scholarly journals Error suppression in adiabatic quantum computing with qubit ensembles

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Naeimeh Mohseni ◽  
Marek Narozniak ◽  
Alexey N. Pyrkov ◽  
Valentin Ivannikov ◽  
Jonathan P. Dowling ◽  
...  
Keyword(s):  
Quantum Computing ◽  
Ground State ◽  
Mean Field Theory ◽  
Mean Field ◽  
Atomic Gases ◽  
Ensemble Size ◽  
Adiabatic Quantum Computing ◽  
Decoherence Rate ◽  
First Excited State ◽  
Error Suppression

AbstractIncorporating protection against quantum errors into adiabatic quantum computing (AQC) is an important task due to the inevitable presence of decoherence. Here, we investigate an error-protected encoding of the AQC Hamiltonian, where qubit ensembles are used in place of qubits. Our Hamiltonian only involves total spin operators of the ensembles, offering a simpler route towards error-corrected quantum computing. Our scheme is particularly suited to neutral atomic gases where it is possible to realize large ensemble sizes and produce ensemble-ensemble entanglement. We identify a critical ensemble size Nc where the nature of the first excited state becomes a single particle perturbation of the ground state, and the gap energy is predictable by mean-field theory. For ensemble sizes larger than Nc, the ground state becomes protected due to the presence of logically equivalent states and the AQC performance improves with N, as long as the decoherence rate is sufficiently low.

Ground State Properties of Z = 114 Isotopes in the Relativistic Mean-Field Theory

1997 ◽  
Vol 14 (4) ◽  
pp. 259-262 ◽  
Author(s):  
Ren Zhong-zhou ◽  
Zhu Zhi-yuan ◽  
Cai Yan-huang ◽  
Shen Yao-song ◽  
Zhan Wen-long ◽  
...  
Keyword(s):  
Field Theory ◽  
Ground State ◽  
Mean Field Theory ◽  
Mean Field ◽  
Relativistic Mean Field Theory ◽  
Relativistic Mean Field ◽  
Ground State Properties

2D ISING MODEL WITH COMPETING INTERACTIONS AND ITS APPLICATION TO CLUSTERS AND ARRAYS OF π-RINGS, GRAPHENE AND ADIABATIC QUANTUM COMPUTING

2009 ◽  
Vol 23 (20n21) ◽  
pp. 3951-3967 ◽  
Author(s):  
ANTHONY O'HARE ◽  
F. V. KUSMARTSEV ◽  
K. I. KUGEL
Keyword(s):  
Quantum Computing ◽  
Ising Model ◽  
Ground State ◽  
Honeycomb Lattice ◽  
Graphene Plane ◽  
Two Dimensional ◽  
Coupling Constant ◽  
Competing Interactions ◽  
Adiabatic Quantum Computing ◽  
Ising Spins

We study the two-dimensional Ising model with competing nearest-neighbour and diagonal interactions and investigate the phase diagram of this model. We show that the ground state at low temperatures is ordered either as stripes or as the Néel antiferromagnet. However, we also demonstrate that the energy of defects and dislocations in the lattice is close to the ground state of the system. Therefore, many locally stable (or metastable) states associated with local energy minima separated by energy barriers may appear forming a glass-like state. We discuss the results in connection with two physically different systems. First, we deal with planar clusters of loops including a Josephson π-junction (a π-rings). Each π-ring carries a persistent current and behaves as a classical orbital moment. The type of particular state associated with the orientation of orbital moments in the cluster depends on the interaction between these orbital moments and can be easily controlled, i.e. by a bias current or by other means. Second, we apply the model to the analysis of the structure of the newly discovered two-dimensional form of carbon, graphene. Carbon atoms in graphene form a planar honeycomb lattice. Actually, the graphene plane is not ideal but corrugated. The displacement of carbon atoms up and down from the plane can be also described in terms of Ising spins, the interaction of which determines the complicated shape of the corrugated graphene plane. The obtained results may be verified in experiments and are also applicable to adiabatic quantum computing where the states are switched adiabatically with the slow change of coupling constant.

scholarly journals The valence-fluctuating ground state of plutonium

2015 ◽  
Vol 1 (6) ◽  
pp. e1500188 ◽  
Author(s):  
Marc Janoschek ◽  
Pinaki Das ◽  
Bismayan Chakrabarti ◽  
Douglas L. Abernathy ◽  
Mark D. Lumsden ◽  
...  
Keyword(s):  
Ground State ◽  
Degrees Of Freedom ◽  
Mean Field Theory ◽  
Mean Field ◽  
Complex Materials ◽  
Theoretical Understanding ◽  
Electronic Correlations ◽  
Valence Fluctuations ◽  
Electronic Configurations ◽  
Control Complex

A central issue in material science is to obtain understanding of the electronic correlations that control complex materials. Such electronic correlations frequently arise because of the competition of localized and itinerant electronic degrees of freedom. Although the respective limits of well-localized or entirely itinerant ground states are well understood, the intermediate regime that controls the functional properties of complex materials continues to challenge theoretical understanding. We have used neutron spectroscopy to investigate plutonium, which is a prototypical material at the brink between bonding and nonbonding configurations. Our study reveals that the ground state of plutonium is governed by valence fluctuations, that is, a quantum mechanical superposition of localized and itinerant electronic configurations as recently predicted by dynamical mean field theory. Our results not only resolve the long-standing controversy between experiment and theory on plutonium’s magnetism but also suggest an improved understanding of the effects of such electronic dichotomy in complex materials.

Mean field theory on the incommensurate ground state of the zigzag spin chain

2002 ◽  
Vol 294 (3-4) ◽  
pp. 239-244 ◽  
Author(s):  
Liqun Sun ◽  
Jianhui Dai ◽  
Shaojin Qin ◽  
Jun Zhang
Keyword(s):  
Field Theory ◽  
Ground State ◽  
Spin Chain ◽  
Mean Field Theory ◽  
Mean Field

scholarly journals A COMPOSITE FERMION APPROACH TO THE ULTRACOLD DILUTE FERMI GAS

2011 ◽  
Vol 25 (03) ◽  
pp. 329-345 ◽  
Author(s):  
M. A. CAZALILLA
Keyword(s):  
Ground State ◽  
Mean Field Theory ◽  
Mean Field ◽  
Fermi Gas ◽  
Fermi Gases ◽  
Fermi Liquids ◽  
Composite Fermions ◽  
Composite Fermion ◽  
Ultracold Fermi Gases ◽  
Simple Picture

It is argued that the recently observed Fermi liquids in strongly interacting ultracold Fermi gases are adiabatically connected to a projected Fermi gas. This conclusion is reached by constructing a set of Jastrow wavefunctions, following Tan's observations on the structure of the physical Hilbert space [Annals of Physics 323, 2952 (2008)]. The Jastrow projection merely implements the Bethe–Peierls condition on the BCS and Fermi gas wavefunctions. This procedure provides a simple picture of the emergence of Fermi polarons as composite fermions in the normal state of the highly polarized gas. It is also shown that the projected BCS wavefunction can be written as a condensate of pairs of composite fermions (or Fermi polarons). A Hamiltonian for the composite fermions is derived. Within a mean-field theory, it is shown that the ground state and excitations of this Hamiltonian are those of a non-interacting Fermi gas although they are described by Jastrow–Slater wavefunctions.

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