Quantum Chemistry on Quantum Computers: A Polynomial-Time Quantum Algorithm for Constructing the Wave Functions of Open-Shell Molecules

2016 ◽  
Vol 120 (32) ◽  
pp. 6459-6466 ◽  
Author(s):  
Kenji Sugisaki ◽  
Satoru Yamamoto ◽  
Shigeaki Nakazawa ◽  
Kazuo Toyota ◽  
Kazunobu Sato ◽  
...  
Keyword(s):  
Quantum Chemistry ◽  
Polynomial Time ◽  
Quantum Algorithm ◽  
Open Shell ◽  
Wave Functions ◽  
Quantum Computers ◽  
Time Quantum

scholarly journals Polynomial-time quantum algorithm for the simulation of chemical dynamics

2008 ◽  
Vol 105 (48) ◽  
pp. 18681-18686 ◽  
Author(s):  
I. Kassal ◽  
S. P. Jordan ◽  
P. J. Love ◽  
M. Mohseni ◽  
A. Aspuru-Guzik
Keyword(s):  
Polynomial Time ◽  
Quantum Algorithm ◽  
Chemical Dynamics ◽  
Time Quantum

scholarly journals Experimental study of quantum simulation for quantum chemistry with a nuclear magnetic resonance simulator

2012 ◽  
Vol 370 (1976) ◽  
pp. 4734-4747 ◽  
Author(s):  
Dawei Lu ◽  
Nanyang Xu ◽  
Boruo Xu ◽  
Zhaokai Li ◽  
Hongwei Chen ◽  
...  
Keyword(s):  
Nuclear Magnetic Resonance ◽  
Magnetic Resonance ◽  
Quantum Chemistry ◽  
Quantum Simulation ◽  
Isomerization Reaction ◽  
Quantum Computers ◽  
One Dimensional ◽  
Time Quantum ◽  
Near Future ◽  
Nuclear Magnetic

Quantum computers have been proved to be able to mimic quantum systems efficiently in polynomial time. Quantum chemistry problems, such as static molecular energy calculations and dynamical chemical reaction simulations, become very intractable on classical computers with scaling up of the system. Therefore, quantum simulation is a feasible and effective approach to tackle quantum chemistry problems. Proof-of-principle experiments have been implemented on the calculation of the hydrogen molecular energies and one-dimensional chemical isomerization reaction dynamics using nuclear magnetic resonance systems. We conclude that quantum simulation will surpass classical computers for quantum chemistry in the near future.

scholarly journals Efficient quantum algorithms for the hidden subgroup problem over semi-direct product groups

2007 ◽  
Vol 7 (5&6) ◽  
pp. 559-570
Author(s):  
Y. Inui ◽  
F. Le Gall
Keyword(s):  
Direct Product ◽  
Polynomial Time ◽  
Efficient Algorithm ◽  
Quantum Algorithms ◽  
Quantum Algorithm ◽  
Black Box ◽  
Hidden Subgroup Problem ◽  
Time Quantum ◽  
Subgroup Problem

In this paper, we consider the hidden subgroup problem (HSP) over the class of semi-direct product groups $\mathbb{Z}_{p^r}\rtimes\mathbb{Z}_q$, for $p$ and $q$ prime. We first present a classification of these groups in five classes. Then, we describe a polynomial-time quantum algorithm solving the HSP over all the groups of one of these classes: the groups of the form $\mathbb{Z}_{p^r}\rtimes\mathbb{Z}_p$, where $p$ is an odd prime. Our algorithm works even in the most general case where the group is presented as a black-box group with not necessarily unique encoding. Finally, we extend this result and present an efficient algorithm solving the HSP over the groups $\mathbb{Z}^m_{p^r}\rtimes\mathbb{Z}_p$.

scholarly journals Quantum Chemistry on Quantum Computers: A Method for Preparation of Multiconfigurational Wave Functions on Quantum Computers without Performing Post-Hartree–Fock Calculations

2018 ◽  
Vol 5 (1) ◽  
pp. 167-175 ◽  
Author(s):  
Kenji Sugisaki ◽  
Shigeaki Nakazawa ◽  
Kazuo Toyota ◽  
Kazunobu Sato ◽  
Daisuke Shiomi ◽  
...  
Keyword(s):  
Quantum Chemistry ◽  
Wave Functions ◽  
Quantum Computers ◽  
Hartree Fock

scholarly journals Lattice Based Mix Network for Location Privacy in Mobile System

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Kunwar Singh ◽  
C. Pandu Rangan ◽  
A. K. Banerjee
Keyword(s):  
Polynomial Time ◽  
Location Privacy ◽  
Quantum Computer ◽  
Quantum Algorithm ◽  
Public Key ◽  
Mobile System ◽  
The Public ◽  
Diffie Hellman ◽  
Cryptographic Primitive ◽  
Time Quantum

In 1981, David Chaum proposed a cryptographic primitive for privacy calledmix network(Mixnet). A mixnet is cryptographic construction that establishes anonymous communication channel through a set of servers. In 2004, Golle et al. proposed a new cryptographic primitive called universal reencryption which takes the input as encrypted messages under the public key of the recipients not the public key of the universal mixnet. In Eurocrypt 2010, Gentry, Halevi, and Vaikunthanathan presented a cryptosystem which is an additive homomorphic and a multiplicative homomorphic for only one multiplication. In MIST 2013, Singh et al. presented a lattice based universal reencryption scheme under learning with error (LWE) assumption. In this paper, we have improved Singh et al.’s scheme using Fairbrother’s idea. LWE is a lattice hard problem for which till now there is no polynomial time quantum algorithm. Wiangsripanawan et al. proposed a protocol for location privacy in mobile system using universal reencryption whose security is reducible to Decision Diffie-Hellman assumption. Once quantum computer becomes a reality, universal reencryption can be broken in polynomial time by Shor’s algorithm. In postquantum cryptography, our scheme can replace universal reencryption scheme used in Wiangsripanawan et al. scheme for location privacy in mobile system.

scholarly journals Localized Quantum Chemistry on Quantum Computers

2021 ◽  
Author(s):  
Matthew Otten ◽  
Matthew Hermes ◽  
Riddhish Pandharkar ◽  
Yuri Alexeev ◽  
Stephen Gray ◽  
...  
Keyword(s):  
Quantum Chemistry ◽  
Quantum Algorithms ◽  
Quantum Algorithm ◽  
System Size ◽  
Coupled Cluster ◽  
Quantum Computers ◽  
Active Space ◽  
Polynomial Reduction ◽  
Quantum Chemistry Calculations ◽  
Self Consistent Field

Quantum chemistry calculations of large, strongly correlated systems are typically limited by the computation cost that scales exponentially with the size of the system. Quantum algorithms, designed specifically for quantum computers, can alleviate this, but the resources required are still too large for today’s quantum devices. Here we present a quantum algorithm that combines a localization of multireference wave functions of chemical systems with quantum phase estimation (QPE) and variational unitary coupled cluster singles and doubles (UCCSD) to compute their ground state energy. Our algorithm, termed “local active space unitary coupled cluster” (LAS-UCC), scales linearly with system size for certain geometries, providing a polynomial reduction in the total number of gates compared with QPE, while providing accuracy above that of the variational quantum eigensolver using the UCCSD ansatz and also above that of the classical local active space self-consistent field. The accuracy of LAS-UCC is demonstrated by dissociating (H2)2 into two H2 molecules and by breaking the two double bonds in trans-butadiene and resources estimates are provided for linear chains of up to 20 H2 molecules.

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