Efficiency of free energy calculations of spin lattices by spectral quantum algorithms

Quantum algorithms are well-suited to calculate estimates of the energy spectra for spin lattice systems. These algorithms are based on the efficient calculation of the discrete Fourier components of the density of states. The efficiency of these algorithms in calculating the free energy per spin of general spin lattices to bounded error is examined. We find that the number of Fourier components required to bound the error in the free energy due to the broadening of the density of states scales polynomially with the number of spins in the lattice. However, the precision with which the Fourier components must be calculated is found to be an exponential function of the system size.Comment: 9 pages, 4 figures; corrected typographical and minor mathematical error

Fast Quantum Search Algorithms in Protein Sequence Comparison - Quantum Biocomputing

Quantum search algorithms are considered in the context of protein sequence comparison in biocomputing. Given a sample protein sequence of length m (i.e m residues), the problem considered is to find an optimal match in a large database containing N residues. Initially, Grover's quantum search algorithm is applied to a simple illustrative case - namely where the database forms a complete set of states over the 2^m basis states of a m qubit register, and thus is known to contain the exact sequence of interest. This example demonstrates explicitly the typical O(sqrt{N}) speedup on the classical O(N) requirements. An algorithm is then presented for the (more realistic) case where the database may contain repeat sequences, and may not necessarily contain an exact match to the sample sequence. In terms of minimizing the Hamming distance between the sample sequence and the database subsequences the algorithm finds an optimal alignment, in O(sqrt{N}) steps, by employing an extension of Grover's algorithm, due to Boyer, Brassard, Hoyer and Tapp for the case when the number of matches is not a priori known.Comment: LaTeX, 5 page

Quantum Entanglement of Excitons in Coupled Quantum Dots

Optically-controlled exciton dynamics in coupled quantum dots is studied. We show that the maximally entangled Bell states and Greenberger-Horne-Zeilinger (GHZ) states can be robustly generated by manipulating the system parameters to be at the avoided crossings in the eigenenergy spectrum. The analysis of population transfer is systematically carried out using a dressed-state picture. In addition to the quantum dot configuration that have been discussed by Quiroga and Johnson [Phys. Rev. Lett. \QTR{bf}{83}, 2270 (1999)], we show that the GHZ states also may be produced in a ray of three quantum dots with a shorter generation time.Comment: 16 pages, 7 figures, to appear in Phys. Rev.

Controllability and universal three-qubit quantum computation with trapped electron states

We show how to control and perform universal three-qubit quantum computation with trapped electron quantum states. The three qubits are the electron spin, and the first two quantum states of the cyclotron and axial harmonic oscillators. We explicitly show how the universal gates can be performed. As an example of a non-trivial quantum algorithm, we outline the implementation of the Deutsch-Jozsa algorithm in this system.Comment: 4 pages, 1 figure. Typos corrected. The original publication is available at http://www.springerlink.co

Solid-State Nuclear Spin Quantum Computer Based on Magnetic Resonance Force Microscopy

We propose a nuclear spin quantum computer based on magnetic resonance force microscopy (MRFM). It is shown that an MRFM single-electron spin measurement provides three essential requirements for quantum computation in solids: (a) preparation of the ground state, (b) one- and two- qubit quantum logic gates, and (c) a measurement of the final state. The proposed quantum computer can operate at temperatures up to 1K.Comment: 16 pages, 5 figure

Tackling Systematic Errors in Quantum Logic Gates with Composite Rotations

We describe the use of composite rotations to combat systematic errors in single qubit quantum logic gates and discuss three families of composite rotations which can be used to correct off-resonance and pulse length errors. Although developed and described within the context of NMR quantum computing these sequences should be applicable to any implementation of quantum computation.Comment: 6 pages RevTex4 including 4 figures. Will submit to Phys. Rev.

Gate errors in solid state quantum computer architectures

We theoretically consider possible errors in solid state quantum computation due to the interplay of the complex solid state environment and gate imperfections. In particular, we study two examples of gate operations in the opposite ends of the gate speed spectrum, an adiabatic gate operation in electron-spin-based quantum dot quantum computation and a sudden gate operation in Cooper pair box superconducting quantum computation. We evaluate quantitatively the non-adiabatic operation of a two-qubit gate in a two-electron double quantum dot. We also analyze the non-sudden pulse gate in a Cooper-pair-box-based quantum computer model. In both cases our numerical results show strong influences of the higher excited states of the system on the gate operation, clearly demonstrating the importance of a detailed understanding of the relevant Hilbert space structure on the quantum computer operations.Comment: 6 pages, 2 figure

An NMR-based nanostructure switch for quantum logic

We propose a nanostructure switch based on nuclear magnetic resonance (NMR) which offers reliable quantum gate operation, an essential ingredient for building a quantum computer. The nuclear resonance is controlled by the magic number transitions of a few-electron quantum dot in an external magnetic field.Comment: 4 pages, 2 separate PostScript figures. Minor changes included. One reference adde

Fast Non-Adiabatic Two Qubit Gates for the Kane Quantum Computer

In this paper we apply the canonical decomposition of two qubit unitaries to find pulse schemes to control the proposed Kane quantum computer. We explicitly find pulse sequences for the CNOT, swap, square root of swap and controlled Z rotations. We analyze the speed and fidelity of these gates, both of which compare favorably to existing schemes. The pulse sequences presented in this paper are theoretically faster, higher fidelity, and simpler than existing schemes. Any two qubit gate may be easily found and implemented using similar pulse sequences. Numerical simulation is used to verify the accuracy of each pulse scheme

Quantum Search with Two-atom Collisions in Cavity QED

We propose a scheme to implement two-qubit Grover's quantum search algorithm using Cavity Quantum Electrodynamics. Circular Rydberg atoms are used as quantum bits (qubits). They interact with the electromagnetic field of a non-resonant cavity . The quantum gate dynamics is provided by a cavity-assisted collision, robust against decoherence processes. We present the detailed procedure and analyze the experimental feasibility.Comment: 4 pages, 2 figure