Noise resistance of adiabatic quantum computation using random matrix theory

Besides the traditional circuit-based model of quantum computation, several quantum algorithms based on a continuous-time Hamiltonian evolution have recently been introduced, including for instance continuous-time quantum walk algorithms as well as adiabatic quantum algorithms. Unfortunately, very little is known today on the behavior of these Hamiltonian algorithms in the presence of noise. Here, we perform a fully analytical study of the resistance to noise of these algorithms using perturbation theory combined with a theoretical noise model based on random matrices drawn from the Gaussian Orthogonal Ensemble, whose elements vary in time and form a stationary random process.Comment: 9 pages, 3 figure

Quantum information and precision measurement

We describe some applications of quantum information theory to the analysis of quantum limits on measurement sensitivity. A measurement of a weak force acting on a quantum system is a determination of a classical parameter appearing in the master equation that governs the evolution of the system; limitations on measurement accuracy arise because it is not possible to distinguish perfectly among the different possible values of this parameter. Tools developed in the study of quantum information and computation can be exploited to improve the precision of physics experiments; examples include superdense coding, fast database search, and the quantum Fourier transform.Comment: 13 pages, 1 figure, proof of conjecture adde

Optimal discrimination of quantum operations

We address the problem of discriminating with minimal error probability two given quantum operations. We show that the use of entangled input states generally improves the discrimination. For Pauli channels we provide a complete comparison of the optimal strategies where either entangled or unentangled input states are used.Comment: 4 pages, no figure

Abelian and non-Abelian geometric phases in adiabatic open quantum systems

We introduce a self-consistent framework for the analysis of both Abelian and non-Abelian geometric phases associated with open quantum systems, undergoing cyclic adiabatic evolution. We derive a general expression for geometric phases, based on an adiabatic approximation developed within an inherently open-systems approach. This expression provides a natural generalization of the analogous one for closed quantum systems, and we prove that it satisfies all the properties one might expect of a good definition of a geometric phase, including gauge invariance. A striking consequence is the emergence of a finite time interval for the observation of geometric phases. The formalism is illustrated via the canonical example of a spin-1/2 particle in a time-dependent magnetic field. Remarkably, the geometric phase in this case is immune to dephasing and spontaneous emission in the renormalized Hamiltonian eigenstate basis. This result positively impacts holonomic quantum computing.Comment: v3: 10 pages, 2 figures. Substantially expanded version. Includes a proof of gauge invariance of the non-Abelian geometric phase, and an appendix on the left and right eigenvectors of the superoperator in the Jordan for

Making Classical Ground State Spin Computing Fault-Tolerant

We examine a model of classical deterministic computing in which the ground state of the classical system is a spatial history of the computation. This model is relevant to quantum dot cellular automata as well as to recent universal adiabatic quantum computing constructions. In its most primitive form, systems constructed in this model cannot compute in an error free manner when working at non-zero temperature. However, by exploiting a mapping between the partition function for this model and probabilistic classical circuits we are able to show that it is possible to make this model effectively error free. We achieve this by using techniques in fault-tolerant classical computing and the result is that the system can compute effectively error free if the temperature is below a critical temperature. We further link this model to computational complexity and show that a certain problem concerning finite temperature classical spin systems is complete for the complexity class Merlin-Arthur. This provides an interesting connection between the physical behavior of certain many-body spin systems and computational complexity.Comment: 24 pages, 1 figur

Symmetric functions of qubits in an unknown basis

Consider an n qubit computational basis state corresponding to a bit string x, which has had an unknown local unitary applied to each qubit, and whose qubits have been reordered by an unknown permutation. We show that, given such a state with Hamming weight |x| at most n/2, it is possible to reconstruct |x| with success probability 1 - |x|/(n-|x|+1), and thus to compute any symmetric function of x. We give explicit algorithms for computing whether or not |x| is at least t for some t, and for computing the parity of x, and show that these are essentially optimal. These results can be seen as generalisations of the swap test for comparing quantum states.Comment: 6 pages, 3 figures; v2: improved results, essentially published versio

Decoherence vs entanglement in coined quantum walks

Quantum versions of random walks on the line and cycle show a quadratic improvement in their spreading rate and mixing times respectively. The addition of decoherence to the quantum walk produces a more uniform distribution on the line, and even faster mixing on the cycle by removing the need for time-averaging to obtain a uniform distribution. We calculate numerically the entanglement between the coin and the position of the quantum walker and show that the optimal decoherence rates are such that all the entanglement is just removed by the time the final measurement is made.Comment: 11 pages, 6 embedded eps figures; v2 improved layout and discussio

Bostonia: The Boston University Alumni Magazine. Volume 11

Founded in 1900, Bostonia magazine is Boston University's main alumni publication, which covers alumni and student life, as well as university activities, events, and programs

Efficient and robust entanglement generation in a many-particle system with resonant dipole-dipole interactions

We propose and discuss a scheme for robust and efficient generation of many-particle entanglement in an ensemble of Rydberg atoms with resonant dipole-dipole interactions. It is shown that in the limit of complete dipole blocking, the system is isomorphic to a multimode Jaynes-Cummings model. While dark-state population transfer is not capable of creating entanglement, other adiabatic processes are identified that lead to complex, maximally entangled states, such as the N-particle analog of the GHZ state in a few steps. The process is robust, works for even and odd particle numbers and the characteristic time for entanglement generation scales with N^a, with a being less than unity.Comment: 4 figure

Engaging with History after Macpherson

The Race Relations Amendment Act (2000) identifies a key role for education, and more specifically history, in promoting ‘race equality’ in Britain. In this article Ian Grosvenor and Kevin Myers consider the extent of young people’s current engagement with the history of ‘diversity, change and immigration’ which underpins the commitment to ‘race equality’. Finding that in many of Britain’s schools and universities a singular and exclusionary version of history continues to dominate the curriculum, they go on to consider the reasons for the neglect of multiculturalism. The authors identify the development of an aggressive national identity that depends on the past for its legitimacy and argue that this sense of the past is an important obstacle to future progress