Implementation of the refined Deutsch-Jozsa algorithn on a 3-bit NMR quantum computer

We implemented the refined Deutsch-Jozsa algorithm on a 3-bit nuclear magnetic resonance quantum computer, which is the meaningful test of quantum parallelism because qubits are entangled. All of the balanced and constant functions were realized exactly. The results agree well with theoretical predictions and clearly distinguish the balanced functions from constant functions. Efficient refocusing schemes were proposed for the soft z-pulse and J-coupling and it is proved that the thermal equilibrium state gives the same results as the pure state for this algorithm.Comment: 5 pages, 2 figures, 1 tables, REVTe

NMR study on the stability of the magnetic ground state in MnCr2{}_2O4{}_4

The canting angles and fluctuation of the magnetic ion spins of spinel oxide MnCr${}_2$O${}_4$ were studied by nuclear magnetic resonance (NMR) at low temperatures, which has a collinear ferrimagnetic order below $T_C$ and a ferrimagnetic spiral order below $T_s < T_C$. Contrary to previous reports, only one spin canting angle of Cr ions was observed. The spin canting angles of Mn and Cr ions in the ferrimagnetic spiral obtained at a liquid-He temperature were $43\,^{\circ}$ and $110\,^{\circ}$, respectively. The nuclear spin-spin relaxation was determined by the Suhl-Nakamura interaction at low temperatures but the relaxation rate $T_2^{-1}$ increases rapidly as the temperature approaches $T_s$. This indicates that the fluctuation of the spiral component becomes faster as the temperature increases but not fast enough to leave an averaged hyperfine field to nuclei in the time scale of nuclear spin precession in the ferrimagnetic phase, which is on the order of $10^{-8}$ s. The spiral volume fraction measured for various temperatures reveals that the collinear and the spiral ferrimagnetic phases are mixed below the transition temperature of the spiral order. The temperature hysteresis in the volume fraction implies that this transition has first-order characteristics.Comment: 13 pages, 5 figure

Storing unitary operators in quantum states

We present a scheme to store unitary operators with self-inverse generators in quantum states and a general circuit to retrieve them with definite success probability. The continuous variable of the operator is stored in a single-qubit state and the information about the kind of the operator is stored in classical states with finite dimension. The probability of successful retrieval is always 1/2 irrespective of the kind of the operator, which is proved to be maximum. In case of failure, the result can be corrected with additional quantum states. The retrieving circuit is almost as simple as that which handles only the single-qubit rotations and CNOT as the basic operations. An interactive way to transfer quantum dynamics, that is, to distribute naturally copy-protected programs for quantum computers is also presented using this scheme.Comment: 4 pages, 3 figures, errors in Eq. (8) and Fig. 3 are fixed, to appear in Phys. Rev.

Fidelity of Quantum Teleportation through Noisy Channels

We investigate quantum teleportation through noisy quantum channels by solving analytically and numerically a master equation in the Lindblad form. We calculate the fidelity as a function of decoherence rates and angles of a state to be teleported. It is found that the average fidelity and the range of states to be accurately teleported depend on types of noise acting on quantum channels. If the quantum channels is subject to isotropic noise, the average fidelity decays to 1/2, which is smaller than the best possible value 2/3 obtained only by the classical communication. On the other hand, if the noisy quantum channel is modeled by a single Lindblad operator, the average fidelity is always greater than 2/3.Comment: 6 pages, 5 figures, accepted for publication in Phys. Rev.

Electron spin relaxations of phosphorus donors in bulk silicon under large electric field

Modulation of donor electron wavefunction via electric fields is vital to quantum computing architectures based on donor spins in silicon. For practical and scalable applications, the donor-based qubits must retain sufficiently long coherence times in any realistic experimental conditions. Here, we present pulsed electron spin resonance studies on the longitudinal $(T_1)$ and transverse $(T_2)$ relaxation times of phosphorus donors in bulk silicon with various electric field strengths up to near avalanche breakdown in high magnetic fields of about 1.2 T and low temperatures of about 8 K. We find that the $T_1$ relaxation time is significantly reduced under large electric fields due to electric current, and $T_2$ is affected as the $T_1$ process can dominate decoherence. Furthermore, we show that the magnetoresistance effect in silicon can be exploited as a means to combat the reduction in the coherence times. While qubit coherence times must be much longer than quantum gate times, electrically accelerated $T_1$ can be found useful when qubit state initialization relies on thermal equilibration.Comment: 7 pages, 5 figure