An efficient and accurate quantum lattice-gas model for the many-body Schrödinger wave equation

Yepez, Jeffrey; Boghosian, Bruce M.

doi:10.1016/s0010-4655(02)00419-8

Cited by 63 publications

(73 citation statements)

References 17 publications

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“…This representation is a generalization of our earlier work [7] on quantum algorithms for the simple NLS and KdV solitons, which was based on the quantum algorithm for the (linear) Schrodinger equation [8]. These quantum lattice gas algorithms can, in principle, be modeled on a liquid NMR quantum computer [9][10][11][12][13].…”

Section: --T + a X 2 A T A Xmentioning

confidence: 99%

“…We can restrict ourselves to the one-particle sectors for qubits q1,) and qubits qi 3 ) in which the basis set elements in Eq.~~~~~~ ~~~ (8) hav onl on2,tht3 wieal hohrn Eq. (8) have only one n0 that is 1 while all the other nil are zero, and similarly for n, 3 .i In essence, for the two qubits 0,qoi), there are 2L such elements which can be labeled using the binary scheme 2 2 21+a) 1= 1...L, a=0,1 so that in this binary scheme the wave function corresponding to the two qubits q0Z 1 )…”

Section: Quantum Lattice Gas Representation For Coupled-nlsmentioning

confidence: 99%

“…To evolve the wave function for the two qubits qo, I) in time, a quantum unitary operator C is constructed from a tensor product of quantum gates, each independently applied on a site-to-site basis To recover NLS, we introduce the square-root-of-swap gate 0 1 = U on a site-by-site basis [8] 01-i 1+i 0…”

Section: Unitary Collision Operator For the Qubit-pair Q(j)mentioning

confidence: 99%

“…In matrix form, the qubit streaming operator i is a It has been shown [14,8] that the effect of an external potential Vl(x) can be modeled by the introduction of a local phase change to the system wave function for the qubit-pair Iq0oi). Let Q 1 denote the wave function for the qubitpair Iqo,1), and Q 2 for the qubit pair -q 2 , 3 ).…”

Section: Unitary Streaming Operator For the Qubit-pair Qoi)mentioning

confidence: 99%

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Quantum lattice gas representation for vector solitons

Vahala

Yepez

2003

SPIE Proceedings

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Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing this collection of Information. Send comments regarding this burden estimate or any other aspect of this collection of information, Including suggestions for reducing this burden to Department of Defense, Washington Headquarters Services, Directorate for Information Operations and Reports (0704-0188), 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to any penalty for failing to comply with a collection of information if it does not display a currentiy valid OMB control number. PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS. 14. ABSTRACT Quantum lattice gas algorithms are developed for the coupled-nonlinear Schrodinger (coupled-NLS) equations, equations that describe the propagation of pulses in birefringent fibers. When the cross-phase modulati6n factor is unity, the coupled-NLS reduce to the Manakov equations. The quantum lattice gas algorithm yields vector solitons for the fully integrable Manakov system that are in excellent agreement with exact results. Simulations are also presented for the interaction between a turbulent 2-soliton mode and a simple NLS 2-soliton mode. The quantum algorithm requires 4 qubits for each spatial node, with quantum entanglement required only between pairs of qubits through a unitary collision operator. The coupling between the qubits is achieved through a local phase change in the absolute value of the paired qubit wave functions. On symmetrizing the unitary streaming operators, the resulting quantum algorithm, which is unconditionally stable, is accurate to 0(62). REPORT DATE (DD-MM-YYYY) SPONSORING ! MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSORIMONITOR'S ACRONYM(S) SPONSORIMONITOR'S REPORT NUMBER(S) DISTRIBUTION I AVAILABILITY STATEMENT SUBJECT TERM:Vector 0 ABSTRACT Quantum lattice gas algorithms are developed for the coupled-nonlinear Schrodinger (coupled-NLS) equations, equations that describe the propagation of pulses in birefringent fibers. When the cross-phase modulation factor is unity, the coupled-NLS reduce to the Manakov equations. The quantum lattice gas algorithm yields vector solitons for the fully integrable Manakov system that are in excellent agreement with exact results. Simulations are also presented for the interaction between a turbulent 2-soliton mode and a simple NLS 2-soliton mode. The quantum algorithm requires 4 qubits for each spatial node, with quantum entanglement required only between pairs of qubits through a unitary collision operator. The coupling between the qubits is achieved through a local phase change in the absolute value of the paired qubit wave functions. On symmetrizing the unitary streaming operators, the resulting quantum algorithm, which is uncon...

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Section: --T + a X 2 A T A Xmentioning

confidence: 99%

Section: Quantum Lattice Gas Representation For Coupled-nlsmentioning

confidence: 99%

Section: Unitary Collision Operator For the Qubit-pair Q(j)mentioning

confidence: 99%

Section: Unitary Streaming Operator For the Qubit-pair Qoi)mentioning

confidence: 99%

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Quantum lattice gas representation for vector solitons

Vahala

Yepez

2003

SPIE Proceedings

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“…For example, papers [9,10] have examined the quantum lattice-gas model. An algorithm similar to the one proposed in this paper has been tested in papers [11][12][13][14] for free particle and for a harmonic oscillator.…”

Section: Introductionmentioning

confidence: 99%

Quantum simulation of the tunnel effect

Ostrowski¹

2015

Bulletin of the Polish Academy of Sciences Technical Sciences

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Abstract. In this paper, we examine whether a quantum computer can efficiently simulate quantum processes such as the tunnel effect. We examine a quantum algorithm that calculates the value of transition and reflection coefficients for the Gaussian wave packet scattered on a rectangular potential. We compare the results obtained in this way with the results of classical simulations and analytical calculations.

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Quantum Algorithms for Continuous Problems and Their Applications

Papageorgiou

Traub

2014

Advances in Chemical Physics

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Many problems in science and engineering are formulated using continuous mathematical models. Usually they can only be solved numerically and therefore approximately. Since they are often difficult to solve on a classical computer it's interesting to investigate whether they can be solved faster on a quantum computer.After a brief introduction to quantum algorithms we report on a wide range of applications including high dimensional integration, path integration, Hamiltonian simulation, and ground state energy estimation. We provide a rather extensive bibliography.

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An efficient and accurate quantum lattice-gas model for the many-body Schrödinger wave equation

Cited by 63 publications

References 17 publications

Quantum lattice gas representation for vector solitons

Quantum lattice gas representation for vector solitons

Quantum simulation of the tunnel effect

Quantum Algorithms for Continuous Problems and Their Applications

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