scholarly journals Circuit complexity in interacting QFTs and RG flows

2018 ◽  
Vol 2018 (10) ◽  
Author(s):  
Arpan Bhattacharyya ◽  
Arvind Shekar ◽  
Aninda Sinha
Keyword(s):  
Circuit Complexity

scholarly journals A framework for reducing the overhead of the quantum oracle for use with Grover’s algorithm with applications to cryptanalysis of SIKE

2020 ◽  
Vol 15 (1) ◽  
pp. 143-156
Author(s):  
Jean-François Biasse ◽  
Benjamin Pring
Keyword(s):  
Search Algorithm ◽  
Circuit Complexity ◽  
Quantum Circuit ◽  
Grover’S Algorithm ◽  
Search Problems ◽  
Trade Offs ◽  
Single Target ◽  
Grover's Algorithm ◽  
Quantum Oracle ◽  
The Cost

AbstractIn this paper we provide a framework for applying classical search and preprocessing to quantum oracles for use with Grover’s quantum search algorithm in order to lower the quantum circuit-complexity of Grover’s algorithm for single-target search problems. This has the effect (for certain problems) of reducing a portion of the polynomial overhead contributed by the implementation cost of quantum oracles and can be used to provide either strict improvements or advantageous trade-offs in circuit-complexity. Our results indicate that it is possible for quantum oracles for certain single-target preimage search problems to reduce the quantum circuit-size from $O\left(2^{n/2}\cdot mC\right)$ (where C originates from the cost of implementing the quantum oracle) to $O(2^{n/2} \cdot m\sqrt{C})$ without the use of quantum ram, whilst also slightly reducing the number of required qubits.This framework captures a previous optimisation of Grover’s algorithm using preprocessing [21] applied to cryptanalysis, providing new asymptotic analysis. We additionally provide insights and asymptotic improvements on recent cryptanalysis [16] of SIKE [14] via Grover’s algorithm, demonstrating that the speedup applies to this attack and impacting upon quantum security estimates [16] incorporated into the SIKE specification [14].

scholarly journals Computational and Proof Complexity of Partial String Avoidability

2021 ◽  
Vol 13 (1) ◽  
pp. 1-25
Author(s):  
Dmitry Itsykson ◽  
Alexander Okhotin ◽  
Vsevolod Oparin
Keyword(s):  
Lower Bounds ◽  
Circuit Complexity ◽  
Conjunctive Normal Form ◽  
Proof Complexity ◽  
Proof Systems ◽  
Finite Set ◽  
Propositional Proof Systems ◽  
Classical Proof ◽  
Exponential Size ◽  
Infinite String

The partial string avoidability problem is stated as follows: given a finite set of strings with possible “holes” (wildcard symbols), determine whether there exists a two-sided infinite string containing no substrings from this set, assuming that a hole matches every symbol. The problem is known to be NP-hard and in PSPACE, and this article establishes its PSPACE-completeness. Next, string avoidability over the binary alphabet is interpreted as a version of conjunctive normal form satisfiability problem, where each clause has infinitely many shifted variants. Non-satisfiability of these formulas can be proved using variants of classical propositional proof systems, augmented with derivation rules for shifting proof lines (such as clauses, inequalities, polynomials, etc.). First, it is proved that there is a particular formula that has a short refutation in Resolution with a shift rule but requires classical proofs of exponential size. At the same time, it is shown that exponential lower bounds for classical proof systems can be translated for their shifted versions. Finally, it is shown that superpolynomial lower bounds on the size of shifted proofs would separate NP from PSPACE; a connection to lower bounds on circuit complexity is also established.

A Better-Than-3n Lower Bound for the Circuit Complexity of an Explicit Function

2016 ◽  
Author(s):  
Magnus Gausdal Find ◽  
Alexander Golovnev ◽  
Edward A. Hirsch ◽  
Alexander S. Kulikov
Keyword(s):  
Lower Bound ◽  
Circuit Complexity ◽  
Explicit Function ◽  
Better Than

scholarly journals Circuit complexity in quantum field theory

2017 ◽  
Vol 2017 (10) ◽  
Author(s):  
Robert A. Jefferson ◽  
Robert C. Myers
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Circuit Complexity ◽  
Quantum Field

A CMOS Temperature Sensor with a Maximum Accuracy of 1.6 °C after One-Point Calibration

2013 ◽  
Vol 336-338 ◽  
pp. 216-220
Author(s):  
Chun Chi Chen ◽  
Keng Chih Liu ◽  
Shih Hao Lin
Keyword(s):  
Temperature Sensor ◽  
Pulse Generator ◽  
Circuit Complexity ◽  
Absolute Temperature ◽  
Cmos Process ◽  
Chip Area ◽  
Test Cost Reduction ◽  
Linear Delay ◽  
Time Amplifier ◽  
Fine Resolution

This paper presents a time-domain CMOS oscillator-based temperature sensor with one-point calibration for test cost reduction. Compared with the former CMOS sensors with linear delay lines, the proposed work composed of a temperature-to-pulse generator with adjustable time gain and a time-to-digital converter (TDC) can achieve lower circuit complexity and smaller area. A temperature-dependent oscillator for temperature sensing was used to generate the period width proportional to absolute temperature (PTAT). With the help of calibration circuit, an adjustable-gain time amplifier was adopted to dynamically adjust the amplified width that was converted by the TDC into the corresponding digital code. After calibration, the fluctuation of the sensor output with process variation can be greatly reduced. The maximum inaccuracy after one-point calibration for six package chips was 1.6 °C within a 0 80 °C temperature range. The proposed sensor fabricated in a 0.35-μm CMOS process occupied a chip area of merely 0.07 mm2, achieved a fine resolution of 0.047 °C/LSB, and consumed a low power of 25 μW@10 samples/s.

Circuit complexity of linear functions: gate elimination and feeble security

2012 ◽  
Vol 188 (1) ◽  
pp. 35-46
Author(s):  
A. P. Davydow ◽  
S. I. Nikolenko
Keyword(s):  
Circuit Complexity ◽  
Linear Functions ◽  
Gate Elimination

scholarly journals Enhancing the Quantum Linear Systems Algorithm Using Richardson Extrapolation

2022 ◽  
Vol 3 (1) ◽  
pp. 1-37
Author(s):  
Almudena Carrera Vazquez ◽  
Ralf Hiptmair ◽  
Stefan Woerner
Keyword(s):  
Necessary Conditions ◽  
Linear Equations ◽  
Circuit Complexity ◽  
Quantum Algorithm ◽  
Richardson Extrapolation ◽  
Classical Simulation ◽  
Hamiltonian Simulation ◽  
Systems Of Linear Equations ◽  
Amplitude Amplification ◽  
Theoretical Results

We present a quantum algorithm to solve systems of linear equations of the form Ax = b , where A is a tridiagonal Toeplitz matrix and b results from discretizing an analytic function, with a circuit complexity of O (1/√ε, poly (log κ, log N )), where N denotes the number of equations, ε is the accuracy, and κ the condition number. The repeat-until-success algorithm has to be run O (κ/(1-ε)) times to succeed, leveraging amplitude amplification, and needs to be sampled O (1/ε 2 ) times. Thus, the algorithm achieves an exponential improvement with respect to N over classical methods. In particular, we present efficient oracles for state preparation, Hamiltonian simulation, and a set of observables together with the corresponding error and complexity analyses. As the main result of this work, we show how to use Richardson extrapolation to enhance Hamiltonian simulation, resulting in an implementation of Quantum Phase Estimation (QPE) within the algorithm with 1/√ε circuits that can be run in parallel each with circuit complexity 1/√ ε instead of 1/ε. Furthermore, we analyze necessary conditions for the overall algorithm to achieve an exponential speedup compared to classical methods. Our approach is not limited to the considered setting and can be applied to more general problems where Hamiltonian simulation is approximated via product formulae, although our theoretical results would need to be extended accordingly. All the procedures presented are implemented with Qiskit and tested for small systems using classical simulation as well as using real quantum devices available through the IBM Quantum Experience.

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