Measuring 4-local qubit observables could probabilistically solve PSPACE

2008 ◽  
Vol 8 (8&9) ◽  
pp. 741-755
Author(s):  
P. Wocjan ◽  
D. Janzing ◽  
T. Decker
Keyword(s):  
Measurement Accuracy ◽  
Quantum Algorithm ◽  
Control Algorithms ◽  
Local Observable ◽  
Spectral Gaps ◽  
Local Quantum ◽  
Quantum Observables ◽  
Probabilistic Solution ◽  
Measurement Algorithm ◽  
Local Observables

We consider a hypothetical apparatus that implements measurements for arbitrary 4-local quantum observables A on n qubits. The apparatus implements the ``measurement algorithm'' after receiving a classical description of A. We show that a few precise measurements applied to a basis state would provide a probabilistic solution of PSPACE problems. The error probability decreases exponentially with the number of runs, if the measurement accuracy is of the order of the spectral gaps of the operator A. Moreover, every decision problem that can be solved by a deterministic quantum algorithm in T time steps can be encoded into a 4-local observable such that the solution requires only measurements of accuracy O(1/T). Provided that BQP$\neq$PSPACE, our result shows that efficient algorithms for precise measurements of general 4-local observables cannot exist. We conjecture that the class of physically existing interactions is large enough to allow the conclusion that precise energy measurements for general many-particle systems require control algorithms with high complexity.

SYMMETRIES IN THEORY OF LOCAL OBSERVABLES AND THE CHOICE OF THE NET OF LOCAL ALGEBRAS

1992 ◽  
Vol 04 (spec01) ◽  
pp. 1-14 ◽  
Author(s):  
HUZIHIRO ARAKI
Keyword(s):  
Scattering Theory ◽  
Local Observable ◽  
Particle Spectrum ◽  
Massive Scalar ◽  
Local Algebras ◽  
Local Observables ◽  
Physical Consequences ◽  
Sector Theory ◽  
Internal Symmetries

For a given net of algebras of local observables, satisfying standard assumptions, we propose the problem of classifying a net of subalgebras which provides the same physical consequences (possibly via Doplicher-Haag-Roberts sector theory) such as particle spectrum and scattering theory. The notion of symmetry of the net of local algebras are introduced and its geometrical aspects are analyzed, with the conclusion that the net reproduces the geometry of supporting regions to some extent. The internal symmetries provides a possible net of subalgebras, as is discussed by Doplicher, Haag and Roberts. We discuss other possibilities by generating subalgebras from a local observable. Results and problems for the simple case of a neutral massive scalar free Held are summarized.

scholarly journals Higher U(1)-gerbe connections in geometric prequantization

2016 ◽  
Vol 28 (06) ◽  
pp. 1650012 ◽  
Author(s):  
Domenico Fiorenza ◽  
Christopher L. Rogers ◽  
Urs Schreiber
Keyword(s):  
Vector Fields ◽  
Geometric Quantization ◽  
Group Extension ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Hamiltonian Vector Fields ◽  
Principal Connection ◽  
Local Quantum ◽  
Local Observables ◽  
Special Case

We promote geometric prequantization to higher geometry (higher stacks), where a prequantization is given by a higher principal connection (a higher gerbe with connection). We show fairly generally how there is canonically a tower of higher gauge groupoids and Courant groupoids assigned to a higher prequantization, and establish the corresponding Atiyah sequence as an integrated Kostant–Souriau [Formula: see text]-group extension of higher Hamiltonian symplectomorphisms by higher quantomorphisms. We also exhibit the [Formula: see text]-group cocycle which classifies this extension and discuss how its restrictions along Hamiltonian [Formula: see text]-actions yield higher Heisenberg cocycles. In the special case of higher differential geometry over smooth manifolds, we find the [Formula: see text]-algebra extension of Hamiltonian vector fields — which is the higher Poisson bracket of local observables — and show that it is equivalent to the construction proposed by the second author in [Formula: see text]-plectic geometry. Finally, we indicate a list of examples of applications of higher prequantization in the extended geometric quantization of local quantum field theories and specifically in string geometry.

scholarly journals A Fixed Length Adaptive Moving Average Filter-Based Synchrophasor Measurement Algorithm for P Class PMUs

Energies ◽  
2019 ◽  
Vol 12 (21) ◽  
pp. 4168
Author(s):  
Hui Xue ◽  
Mengjie Ruan ◽  
Yifan Cheng
Keyword(s):  
Disturbance Rejection ◽  
Measurement Accuracy ◽  
Moving Average ◽  
Reliable Operation ◽  
Moving Average Filter ◽  
Fixed Length ◽  
Distorted Grid ◽  
Measurement Units ◽  
Measurement Algorithm ◽  
Average Filter

Accurate and fast synchrophasor measurement is the key to the wide applications of PMUs in the system-wide monitoring and reliable operation of smart grid. To address this issue, a fixed length moving average filter-based synchrophasor measurement algorithm for P class phasor measurement units (PMUs) (FA-PSMA) is proposed in this paper. Firstly, a novel fixed length adaptive moving average filter (FAMAF) is proposed. The FAMAF has an adaptive filter capability with a fixed data window length. Then, the FAMAF is applied after a phase-locked loop (PLL) for enhanced disturbance rejection capability under frequency drifts. Finally, a detailed performance assessment is presented to validate the performance of the proposed FA-PSMA. Theoretical analysis and simulation results validate that the proposed FA-PSMA can track the grid frequency and phasor accurately under distorted grid conditions. The response time and measurement accuracy satisfy the requirements specified in IEC/IEEE 60255-118-1.

Quantum-based algorithm and circuit design for bounded Knapsack optimization problem

2020 ◽  
Vol 20 (9&10) ◽  
pp. 766-786
Author(s):  
Wenjun Hou ◽  
Marek Perkowski
Keyword(s):  
Circuit Design ◽  
Knapsack Problem ◽  
Decision Problem ◽  
Optimization Problem ◽  
Quantum Algorithm ◽  
Quantum Circuits ◽  
Local Quantum ◽  
Speed Up ◽  
Grover Search ◽  
Quantum Simulator

The Knapsack Problem is a prominent problem that is used in resource allocation and cryptography. This paper presents an oracle and a circuit design that verifies solutions to the decision problem form of the Bounded Knapsack Problem. This oracle can be used by Grover Search to solve the optimization problem form of the Bounded Knapsack Problem. This algorithm leverages the quadratic speed-up offered by Grover Search to achieve a quantum algorithm for the Knapsack Problem that shows improvement with regard to classical algorithms. The quantum circuits were designed using the Microsoft Q# Programming Language and verified on its local quantum simulator. The paper also provides analyses of the complexity and gate cost of the proposed oracle. The work in this paper is the first such proposed method for the Knapsack Optimization Problem.

scholarly journals ANY COMPACT GROUP IS A GAUGE GROUP

2002 ◽  
Vol 14 (07n08) ◽  
pp. 873-885 ◽  
Author(s):  
SERGIO DOPLICHER ◽  
GHERARDO PIACITELLI
Keyword(s):  
Compact Group ◽  
Gauge Group ◽  
Infinite Product ◽  
Free Field ◽  
Gauge Transformations ◽  
Normal Algebra ◽  
Local Algebras ◽  
Local Quantum ◽  
Split Property ◽  
Local Observables

The assignment of the local observables in the vacuum sector, fulfilling the standard axioms of local quantum theory, is known to determine uniquely a compact group G of gauge transformations of the first kind together with a central involutive element k of G, and a complete normal algebra of fields carrying the localizable charges, on which k defines the Bose/Fermi grading. We show here that any such pair {G, k}, where G is compact metrizable, does actually appear. The corresponding model can be chosen to fulfill also the split property. This is not a dynamical phenomenon: a given {G, k} arises as the gauge group of a model where the local algebras of observables are a suitable subnet of local algebras of a possibly infinite product of free field theories.

scholarly journals Unified Framework for Correlations in Terms of Local Quantum Observables

2010 ◽  
Vol 104 (14) ◽  
Author(s):  
A. Acín ◽  
R. Augusiak ◽  
D. Cavalcanti ◽  
C. Hadley ◽  
J. K. Korbicz ◽  
...  
Keyword(s):  
Unified Framework ◽  
Local Quantum ◽  
Quantum Observables

scholarly journals CONSTRUCTION AND TEST OF BIO-INSPIRED IMAGING POLARIZATION NAVIGATION PROTOTYPE

2020 ◽  
Vol XLIII-B1-2020 ◽  
pp. 323-329
Author(s):  
H. Lu ◽  
Y. Xie ◽  
K. Zhang ◽  
H. Zhang ◽  
X. M. Zou ◽  
...  
Keyword(s):  
Real Time ◽  
Measurement Accuracy ◽  
Recognition Algorithm ◽  
Dynamic Experiment ◽  
Polarization Imaging ◽  
Polarization Image ◽  
Intensity Images ◽  
Measurement Algorithm ◽  
Imaging Sensor ◽  
Navigation Method

Abstract. Bio-inspired polarization navigation is a promising navigation method inspired by insects’ autonomous foraging and homing behaviour. Many insects acquire their spatial orientation by sensing the polarization pattern of the skylight. We propose utilization of solar meridian in the polarized skylight as an orientation cue because of its significant features. Using its features, we then design and construct an imaging polarization navigation prototype. The prototype consists of a field-division polarization imaging sensor, the corresponding software, an interface, and the solar-meridian recognizing and measurement algorithm. The field-division polarization imaging sensor is the core component of the prototype and acquires polarized intensity images. To adapt to the demand of real-time on navigation system, we then propose an optimized real-time polarization image processing and pattern recognition algorithm based on Hough transform. The azimuth measurement accuracy of the sensor is then calibrated using a facility that is able to get higher azimuth accuracy by measurement of the star light. To verify the navigation capability of the developed system, we use a dynamic experiment, where the prototype is installed on the top of a vehicle and its navigation performance is compared with GNSS.

Quantum correlations for two-qubit X states through the local quantum uncertainty

2017 ◽  
Vol 15 (03) ◽  
pp. 1750020 ◽  
Author(s):  
L. Jebli ◽  
B. Benzimoun ◽  
M. Daoud
Keyword(s):  
Quantum Correlations ◽  
Quantum Systems ◽  
Local Observable ◽  
Quantum Metrology ◽  
Quantum Uncertainty ◽  
Bipartite State ◽  
Local Quantum Uncertainty ◽  
Local Quantum ◽  
Qubit States ◽  
Spin Coherent States

Local quantum uncertainty is defined as the minimum amount of uncertainty in measuring a local observable for a bipartite state. It provides a well-defined measure of pairwise quantum correlations in quantum systems and has operational significance in quantum metrology. In this work, we analytically derive the expression of local quantum uncertainty for two-qubit [Formula: see text] states which are of paramount importance in various fields of quantum information. As an illustration, we consider two-qubit states extracted from even and odd spin coherent states.

Colorimetric Temperature Measurement Algorithm Based on Multi-Sensor Data Fusion

2014 ◽  
Vol 530-531 ◽  
pp. 146-150
Author(s):  
Fan Wei Meng ◽  
Qing Tian ◽  
You Liang Yang
Keyword(s):  
Standard Deviation ◽  
Temperature Measurement ◽  
Real Time ◽  
Measurement System ◽  
Measurement Accuracy ◽  
Image Sensor ◽  
Sensor Data ◽  
The Real ◽  
Measurement Algorithm ◽  
Temperature Measurement System

Wavelength and other factors have a deep influence on temperature measurement system based on CCD image sensor. Deviations between measurement values sometimes are large. In order to reduce error, the temperature outputs in different wavelength combinations do have multi-sensor correlation properties in point of colorimetric temperature measurement system view. The colorimetric temperature measurement algorithm based on real-time adaptive weighted is put forward by such performance index that minimum of standard deviation. According to measured value of each sensor, we will find out the corresponding weights in adaptive manner. And discuss the statistical properties of the estimated standard deviation. Estimation unbiasedness is proved. The algorithm has the following advantages .A much smaller amount of calculation, without any a priori knowledge, only relying on the output of each sensor. All of these make temperature estimation be optimal, measurement accuracy and the real-time performance of the system are improved. Theoretical analysis and experimental results show that the colorimetric temperature measurement algorithm based on the real-time adaptive weighted improves obviously when comparing with the traditional means algorithm in measurement accuracy.

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