scholarly journals Detailed Account of Complexity for Implementation of Circuit-Based Quantum Algorithms

2021 ◽  
Vol 9 ◽  
Author(s):  
Fernando R. Cardoso ◽  
Daniel Yoshio Akamatsu ◽  
Vivaldo Leiria Campo Junior ◽  
Eduardo I. Duzzioni ◽  
Alfredo Jaramillo ◽  
...  
Keyword(s):  
Detailed Analysis ◽  
Quantum System ◽  
Quantum Algorithms ◽  
Quantum Algorithm ◽  
Review Article ◽  
Detailed Account ◽  
Final States ◽  
Superposition State ◽  
Final State ◽  
State Preparation

In this review article, we are interested in the detailed analysis of complexity aspects of both time and space that arises from the implementation of a quantum algorithm on a quantum based hardware. In particular, some steps of the implementation, as the preparation of an arbitrary superposition state and readout of the final state, in most of the cases can surpass the complexity aspects of the algorithm itself. We present the complexity involved in the full implementation of circuit-based quantum algorithms, from state preparation to the number of measurements needed to obtain good statistics from the final states of the quantum system, in order to assess the overall space and time costs of the processes.

scholarly journals Quantum Gate Pattern Recognition and Circuit Optimization for Scientific Applications

2021 ◽  
Vol 251 ◽  
pp. 03023
Author(s):  
Wonho Jang ◽  
Koji Terashi ◽  
Masahiko Saito ◽  
Christian W. Bauer ◽  
Benjamin Nachman ◽  
...  
Keyword(s):  
High Energy Physics ◽  
Quantum Computer ◽  
Quantum Algorithms ◽  
Circuit Complexity ◽  
Quantum Algorithm ◽  
Quantum Circuit ◽  
High Energy ◽  
Circuit Optimization ◽  
Final State ◽  
State Radiation

There is no unique way to encode a quantum algorithm into a quantum circuit. With limited qubit counts, connectivities, and coherence times, circuit optimization is essential to make the best use of quantum devices produced over a next decade. We introduce two separate ideas for circuit optimization and combine them in a multi-tiered quantum circuit optimization protocol called AQCEL. The first ingredient is a technique to recognize repeated patterns of quantum gates, opening up the possibility of future hardware optimization. The second ingredient is an approach to reduce circuit complexity by identifying zero- or low-amplitude computational basis states and redundant gates. As a demonstration, AQCEL is deployed on an iterative and effcient quantum algorithm designed to model final state radiation in high energy physics. For this algorithm, our optimization scheme brings a significant reduction in the gate count without losing any accuracy compared to the original circuit. Additionally, we have investigated whether this can be demonstrated on a quantum computer using polynomial resources. Our technique is generic and can be useful for a wide variety of quantum algorithms.

scholarly journals Practical Quantum Computing

2021 ◽  
Vol 2 (1) ◽  
pp. 1-35
Author(s):  
Adrien Suau ◽  
Gabriel Staffelbach ◽  
Henri Calandra
Keyword(s):  
Wave Equation ◽  
Quantum Computer ◽  
Quantum Algorithms ◽  
Quantum Algorithm ◽  
Quantum Circuit ◽  
Equation Solving ◽  
Small Quantum ◽  
Quantum Wave ◽  
Variational Algorithms ◽  
The One

In the last few years, several quantum algorithms that try to address the problem of partial differential equation solving have been devised: on the one hand, “direct” quantum algorithms that aim at encoding the solution of the PDE by executing one large quantum circuit; on the other hand, variational algorithms that approximate the solution of the PDE by executing several small quantum circuits and making profit of classical optimisers. In this work, we propose an experimental study of the costs (in terms of gate number and execution time on a idealised hardware created from realistic gate data) associated with one of the “direct” quantum algorithm: the wave equation solver devised in [32]. We show that our implementation of the quantum wave equation solver agrees with the theoretical big-O complexity of the algorithm. We also explain in great detail the implementation steps and discuss some possibilities of improvements. Finally, our implementation proves experimentally that some PDE can be solved on a quantum computer, even if the direct quantum algorithm chosen will require error-corrected quantum chips, which are not believed to be available in the short-term.

scholarly journals Deep neural networks for quantum circuit mapping

2021 ◽  
Author(s):  
Giovanni Acampora ◽  
Roberto Schiattarella
Keyword(s):  
Neural Networks ◽  
Deep Neural Networks ◽  
Quantum Algorithms ◽  
Quantum Algorithm ◽  
Quantum Circuit ◽  
Machine Learning Techniques ◽  
Quantum Computers ◽  
Physical Constraints ◽  
Proper Mapping ◽  
Correct Execution

AbstractQuantum computers have become reality thanks to the effort of some majors in developing innovative technologies that enable the usage of quantum effects in computation, so as to pave the way towards the design of efficient quantum algorithms to use in different applications domains, from finance and chemistry to artificial and computational intelligence. However, there are still some technological limitations that do not allow a correct design of quantum algorithms, compromising the achievement of the so-called quantum advantage. Specifically, a major limitation in the design of a quantum algorithm is related to its proper mapping to a specific quantum processor so that the underlying physical constraints are satisfied. This hard problem, known as circuit mapping, is a critical task to face in quantum world, and it needs to be efficiently addressed to allow quantum computers to work correctly and productively. In order to bridge above gap, this paper introduces a very first circuit mapping approach based on deep neural networks, which opens a completely new scenario in which the correct execution of quantum algorithms is supported by classical machine learning techniques. As shown in experimental section, the proposed approach speeds up current state-of-the-art mapping algorithms when used on 5-qubits IBM Q processors, maintaining suitable mapping accuracy.

scholarly journals RECENT τ LEPTON RESULTS FROM BABAR

2014 ◽  
Vol 35 ◽  
pp. 1460440
Author(s):  
ALBERTO LUSIANI
Keyword(s):  
Standard Model ◽  
Branching Fractions ◽  
Charged Particles ◽  
Babar Collaboration ◽  
Final States ◽  
Final State ◽  
Experimental Knowledge ◽  
Electron Positron ◽  
The Standard Model ◽  
Positron Collisions

We report recent measurements on τ leptons obtained by the BABAR collaboration using the entire recorded sample of electron-positron collisions at and around the Υ(4S) (about 470fb-1). The events were recorded at the PEP-II asymmetric collider at the SLAC National Accelerator Laboratory. The measurements include high multiplicity τ decay branching fractions with 3 or 5 charged particles in the final state, a search for the second class current the τ decay τ → πη′ν, τ branching fractions into final states containing two KS mesons, [Formula: see text], with h = π, K, and preliminary measurements of hadronic spectra of τ decays with three hadrons (τ- → h-h+h-ντ decays, where h = π, K). The results improve the experimental knowledge of the τ lepton properties and can be used to improve the precision tests of the Standard Model.

SEARCH FOR NEW PHYSICS IN eμX DATA AT THE TEVATRON USING SLEUTH: A QUASI-MODEL-INDEPENDENT SEARCH STRATEGY FOR NEW PHYSICS

2001 ◽  
Vol 16 (supp01b) ◽  
pp. 888-890
Author(s):  
◽  
BRUCE KNUTESON
Keyword(s):  
Standard Model ◽  
Search Strategy ◽  
New Physics ◽  
Beyond The Standard Model ◽  
Final States ◽  
Final State ◽  
The Standard Model ◽  
Model Independent

We present a quasi-model-independent search for physics beyond the standard model. We define final states to be studied, and construct a rule that identifies a set of variables appropriate for any particular final state. A new algorithm ("Sleuth") searches for regions of excess in the space of those variables and quantifies the significance of any detected excess. After demonstrating the sensititvity of the method, we apply it to the semi-inclusive channel eμX collected in ≈108 pb -1 of [Formula: see text] collisions at [Formula: see text] at the DØ experiment at the Fermilab Tevatron. We find no evidence of new high pT physics in this sample.

Quantum universality by state distillationIndirect quantum control for finite-dimensional coupled systems

2010 ◽  
Vol 10 (1&2) ◽  
pp. 87-96
Author(s):  
J. Nie ◽  
H.C. Fu ◽  
X.X. Yi
Keyword(s):  
Quantum System ◽  
Quantum Control ◽  
Coherent Control ◽  
Coupled Systems ◽  
Preparation Technology ◽  
State Preparation ◽  
Finite Dimensional ◽  
State Dependent ◽  
Control Scheme ◽  
Initial States

We present a new analysis on the quantum control for a quantum system coupled to a quantum probe. This analysis is based on the coherent control for the quantum system and a hypothesis that the probe can be prepared in specified initial states. The results show that a quantum system can be manipulated by probe state-dependent coherent control. In this sense, the present analysis provides a new control scheme which combines the coherent control and state preparation technology.

scholarly journals Exact quantum algorithms have advantage for almost all Boolean functions

2015 ◽  
pp. 435-452
Author(s):  
Andris Ambainis ◽  
Jozef Gruska ◽  
Shenggen Zheng
Keyword(s):  
Boolean Function ◽  
Boolean Functions ◽  
Quantum Algorithms ◽  
Quantum Algorithm ◽  
Query Complexity ◽  
Exact Quantum ◽  
Quantum Query Complexity ◽  
Almost All ◽  
Quantum Query

It has been proved that almost all n-bit Boolean functions have exact classical query complexity n. However, the situation seemed to be very different when we deal with exact quantum query complexity. In this paper, we prove that almost all n-bit Boolean functions can be computed by an exact quantum algorithm with less than n queries. More exactly, we prove that ANDn is the only n-bit Boolean function, up to isomorphism, that requires n queries.

scholarly journals Searching for axionlike particles with low masses in pPb and PbPb collisions

2021 ◽  
Vol 81 (6) ◽  
Author(s):  
V. P. Gonçalves ◽  
D. E. Martins ◽  
M. S. Rangel
Keyword(s):  
Detailed Analysis ◽  
Cross Section ◽  
Experimental Analysis ◽  
Mass Range ◽  
Final State ◽  
Lhcb Detector ◽  
The Cross ◽  
Photon Coupling

AbstractThe production of axionlike particles (ALPs) with small masses in ultraperipheral Pb–p and Pb–Pb collisions at the LHC is investigated. The cross section and kinematical distributions associated to the diphoton final state produced in the $$\gamma \gamma \rightarrow a \rightarrow \gamma \gamma $$ γ γ → a → γ γ subprocesses are estimated considering a realistic set of kinematical cuts. A detailed analysis of the backgrounds is performed and the expected sensitivity to the ALP production is derived. Our results demonstrate that a future experimental analysis of the exclusive diphoton production for the forward rapidities probed by the LHCb detector can improve the existing exclusion limits on the ALP–photon coupling in the mass range 2 GeV $$\le m_a \le $$ ≤ m a ≤ 5 GeV.

scholarly journals Electron Momentum Spectroscopy

1986 ◽  
Vol 39 (5) ◽  
pp. 587 ◽  
Author(s):  
IE McCarthy
Keyword(s):  
Impulse Approximation ◽  
High Electron ◽  
Final States ◽  
Final State ◽  
Structure Information ◽  
Plane Wave Impulse Approximation ◽  
Ion Structure ◽  
Spectroscopic Factors ◽  
Electron Momentum Spectroscopy ◽  
Energy And Momentum

For sufficiently high electron energies (greater than a few hundred eV) and sufficiently low recoil momenta Oess than a few atomic units) the differential cross section for the non-coplanar symmetric (e,2e) reaction on an atom or molecule depends on the target and ion structure only through the target-ion overlap. Experimental criteria for the energy and momentum are that the apparent structure information does not change when the energy and momentum are varied. The plane-wave impulse approximation is a sufficient description of the reaction mechanism for determining spherically averaged squares of momentum-space orbitals for atoms and molecules and for coefficients describing initial- and final-state correlations. For mainly uncorrelated initial states, spectroscopic factors for final states belonging to the same manifold are uniquely determined. For molecules, summed spectroscopic factors can be compared for different ion manifolds. For atoms, summed spectroscopic factors and higher-momentum profiles require the dist~rted-wave impulse approximation.

The Early and Final States of an Epidemic in a Large Heterogeneous Population by a Small Initial Number of Infectives

1994 ◽  
Vol 26 (03) ◽  
pp. 671-689
Author(s):  
Steven M. Butler
Keyword(s):  
Random Number ◽  
Death Process ◽  
Time Interval ◽  
Final States ◽  
Birth And Death Process ◽  
Initial Number ◽  
Threshold Behavior ◽  
Final State ◽  
Epidemic Process ◽  
Susceptibility To Infection

This paper describes the early and final properties of a general S–I–R epidemic process in which the infectives behave independently, each infective has a random number of contacts with the others in the population, and individuals vary in their susceptibility to infection. For the case of a large initial number of susceptibles and a small (finite) initial number of infectives, we derive the threshold behavior and the limiting distribution for the final state of the epidemic. Also, we show strong convergence of the epidemic process over any finite time interval to a birth and death process, extending the results of Ball (1983). These complement some results due to Butler (1994), who considers the case of a large initial number of infectives.

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