Circuit complexity
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Circuit complexity in interacting QFTs and RG flows Open
A bstract We consider circuit complexity in certain interacting scalar quantum field theories, mainly focusing on the ϕ 4 theory. We work out the circuit complexity for evolving from a nearly Gaussian unentangled reference state to the ent…
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Linear growth of quantum circuit complexity Open
The complexity of quantum states has become a key quantity of interest across various subfields of physics, from quantum computing to the theory of black holes. The evolution of generic quantum systems can be modelled by considering a coll…
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On the Complexity of Quantum Circuit Compilation Open
Quantum circuit compilation (QCC) is an important problem in the emerging field of quantum computing. The problem has a strong relevance to combinatorial search, as solving approaches recently published include constraint programming and t…
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Statistical complexity of quantum circuits Open
In theoretical machine learning, the statistical complexity is a notion that measures the richness of a hypothesis space. In this work, we apply a particular measure of statistical complexity, namely the Rademacher complexity, to the quant…
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Entangling Power and Quantum Circuit Complexity Open
Notions of circuit complexity and cost play a key role in quantum computing and simulation where they capture the (weighted) minimal number of gates that is required to implement a unitary. Similar notions also become increasingly prominen…
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Aspects of the first law of complexity Open
We investigate the first law of complexity proposed in arXiv:1903.04511,\ni.e., the variation of complexity when the target state is perturbed, in more\ndetail. Based on Nielsen's geometric approach to quantum circuit complexity, we\nfind …
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Circuit complexity for fermionic thermofield double states Open
Motivated by the holographic complexity proposals, in this paper, we\ninvestigate the time dependence of the complexity for the Fermionic thermofield\ndouble state (TFD) using the Nielsen approach and Fubini-Study (FS) approach\nseparately…
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Circuit-PSI With Linear Complexity via Relaxed Batch OPPRF Open
In 2-party Circuit-based Private Set Intersection (Circuit-PSI), P0 and P1 hold sets S0 and S1 respectively and wish to securely compute a function f over the set S0 ∩ S1 (e.g., cardinality, sum over associated attributes, or threshold int…
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Complexity functionals and complexity growth limits in continuous MERA circuits Open
Using the path integral associated to a cMERA tensor network, we provide an operational definition for the complexity of a cMERA circuit/state which is relevant to investigate the complexity of states in quantum field theory. In this frame…
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Complexity measures in QFT and constrained geometric actions Open
A bstract We study the conditions under which, given a generic quantum system, complexity metrics provide actual lower bounds to the circuit complexity associated to a set of quantum gates. Inhomogeneous cost functions — many examples of w…
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Automated design of superconducting circuits and its application to 4-local couplers Open
Superconducting circuits have emerged as a promising platform to build quantum processors. The challenge of designing a circuit is to compromise between realizing a set of performance metrics and reducing circuit complexity and noise sensi…
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Fast Radix-32 Approximate DFTs for 1024-Beam Digital RF Beamforming Open
The discrete Fourier transform (DFT) is widely employed for multi-beam\ndigital beamforming. The DFT can be efficiently implemented through the use of\nfast Fourier transform (FFT) algorithms, thus reducing chip area, power\nconsumption, p…
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Nonanalyticity of circuit complexity across topological phase transitions Open
The presence of nonanalyticity in observables is a manifestation of phase\ntransitions. Through the study of two paradigmatic topological models in one\nand two dimensions, in this work we show that the circuit complexity based on\nour spe…
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Towards a Low-SWaP 1024-Beam Digital Array: A 32-Beam Subsystem at 5.8 GHz Open
Millimeter wave communications require multibeam beamforming in order to utilize wireless channels that suffer from obstructions, path loss, and multi-path effects. Digital multibeam beamforming has maximum degrees of freedom compared to a…
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On the NP-Completeness of the Minimum Circuit Size Problem Open
We study the Minimum Circuit Size Problem (MCSP): given the truth-table of a Boolean function f and a number k, does there exist a Boolean circuit of size at most k computing f? This is a fundamental NP problem that is not known to be NP-c…
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Fast and Deterministic Constant Factor Approximation Algorithms for LCS Imply New Circuit Lower Bounds Open
The Longest Common Subsequence (LCS) is one of the most basic similarity measures and it captures important applications in bioinformatics and text analysis. Following the SETH-based nearly-quadratic time lower bounds for LCS from recent y…
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Low Computational Complexity for Optimizing Energy Efficiency in mm-wave Hybrid Precoding System for 5G Open
Millimeter-wave (mm-wave) communication is the spectral frontier to meet the anticipated significant volume of high data traffic processing in next-generation systems. The primary challenges in mm-wave can be overcome by reducing complexit…
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Complexity of warped conformal field theory Open
Warped conformal field theories in two dimensions are exotic nonlocal, Lorentz violating field theories characterized by Virasoro–Kac–Moody symmetries and have attracted a lot of attention as candidate boundary duals to warped AdS $$_3$$ …
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Sharp threshold results for computational complexity Open
© 2020 ACM. We establish several "sharp threshold" results for computational complexity. For certain tasks, we can prove a resource lower bound of nc for c ≥ 1 (or obtain an efficient circuit-analysis algorithm for nc size), there is stron…
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NP-hardness of circuit minimization for multi-output functions Open
Can we design efficient algorithms for finding fast algorithms? This question is captured by various circuit minimization problems, and algorithms for the corresponding tasks have significant practical applications. Following the work of C…
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Improved Circuit Design of Analog Joint Source Channel Coding for Low-Power and Low-Complexity Wireless Sensors Open
To enable low-power and low-complexity wireless monitoring, an improved\ncircuit design of Analog Joint Source Channel Coding (AJSCC) is proposed for\nwireless sensor nodes. This innovative design is based on Analog Divider Blocks\n(ADB) w…
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Functional Lower Bounds for Arithmetic Circuits and Connections to Boolean Circuit Complexity Open
We say that a circuit C over a field F {functionally} computes a polynomial P in F[x_1, x_2, ..., x_n] if for every x in {0,1}^n we have that C(x) = P(x). This is in contrast to syntactically computing P, when C = P as formal polynomials. …
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A Fixed-Depth Size-Hierarchy Theorem for AC$^0[\\oplus]$ via the Coin\n Problem Open
We prove the first Fixed-depth Size-hierarchy Theorem for uniform\nAC$^0[\\oplus]$ circuits; in particular, for fixed $d$, the class\n$\\mathcal{C}_{d,k}$ of uniform AC$^0[\\oplus]$ formulas of depth $d$ and size\n$n^k$ form an infinite hi…
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Frege Systems for Quantified Boolean Logic Open
We define and investigate Frege systems for quantified Boolean formulas (QBF). For these new proof systems, we develop a lower bound technique that directly lifts circuit lower bounds for a circuit class C to the QBF Frege system operating…
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Strong average-case lower bounds from non-trivial derandomization Open
We prove that for all constants a, NQP = NTIME[n polylog(n)] cannot be (1/2 + 2−log a n )-approximated by 2log a n -size ACC 0 ∘ THR circuits ( ACC 0 circuits with a bottom layer of THR gates). Previously, it was even open whether E NP can…
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Memristive Oscillatory Circuits for Resolution of NP-Complete Logic Puzzles: Sudoku Case Open
Memristor networks are capable of low-power and massive parallel processing and information storage. Moreover, they have presented the ability to apply for a vast number of intelligent data analysis applications targeting mobile edge devic…
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Algebraic proof complexity Open
We survey recent progress in the proof complexity of strong proof systems and its connection to algebraic circuit complexity, showing how the synergy between the two gives rise to new approaches to fundamental open questions, solutions to …
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Circuit complexity for Carrollian Conformal (BMS) field theories Open
A bstract We systematically explore the construction of Nielsen’s circuit complexity to a non-Lorentzian field theory keeping in mind its connection with flat holography. We consider a 2 d boundary field theory dual to 3 d asymptotically f…
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Inherent Charge-Sharing-Free Dynamic Logic Gates Employing Transistors With Multiple Independent Inputs Open
Charge sharing poses a fundamental problem in the design of dynamic logic gates, which is nearly as old as digital circuit design itself. Although, many solutions are known, up to now most of them add additional complexity to a given circu…
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Robustness of average-case meta-complexity via pseudorandomness Open
We show broad equivalences in the average-case complexity of many different meta-complexity problems, including Kolmogorov complexity, time-bounded Kolmogorov complexity, and the Minimum Circuit Size Problem. These results hold for a wide …