We consider the use of quantum error-detecting codes, together with energy penalties against leaving the code space, as a method for suppressing environmentally induced errors in Hamiltonian-based quantum computation. This method was introduced in Jordan et al. [Phys. Rev. A 74, 052322 (2006)] in the context of quantum adiabatic computation, but we consider it more generally. Specifically, we consider a computational Hamiltonian, which has been encoded using the logical qubits of a single-qubit error-detecting code, coupled to an environment of qubits by interaction terms that act one-locally on the system. Additional energy penalty terms penalize states outside of the code space. We prove that in the limit of infinitely large penalties, one-local errors are completely suppressed, and we derive some bounds for the finite penalty case. Our proof technique involves exact integration of the Schrodinger equation, making no use of master equations or their assumptions. We perform long time numerical simulations on a small (one logical qubit) computational system coupled to an environment and the results suggest that the energy penalty method achieves even greater protection than our bounds indicate.
Quantum Walks are unitary processes describing the evolution of an initially localized wavefunction on a lattice potential. The complexity of the dynamics increases significantly when several indistinguishable quantum walkers propagate on the same lattice simultaneously, as these develop non-trivial spatial correlations that depend on the particle's quantum statistics, mutual interactions, initial positions, and the lattice potential. We show that even in the simplest case of a quantum walk on a one dimensional graph, these correlations can be shaped to yield a complete set of compact quantum logic operations. We provide detailed recipes for implementing quantum logic on one-dimensional quantum walks in two general cases. For non-interacting bosons-such as photons in waveguide lattices-we find high-fidelity probabilistic quantum gates that could be integrated into linear optics quantum computation schemes. For interacting quantum-walkers on a one-dimensional lattice-a situation that has recently been demonstrated using ultra-cold atoms-we find deterministic logic operations that are universal for quantum information processing. The suggested implementation requires minimal resources and a level of control that is within reach using recently demonstrated techniques. Further work is required to address error-correction.npj Quantum Information (2018) 4:2 ;
In this paper we give an overview of the quantum computational complexity class QMA and a description of known QMA-complete problems to date (The reader is invited to share more proven QMA-complete problems with the author). Such problems are believed to be difficult to solve, even with a quantum computer, but have the property that if a purported solution to the problem is given, a quantum computer would easily be able to verify whether it is correct. An attempt has been made to make this paper as self-contained as possible so that it can be accessible to computer scientists, physicists, mathematicians, and quantum chemists. Problems of interest to all of these professions can be found here.
The velocity of polaron migration in the long poly-DNA chain (∼40 base pairs) in an applied electric field has been studied within a polaron model. A small polaron shows a slow propagation and strong tolerance to the electric field, while a large polaron is much faster and less stable with increasing electric field. Moreover, the conductance of the DNA molecule within the polaron model is found to be sensitive to structural disorders in the DNA geometry.
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