Abrams D S and Lloyd S, Simulation of Many-Body Fermi Systems on a Universal Quantum Com68 puter, Phys.Rev.Lett. 79 2586--2589, 1997  Home/Search   Document Not in Database   Summary   Related Articles   Check

....et al. [KWHZK95,KWZ96] In particular, the algorithm also uses O( p N) stages of unitary operations, each quite similar to a stage of the quantum Zeno sensing method. Grover refined his result to require only a single query [Gro97] and to use almost any unitary transformation [Gro98] Zalka [Zal97] showed Grover s algorithm can not be further asymptotically sped up and so is optimal for data base search, and Pati [PAT98] gave further improvements to the bounds. Biron et al. [BBB 98] extended Grover s algorithm to arbitrary initial amplitude distribution. Cockshott [Coc97] gave fast quantum ....

.... principle, quantum computers provide universal quantum simulation of any quantum mechanical physical system (Lloyd [Llo96] Zalka[Zal96a] Boghosian [Bog98] Proposed QC simulations of quantum mechanical systems include: many body systems (Wiesner[Wie96] many body Fermi systems (Abrams, Lloyd [AL97] multiparticle (ballistic) evolution (Benioff [Ben96] quantum lattice gas models (Boghosian, Taylor [BT96] Meyer [Mey96a, Mey96b] Ising spin glasses (Lidar, Biham [LB97] the thermal rate constant (Lidar, Wang [LW98] quantum chaos (Schack [Sch97] ffl Quantum Cryptography. Bennett et ....

D. S. Abrams, S. Lloyd, Simulation of Many-Body Fermi Systems on a Universal Quantum Computer, (Online preprint quant-ph/9703054), Phys.Rev.Lett. 79 (1997) 2586-2589.

....et al. [KWHZK95,KWZ96] In particular, the algorithm also uses O( p N) stages of unitary operations, each quite similar to a stage of the quantum Zeno sensing method. Grover refined his result to require only a single query [Gro97] and to use almost any unitary transformation [Gro98] Zalka [Zal97] showed Grover s algorithm can not be further asymptotically sped up and so is optimal for data base search, and Pati [PAT98] gave further improvements to the bounds. Biron et al. [BBB 98] extended Grover s algorithm to arbitrary initial amplitude distribution. Cockshott [Coc97] gave fast quantum ....

.... principle, quantum computers provide universal quantum simulation of any quantum mechanical physical system (Lloyd [Llo96] Zalka[Zal96a] Boghosian [Bog98] Proposed QC simulations of quantum mechanical systems include: many body systems (Wiesner[Wie96] many body Fermi systems (Abrams, Lloyd [AL97] multiparticle (ballistic) evolution (Benioff [Ben96] quantum lattice gas models (Boghosian, Taylor [BT96] Meyer [Mey96a, Mey96b] Ising spin glasses (Lidar, Biham [LB97] the thermal rate constant (Lidar, Wang [LW98] quantum chaos (Schack [Sch97] ffl Quantum Cryptography. Bennett et ....

Abrams, D. S., Lloyd, S. Simulation of many-body fermi systems on a universal quantum computer. (Online preprint quant-ph/9703054.) (1997).

.... branch in quantum complexity theory is the study of a class of problems which is the quantum analog of the complexity class NP[126] Another interesting direction in quantum computation is concerned with quantum computers simulating efficiently other physical systems such as many body Fermi systems[203, 1, 197, 42]. This direction pursues the original suggestion by Feynman[93] who noticed that quantum systems are hard to simulate by classical devices. An important direction of investigation is the search for a different, perhaps stronger, quantum computation model. For example, consider the introduction of ....

Abrams D S and Lloyd S, Simulation of Many-Body Fermi Systems on a Universal Quantum Computer, Phys.Rev.Lett. 79 2586--2589, 1997

....which particles move to positions x; y and y; x will contribute amplitudes which add with no change of sign, as is appropriate for Bose statistics. It is possible to modify the algorithm to incorporate Fermi statistics, however this requires somewhat more bookkeeping. This issue was discussed in [19]. 3.6 Computational complexity We have now described a class of algorithms for simulating the nonrelativistic many body Schrodinger equation on a quantum computer. As discussed in Section 3.1, simulating n quantum particles on a lattice of size l d requires a computation of complexity O(l dn ) ....

....for a simulation on a classical computer. In discussing the computational complexity of these simulation algorithms, it is worth noting that if we simulate nonrelativistic fermions extra work must be done to keep track of the phase of the state. Using the bookkeeping method suggested in [19], for example, we must define a canonical ordering for all the particles, and we must check to see when the propagation changes the ordering of any pair of particles. This will take roughly on the order of d 2 l 2d operations per time step, just as for the interparticle interaction. In fact, ....

D. S. Abrams and S. Lloyd, Simulation of Many-Body Fermi Systems on a Universal Quantum Computer, MIT preprint, November 1996.

....described by our model, they cannot be used to compute functions not in BQP in polynomial time. This could be accomplished by showing that systems with such Hamiltonians can be efficiently simulated by a quantum computer. Some work has been done on simulating Hamiltonians on quantum computers [1, 24, 33], but I do not believe this question has been completely addressed yet. An important aspect of quantum mechanics not used in the quantum circuit model is that identical particles are indistinguishable; in general they must obey either Fermi Dirac or Einstein Bose statistics when they are ....

....taught a course on quantum computing and quantum information, and his excellent set of lecture notes is available on the web [26] As Feynman suggested, it appears that quantum computing is good at computing simulations of quantum mechanical dynamics. Some work has already appeared showing this [1, 24, 33], but much remains to be done. A significant algorithm in quantum computing is L. K. Grover s search algorithm, which searches an unordered list of N items (or the range of an efficiently computable function) for a specific item in time O( p N) an improvement on the optimal classical algorithm, ....

D. S. Abrams and S. Lloyd, Simulation of many-body Fermi systems on a universal quantum computer, Phys. Rev. Lett. 79 (1997), 2586-2589.

....et al. [KWHZK95,KWZ96] In particular, the algorithm also uses O( p N) stages of unitary operations, each quite similar to a stage of the quantum Zeno sensing method. Grover refined his result to require only a single query [Gro97] and to use almost any unitary transformation [Gro98] Zalka [Zal97] showed Grover s algorithm can not be further asymptotically sped up and so is optimal for data base search, and Pati [PAT98] gave further improvements to the bounds. Biron et al. [BBB 98] extended Grover s algorithm to arbitrary initial amplitude distribution. Cockshott [Coc97] gave fast quantum ....

.... quantum computers provide universal quantum simulation of any quantum mechanical physical system (Lloyd [Llo96] Zalka[Zal96a] Boghosian [Bog98] Proposed QC simulations of quantum mechanical systems include: many body systems (Wiesner[Wie96] many body Fermi systems (Abrams, Lloyd [AL97] multiparticle (ballistic) evolution (Benioff [Ben96] quantum lattice gas models (Boghosian, Taylor [BT96] Meyer [Mey96a, Mey96b] Ising spin glasses (Lidar, Biham [LB97] the thermal rate constant (Lidar, Wang [LW98] quantum chaos (Schack [Sch97] ffl Quantum Learning. QC may have ....

D. S. Abrams, S. Lloyd, Simulation of Many-Body Fermi Systems on a Universal Quantum Computer, (Online preprint quant-ph/9703054), Phys.Rev.Lett. 79 (1997) 2586-2589.

....et al. [KWHZK95,KWZ96] In particular, the algorithm also uses O( p N) stages of unitary operations, each quite similar to a stage of the quantum Zeno sensing method. Grover refined his result to require only a single query [Gro97] and to use almost any unitary transformation [Gro98] Zalka [Zal97] showed Grover s algorithm can not be further asymptotically sped up and so is optimal for data base search, and Pati [PAT98] gave further improvements to the bounds. Biron et al. [BBB 98] extended Grover s algorithm to arbitrary initial amplitude distribution. Cockshott [Coc97] gave fast quantum ....

.... quantum computers provide universal quantum simulation of any quantum mechanical physical system (Lloyd [Llo96] Zalka[Zal96a] Boghosian [Bog98] Proposed QC simulations of quantum mechanical systems include: many body systems (Wiesner[Wie96] many body Fermi systems (Abrams, Lloyd [AL97] multiparticle (ballistic) evolution (Benioff [Ben96] quantum lattice gas models (Boghosian, Taylor [BT96] Meyer [Mey96a, Mey96b] Ising spin glasses (Lidar, Biham [LB97] the thermal rate constant (Lidar, Wang [LW98] quantum chaos (Schack [Sch97] ffl Quantum Learning. QC may have ....

Abrams, D. S., Lloyd, S. Simulation of many-body fermi systems on a universal quantum computer. (Online preprint quant-ph/9703054.) (1997).

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Abrams D S and Lloyd S, Simulation of Many-Body Fermi Systems on a Universal Quantum Com68 puter, Phys.Rev.Lett. 79 2586--2589, 1997

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D. S. Abrams and S. Lloyd, "Simulation of many-body Fermi systems on a universal quantum computer", Phys. Rev. Lett. 79 (1997) 2586--2589.

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Abrams, D., Lloyd, S., "Simulation of many-body Fermi systems on a universal quantum computer," quant-ph/9703054. 28 Mar 97.

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D. S. Abrams and S. Lloyd, "Simulation of many-body fermi systems on a universal quantum computer," Phys. Rev. Lett. 79, 2586--2589 (1997) and quant-ph/9703054.

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Abrams, D. S. and S. Lloyd, "Simulation of many-body fermi systems on a universal quantum computer," Phys. Rev. Lett. 79 (1997), 2586--2589 and quant-ph/9703054.

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