arXiv subjects

Jeongho Bang

Publications and source records attributed to Jeongho Bang.

61 records · Page 4Linked to original sources

arXiv2014

A quantum algorithm for obtaining the lowest eigenstate of a Hamiltonian assisted with an ancillary qubit system

We propose a quantum algorithm to obtain the lowest eigenstate of any Hamiltonian simulated by a quantum computer. The proposed algorithm begins with an arbitrary initial state of the simulated system. A finite series of transforms is iteratively applied to the initial state assisted with an ancillary qubit. The fraction of the lowest eigenstate in the initial state is then amplified up to $\simeq 1$. We prove that our algorithm can faithfully work for any arbitrary Hamiltonian in the theoretical analysis. Numerical analyses are also carried out. We firstly provide a numerical proof-of-principle demonstration with a simple Hamiltonian in order to compare our scheme with the so-called "Demon-like algorithmic cooling (DLAC)", recently proposed in [Nature Photonics 8, 113 (2014)]. The result shows a good agreement with our theoretical analysis, exhibiting the comparable behavior to the best "cooling" with the DLAC method. We then consider a random Hamiltonian model for further analysis of our algorithm. By numerical simulations, we show that the total number $n_c$ of iterations is proportional to $\simeq {\cal O}(D^{-1}ε^{-0.19})$, where $D$ is the difference between the two lowest eigenvalues, and $ε$ is an error defined as the probability that the finally obtained system state is in an unexpected (i.e. not the lowest) eigenstate.

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arXiv2014

Strategy for quantum algorithm design assisted by machine learning

We propose a method for quantum algorithm design assisted by machine learning. The method uses a quantum-classical hybrid simulator, where a "quantum student" is being taught by a "classical teacher." In other words, in our method, the learning system is supposed to evolve into a quantum algorithm for a given problem assisted by classical main-feedback system. Our method is applicable to design quantum oracle-based algorithm. As a case study, we chose an oracle decision problem, called a Deutsch-Jozsa problem. We showed by using Monte-Carlo simulations that our simulator can faithfully learn quantum algorithm to solve the problem for given oracle. Remarkably, learning time is proportional to the square root of the total number of parameters instead of the exponential dependance found in the classical machine learning based method.

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arXiv2014

Experimental demonstration of error-insensitive approximate universal-NOT gates

We propose and experimentally demonstrate an approximate universal-NOT (U-NOT) operation that is robust against operational errors. In our proposal, the U-NOT operation is composed of stochastic unitary operations represented by the vertices of regular polyhedrons. The operation is designed to be robust against random operational errors by increasing the number of unitary operations (i.e., reference axes). Remarkably, no increase in the total number of measurements nor additional resources are required to perform the U-NOT operation. Our method can be applied in general to reduce operational errors to an arbitrary degree of precision when approximating any anti-unitary operation in a stochastic manner.

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arXiv2014

Inseparability Criterion Using Higher-Order Schrödinger-Robertson Uncertainty Relation

We formulate an inseparability criterion based on the recently derived generalized Schrödinger-Robertson uncertainty relation (SRUR) [Ivan {\it et al.} J. Phys. A :Math. Theor. {\bf 45}, 195305 (2012)] together with the negativity of partial transpose (PT). This generalized SRUR systematically deals with two orthogonal quadrature amplitudes to higher-orders, so is relevant to characterize non-Gaussian quantum statistics. We first present a method that relies on the single-mode marginal distribution of two-mode fields under PT followed by beam-splitting operation. We then extend the SRUR to two-mode cases and develop a full two-mode version of inseparability criterion. We find that our formulation can be useful to detect entanglement of non-Gaussian states even when, e.g., the entropic criterion that also involves higher-order moments fails.

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arXiv2012

Procedures for realizing an approximate universal NOT gate

We consider procedures to realize an approximate universal NOT gate in terms of average fidelity and fidelity deviation. The average fidelity indicates the optimality of operation on average, while the fidelity deviation does the universality of operation. We show that one-qubit operations have a sharp trade-off relation between average fidelity and fidelity deviation, and two-qubit operations show a looser trade-off relation. The genuine universality holds for operations of more than two qubits, and those of even more qubits are beneficial to compensating imperfection of control. In addition, we take into account operational noises which contaminate quantum operation in realistic circumstances. We show that the operation recovers from the contamination by a feedback procedure of differential evolution. Our feedback scheme is also applicable to finding an optimal and universal operation of NOT.

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arXiv2012

Quantum heuristic algorithm for traveling salesman problem

We propose a quantum heuristic algorithm to solve a traveling salesman problem by generalizing Grover search. Sufficient conditions are derived to greatly enhance the probability of finding the tours with extremal costs, reaching almost to unity and they are shown characterized by statistical properties of tour costs. In particular for a Gaussian distribution of the tours along the cost we show that the quantum algorithm exhibits the quadratic speedup of its classical counterpart, similarly to Grover search.

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arXiv2008

Quantum Learning Machine

We propose a novel notion of a quantum learning machine for automatically controlling quantum coherence and for developing quantum algorithms. A quantum learning machine can be trained to learn a certain task with no a priori knowledge on its algorithm. As an example, it is demonstrated that the quantum learning machine learns Deutsch's task and finds itself a quantum algorithm, that is different from but equivalent to the original one.

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