Qubit Register Research Articles

Quantum analog-to-digital and digital-to-analog conversion

An algorithm is proposed which transfers the quantum information of a wave function (analogue signal) into a register of qubits (digital signal) such that $n$ qubits describe the amplitudes and phases of $2^n$ points of a sufficiently smooth wave function. We assume that the continuous degree of freedom couples to one or more qubits of a quantum register via a Jaynes Cummings Hamiltonian and that we have universal quantum computation capabilities on the register as well as the possibility to perform bang-bang control on the qubits. The transfer of information is mainly based on the application of the quantum phase-estimation algorithm in both directions. Here, the running time increases exponentially with the number of qubits. We pose it as an open question which interactions would allow polynomial running time. One example would be interactions which enable exact squeezing operations.

SPIN CLUSTER AS A QUBIT: ROBUST AGAINST DISSIPATION OF THERMAL RADIATION FIELDS

A spin cluster of 3 spin 1/2 particles has been studied as a qubit system. A time dependent magnetic field is applied to control the time evolution of the cluster. The lowest energy level of the cluster has the total spin 1/2 separated far away from the excited states and can be used as a qubit register. The universal 1-qubit logic gate can be constructed from the time evolution operator of the non-autonomous many-body system, and the 6 basic 1-qubit gates can be realized by adjusting the applied time dependent magnetic field. As a many-body system, this qubit system is expected to be robust against the dissipation effect of the thermal radiation fields from the environment.

Scalable register initialization for quantum computing in an optical lattice

The Mott insulator state created by loading an atomic Bose–Einstein condensate (BEC) into an optical lattice may be used as a means to prepare a register of atomic qubits in a quantum computer. Such architecture requires a lattice commensurately filled with atoms, which corresponds to the insulator state only in the limit of zero inter-well tunnelling. We show that a lattice with spatial inhomogeneity created by a quadratic magnetic trapping potential can be used to isolate a subspace in the centre which is impervious to hole-hoping. Components of the wavefunction with more than one atom in any well can be projected out by selective measurement on a molecular photo-associative transition. Maintaining the molecular coupling can sustain a commensurately filled register for the duration of a quantum computation.

Implementation of the Semiclassical Quantum Fourier Transform in a Scalable System

We report the implementation of the semiclassical quantum Fourier transform in a system of three beryllium ion qubits (two-level quantum systems) confined in a segmented multizone trap. The quantum Fourier transform is the crucial final step in Shor's algorithm, and it acts on a register of qubits to determine the periodicity of the quantum state's amplitudes. Because only probability amplitudes are required for this task, a more efficient semiclassical version can be used, for which only single-qubit operations conditioned on measurement outcomes are required. We apply the transform to several input states of different periodicities; the results enable the location of peaks corresponding to the original periods. This demonstration incorporates the key elements of a scalable ion-trap architecture, suggesting the future capability of applying the quantum Fourier transform to a large number of qubits as required for a useful quantum factoring algorithm.

Efficient and robust initialization of a qubit register with fermionic atoms.

We show that fermionic atoms have crucial advantages over bosonic atoms in terms of loading in optical lattices for use as a possible quantum computation device. After analyzing the change in the level structure of a nonuniform confining potential as a periodic potential is superimposed to it, we show how this structure combined with the Pauli principle and fermion degeneracy can be exploited to create unit occupancy of the lattice sites with very high efficiency.

Implementing Shor’s algorithm on Josephson charge qubits

We investigate the physical implementation of Shor's factorization algorithm on a Josephson charge qubit register. While we pursue a universal method to factor a composite integer of any size, the scheme is demonstrated for the number 21. We consider both the physical and algorithmic requirements for an optimal implementation when only a small number of qubits are available. These aspects of quantum computation are usually the topics of separate research communities; we present a unifying discussion of both of these fundamental features bridging Shor's algorithm to its physical realization using Josephson junction qubits. In order to meet the stringent requirements set by a short decoherence time, we accelerate the algorithm by decomposing the quantum circuit into tailored two- and three-qubit gates and we find their physical realizations through numerical optimization.

Spin Switch and Qubit Register from a Spin Particle Controlledby a Time-Dependent Magnetic Field

A spin particle subjected to any time-dependent magnetic field isinvestigated in detail at different magnetic field configurations. Spin flipprobability, spin alignment, cyclic and noncyclic nonadiabatic geometricphases are calculated exactly and their analytical expressions are presented.Our theoretical study shows that a spin particle controlled by a resonanttime-dependent magnetic field can be used as efficient controllable devicesof spin switch or qubit register.

Micro-optical realization of arrays of selectively addressable dipole traps: a scalable configuration for quantum computation with atomic qubits.

We experimentally demonstrate novel structures for the realization of registers of atomic qubits: We trap neutral atoms in one- and two-dimensional arrays of far-detuned dipole traps obtained by focusing a red-detuned laser beam with a microfabricated array of microlenses. We are able to selectively address individual trap sites due to their large lateral separation of 125 microm. We initialize and read out different internal states for the individual sites. We also create two interleaved sets of trap arrays with adjustable separation, as required for many proposed implementations of quantum gate operations.

Nanoscale superconducting quantum bits

Various physical systems were proposed for quantum information processing. Among those nanoscale devices appear most promising for integration in electronic circuits and large-scale applications. We discuss Josephson junction circuits in two regimes where they can be used for quantum computing. These systems combine intrinsic coherence of the superconducting state with control possibilities of single-charge circuits. In the regime where the typical charging energy dominates over the Josephson coupling, the low-temperature dynamics is limited to two states differing by a Cooper-pair charge on a superconducting island. In the opposite regime of prevailing Josephson energy, the phase (or flux) degree of freedom can be used to store and process quantum information. Under suitable conditions the system reduces to two states with different flux configurations. Several qubits can be joined together into a register. The quantum state of a qubit register can be manipulated by voltage and magnetic field pulses. The qubits are inevitably coupled to the environment. However, estimates of the phase coherence time show that many elementary quantum logic operations can be performed before the phase coherence is lost. In addition to manipulations, the final state of the qubits has to be read out. This quantum measurement process can be accomplished using a single-electron transistor for charge Josephson qubits, and a d.c.-SQUID for flux qubits. Recent successful experiments with superconducting qubits demonstrate for the first time quantum coherence in macroscopic systems.

Fast quantum search algorithms in protein sequence comparisons: quantum bioinformatics.

Quantum search algorithms are considered in the context of protein sequence comparison in bioinformatics. 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(square root of [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(square root of [N]) steps, by employing an extension of Grover's algorithm, due to Boyer et al. for the case when the number of matches is not a priori known.