A quantum algorithm providing exponential speed increase for finding eigenvalues and eigenvectors

We describe a new polynomial time quantum algorithm that uses the quantum fast fourier transform to find eigenvalues and eigenvectors of a Hamiltonian operator, and that can be applied in cases (commonly found in ab initio physics and chemistry problems) for which all known classical algorithms require exponential time. Applications of the algorithm to specific problems are considered, and we find that classically intractable and interesting problems from atomic physics may be solved with between 50 and 100 quantum bits.Comment: 10 page

Higher Order Methods for Simulations on Quantum Computers

To efficiently implement many-qubit gates for use in quantum simulations on quantum computers we develop and present methods reexpressing exp[-i (H_1 + H_2 + ...) \Delta t] as a product of factors exp[-i H_1 \Delta t], exp[-i H_2 \Delta t], ... which is accurate to 3rd or 4th order in \Delta t. The methods we derive are an extended form of symplectic method and can also be used for the integration of classical Hamiltonians on classical computers. We derive both integral and irrational methods, and find the most efficient methods in both cases.Comment: 21 pages, Latex, one figur

Nonlinear quantum mechanics implies polynomial-time solution for NP-complete and #P problems

If quantum states exhibit small nonlinearities during time evolution, then quantum computers can be used to solve NP-complete problems in polynomial time. We provide algorithms that solve NP-complete and #P oracle problems by exploiting nonlinear quantum logic gates. It is argued that virtually any deterministic nonlinear quantum theory will include such gates, and the method is explicitly demonstrated using the Weinberg model of nonlinear quantum mechanics.Comment: 10 pages, no figures, submitted to Phys. Rev. Let

Low zinc status and absorption exist in infants with jejunostomies or ileostomies which persists after intestinal repair.

There is very little data regarding trace mineral nutrition in infants with small intestinal ostomies. Here we evaluated 14 infants with jejunal or ileal ostomies to measure their zinc absorption and retention and biochemical zinc and copper status. Zinc absorption was measured using a dual-tracer stable isotope technique at two different time points when possible. The first study was conducted when the subject was receiving maximal tolerated feeds enterally while the ostomy remained in place. A second study was performed as soon as feasible after full feeds were achieved after intestinal repair. We found biochemical evidence of deficiencies of both zinc and copper in infants with small intestinal ostomies at both time points. Fractional zinc absorption with an ostomy in place was 10.9% ± 5.3%. After reanastamosis, fractional zinc absorption was 9.4% ± 5.7%. Net zinc balance was negative prior to reanastamosis. In conclusion, our data demonstrate that infants with a jejunostomy or ileostomy are at high risk for zinc and copper deficiency before and after intestinal reanastamosis. Additional supplementation, especially of zinc, should be considered during this time period

New summing algorithm using ensemble computing

We propose an ensemble algorithm, which provides a new approach for evaluating and summing up a set of function samples. The proposed algorithm is not a quantum algorithm, insofar it does not involve quantum entanglement. The query complexity of the algorithm depends only on the scaling of the measurement sensitivity with the number of distinct spin sub-ensembles. From a practical point of view, the proposed algorithm may result in an exponential speedup, compared to known quantum and classical summing algorithms. However in general, this advantage exists only if the total number of function samples is below a threshold value which depends on the measurement sensitivity.Comment: 13 pages, 0 figures, VIth International Conference on Quantum Communication, Measurement and Computing (Boston, 2002

Quantum Computational Complexity in the Presence of Closed Timelike Curves

Quantum computation with quantum data that can traverse closed timelike curves represents a new physical model of computation. We argue that a model of quantum computation in the presence of closed timelike curves can be formulated which represents a valid quantification of resources given the ability to construct compact regions of closed timelike curves. The notion of self-consistent evolution for quantum computers whose components follow closed timelike curves, as pointed out by Deutsch [Phys. Rev. D {\bf 44}, 3197 (1991)], implies that the evolution of the chronology respecting components which interact with the closed timelike curve components is nonlinear. We demonstrate that this nonlinearity can be used to efficiently solve computational problems which are generally thought to be intractable. In particular we demonstrate that a quantum computer which has access to closed timelike curve qubits can solve NP-complete problems with only a polynomial number of quantum gates.Comment: 8 pages, 2 figures. Minor changes and typos fixed. Reference adde

Generation of eigenstates using the phase-estimation algorithm

The phase estimation algorithm is so named because it allows the estimation of the eigenvalues associated with an operator. However it has been proposed that the algorithm can also be used to generate eigenstates. Here we extend this proposal for small quantum systems, identifying the conditions under which the phase estimation algorithm can successfully generate eigenstates. We then propose an implementation scheme based on an ion trap quantum computer. This scheme allows us to illustrate two simple examples, one in which the algorithm effectively generates eigenstates, and one in which it does not.Comment: 5 pages, 3 Figures, RevTeX4 Introduction expanded, typos correcte

Computational capacity of the universe

Merely by existing, all physical systems register information. And by evolving dynamically in time, they transform and process that information. The laws of physics determine the amount of information that a physical system can register (number of bits) and the number of elementary logic operations that a system can perform (number of ops). The universe is a physical system. This paper quantifies the amount of information that the universe can register and the number of elementary operations that it can have performed over its history. The universe can have performed no more than $10^{120}$ ops on $10^{90}$ bits.Comment: 17 pages, TeX. submitted to Natur

Simulation of Many-Body Fermi Systems on a Universal Quantum Computer

We provide fast algorithms for simulating many body Fermi systems on a universal quantum computer. Both first and second quantized descriptions are considered, and the relative computational complexities are determined in each case. In order to accommodate fermions using a first quantized Hamiltonian, an efficient quantum algorithm for anti-symmetrization is given. Finally, a simulation of the Hubbard model is discussed in detail.Comment: Submitted 11/7/96 to Phys. Rev. Lett. 10 pages, 0 figure