are these computations carried out by domain-general circuits or by circuits that store domain-specific representations? Recent work has characterized the roles in language comprehension of the language network, which is selective for high-level language processing, and the multiple-demand (MD) network, which has been implicated in executive functions and linked to fluid intelligence and thus is a prime candidate for implementing computations that support information processing across domains. The language network responds robustly to diverse aspects of comprehension, but the MD network shows no sensitivity to linguistic variables. We therefore argue that the MD network does not play a core role in language comprehension and that past findings suggesting the contrary are likely due to methodological artifacts. Although future studies may reveal some aspects of language comprehension that require the MD network, evidence to date suggests that those will not be related to core linguistic processes such as lexical access or composition. The finding that the circuits that store linguistic knowledge carry out computations on those representations aligns with general arguments against the separation of memory and computation in the mind and brain.

Equivalent-Circuit Modeling of Lossless and Lossy Bi-Periodic Scatterers by an Eigenstate Approach

The use of an eigenstate based equivalent circuit topology is proposed for the analysis and modeling of lossless and lossy bi-periodic scatterers. It can significantly simplify the design of this kind of surfaces, since it reduces the number of elements with respect to other general circuits. It contains at most only two admittances and two transformers depending on one unique transformation ratio. The real parts of these admittances can be assured to be non-negative, an interesting aspect in the modeling of lossy surfaces such as those present in asorbers. Moreover, due to the capability of decomposition into the eigenexcitations of the structure, the circuit provides important physical insight. Different cases of scatterers have been analyzed: symmetric and asymmetric, lossy and lossless. In all these cases, the modeling of the circuit admittances has been successfully achieved with a few RLC elements, positive and frequency independent. In the case of structures with symmetries, the transformation ratio directly reflects the physical orientation of the eigenexcitations of the scatterer. Furthermore, in the case of lossy scatterers but without symmetries, the resulting equivalent circuit reveals that their eigenexcitations are not linear polarizations, but elliptic polarizations whose properties are described by the complex transformation ratio.

Equivalent-Circuit Modeling of Lossless and Lossy Bi-Periodic Scatterers by an Eigenstate Approach

The use of an eigenstate based equivalent circuit topology is proposed for the analysis and modeling of lossless and lossy bi-periodic scatterers. It can significantly simplify the design of this kind of surfaces, since it reduces the number of elements with respect to other general circuits. It contains at most only two admittances and two transformers depending on one unique transformation ratio. The real parts of these admittances can be assured to be non-negative, an interesting aspect in the modeling of lossy surfaces such as those present in asorbers. Moreover, due to the capability of decomposition into the eigenexcitations of the structure, the circuit provides important physical insight. Different cases of scatterers have been analyzed: symmetric and asymmetric, lossy and lossless. In all these cases, the modeling of the circuit admittances has been successfully achieved with a few RLC elements, positive and frequency independent. In the case of structures with symmetries, the transformation ratio directly reflects the physical orientation of the eigenexcitations of the scatterer. Furthermore, in the case of lossy scatterers but without symmetries, the resulting equivalent circuit reveals that their eigenexcitations are not linear polarizations, but elliptic polarizations whose properties are described by the complex transformation ratio.

Graph-theoretic Simplification of Quantum Circuits with the ZX-calculus

We present a completely new approach to quantum circuit optimisation, based on the ZX-calculus. We first interpret quantum circuits as ZX-diagrams, which provide a flexible, lower-level language for describing quantum computations graphically. Then, using the rules of the ZX-calculus, we give a simplification strategy for ZX-diagrams based on the two graph transformations of local complementation and pivoting and show that the resulting reduced diagram can be transformed back into a quantum circuit. While little is known about extracting circuits from arbitrary ZX-diagrams, we show that the underlying graph of our simplified ZX-diagram always has a graph-theoretic property called generalised flow, which in turn yields a deterministic circuit extraction procedure. For Clifford circuits, this extraction procedure yields a new normal form that is both asymptotically optimal in size and gives a new, smaller upper bound on gate depth for nearest-neighbour architectures. For Clifford+T and more general circuits, our technique enables us to to `see around' gates that obstruct the Clifford structure and produce smaller circuits than naïve `cut-and-resynthesise' methods.

Quantifying magic for multi-qubit operations

The development of a framework for quantifying ‘non-stabilizerness’ of quantum operations is motivated by the magic state model of fault-tolerant quantum computation and by the need to estimate classical simulation cost for noisy intermediate-scale quantum (NISQ) devices. The robustness of magic was recently proposed as a well-behaved magic monotone for multi-qubit states and quantifies the simulation overhead of circuits composed of Clifford + T gates, or circuits using other gates from the Clifford hierarchy. Here we present a general theory of the ‘non-stabilizerness’ of quantum operations rather than states, which are useful for classical simulation of more general circuits. We introduce two magic monotones, called channel robustness and magic capacity, which are well-defined for general n -qubit channels and treat all stabilizer-preserving CPTP maps as free operations. We present two complementary Monte Carlo-type classical simulation algorithms with sample complexity given by these quantities and provide examples of channels where the complexity of our algorithms is exponentially better than previously known simulators. We present additional techniques that ease the difficulty of calculating our monotones for special classes of channels.

Rewriting Environment for Arithmetic Circuit Verification

The paper describes a practical software tool for the verification of integer arithmetic circuits. It covers different types of integer multipliers, fused add-multiply circuits, and constant dividers - in general, circuits whose computation can be represented as a polynomial. The verification uses an algebraic model of the circuit and is accomplished by rewriting the polynomial of the binary encoding of the primary outputs (output signature), using the polynomial models of the logic gates, into a polynomial over the primary inputs (input signature). The resulting polynomial represents arithmetic function implemented by the circuit and hence can be used to extract functional specification from its gate-level implementation. The rewriting uses an efficient And-Inverter Graph (AIG) representation to enable extraction of the essential arithmetic components of the circuit. The tool is integrated with the popular ABC system. Its efficiency is illustrated with impressive results for integer multipliers, fused add-multiply circuits, and divide-by-constant circuits. The entire verification system is offered in an open source ABC environment together with an extensive set of benchmarks.