Large Number Of Qubits Research Articles

Evolution of pairwise entanglement in a coupledn-body system

We study the exact evolution of two noninteracting qubits, initially in a Bell state, in the presence of an environment, modeled by a kicked Ising spin chain. Dynamics of this model range from integrable to chaotic and we can handle numerics for a large number of qubits. We find that the entanglement (as measured by concurrence) of the two qubits has a close relation to the purity of the pair, and closely follows an analytic relation derived for Werner states. As a collateral result we find that an integrable environment causes quadratic decay of concurrence as well as of purity, while a chaotic environment causes linear decay. Both quantities display recurrences in an integrable environment.

MODELING FULL ADDER IN ISING SPIN QUANTUM COMPUTER WITH 1000 QUBITS USING QUANTUM MAPS

The quantum adder is an essential attribute of a quantum computer, just as classical adder is needed for operation of a digital computer. We model the quantum full adder as a realistic complex algorithm on a large number of qubits in an Ising spin quantum computer. Our results are an important step toward effective modeling of the quantum modular adder which is needed for Shor's and other quantum algorithms. Our full adder has the following features. (i) The near-resonant transitions with small detunings are completely suppressed, which allows us to decrease errors by several orders of magnitude and to model a 1000-qubit full adder. (We add a 1000-bit number using 2001 spins.) (ii) We construct the full adder gates directly as sequences of radio-frequency pulses, rather than breaking them down into generalized logical gates, such as Control-Not and one qubit gates. This substantially reduces the number of pulses needed to implement the full adder. (The maximum number of pulses required to add one bit (F-gate) is 15.) (iii) Full adder is realized in a homogeneous spin chain. (iv) The phase error is minimized: the F-gates generate approximately the same phase for different states of the superposition. (v) Modeling of the full adder is performed using quantum maps instead of differential equations. This allows us to reduce the calculation time to a reasonable value.

PATH INTEGRALS FOR QUBITS

Feynman started the theory of quantum computation by observing that quantum mechanical amplitudes cannot be simulated efficiently on a computer, since path integrals are computationally hard. Path integrals are heuristic tools for Schrödinger's hamiltonians, at least for real time dynamics. On the contrary they have a rigorous mathematical meaning for quantum systems which are worth a finite but no matter how large number of qubits.

Teleportation in a Noisy Environment: A Quantum Trajectories Approach

We study the fidelity of quantum teleportation for the situation in which quantum logic gates are used to provide the long distance entanglement required in the protocol, and where the effect of a noisy environment is modeled by means of a generalized amplitude damping channel. Our results demonstrate the effectiveness of the quantum trajectories approach, which allows the simulation of open systems with a large number of qubits (up to 24). This shows that the method is suitable for modeling quantum information protocols in realistic environments.

Is quantum computing with solid state devices possible?

Experiments with a few qubits, the basic elements of a quantum computer, using the methods of nuclear magnetic resonance (NMR) have demonstrated that quantum computing is possible. A useful quantum computer would need to use many qubits, while it appears that NMR with molecules is limited to about ten qubits. The easiest way to assemble a large number of qubits would be to use the existing solid state technology. However, the accuracy with which large numbers of solid state devices can be fabricated does not match the high-precision methods that have made quantum computing with magnetic resonance possible. Quantum computing with solid state devices must expect to encounter a new set of problems posed by differences between nominally identical devices. The difficulties are illustrated with examples of proposed qubits. Specific questions that must be addressed in attempts to use solid state devices for quantum computing are suggested.

Perturbation theory for quantum computation with a large number of qubits

We describe a new and consistent perturbation theory for solid-state quantum computation with many qubits. The errors in the implementation of simple quantum logic operations caused by non-resonant transitions are estimated. We verify our perturbation approach using exact numerical solution for relatively small (L=10) number of qubits. A preferred range of parameters is found in which the errors in processing quantum information are small. Our results are needed for experimental testing of scalable solid-state quantum computers.

Simulations of quantum-logic operations in a quantum computer with a large number of qubits

We report the first simulations of the dynamics of quantum logic operations with a large number of qubits (up to 1000). A nuclear spin chain in which selective excitations of spins is provided by the gradient of the external magnetic field is considered. The spins interact with their nearest neighbors. We simulate the quantum control-not (CN) gate implementation for remote qubits which provides the long-distance entanglement. Our approach can be applied to any implementation of quantum logic gates involving a large number of qubits.

Josephson Junction based Quantum Computing

Among the physical realizations of the elements required for quantum computation nano-scale electronic devices [2, 10, 12, 16] are very promising. They can be easily integrated into electronic circuits and scaled up to large numbers of qubits. Here we describe qubits based on low-capacitance Josephson junctions. In these systems Coulomb blockade effects allow the control of the charge on a superconducting island. They constitute quantum bits, with logical states differing by the charge on one island. Single- and two-bit operations can be performed by manipulating applied gate voltages. The phase coherence time is sufficiently long to allow a series of these steps. In addition to the manipulation of qubits, the resulting quantum state can be read out by coupling a single-electron transistor capacitively to the qubit.