Progress toward scalable tomography of quantum maps using twirling-based methods and information hierarchies

We present in a unified manner the existing methods for scalable partial quantum process tomography. We focus on two main approaches: the one presented in Bendersky et al. [Phys. Rev. Lett. 100, 190403 (2008)], and the ones described, respectively, in Emerson et al. [Science 317, 1893 (2007)] and L\'{o}pez et al. [Phys. Rev. A 79, 042328 (2009)], which can be combined together. The methods share an essential feature: They are based on the idea that the tomography of a quantum map can be efficiently performed by studying certain properties of a twirling of such a map. From this perspective, in this paper we present extensions, improvements and comparative analyses of the scalable methods for partial quantum process tomography. We also clarify the significance of the extracted information, and we introduce interesting and useful properties of the $\chi$-matrix representation of quantum maps that can be used to establish a clearer path toward achieving full tomography of quantum processes in a scalable way.Comment: Replaced with published version (only minor changes respect to the first version

Chiral-mediated entanglement in an Aharonov-Bohm ring

We study the orbital entanglement in a biased Aharonov-Bohm ring connected in a four-terminal setup. We find that the concurrence achieves a maximum when the magnetic flux B coincides with an integer number of a half flux quantum 0 /2. We show that this behavior is a consequence of the existence of degenerate states of the ring having opposite chirality. We also analyze the behavior of the noise as a function of and discuss the reliability of this quantity as evidence of entanglement.Comment: 7 pages, 5 figures; To appear in Phys. Rev.

A quantum gate array can be programmed to evaluate the expectation value of any operator

A programmable gate array is a circuit whose action is controlled by input data. In this letter we describe a special--purpose quantum circuit that can be programmed to evaluate the expectation value of any operator $O$ acting on a space of states of $N$ dimensions. The circuit has a program register whose state $|\Psi(O)>_P$ encodes the operator $O$ whose expectation value is to be evaluated. The method requires knowledge of the expansion of $O$ in a basis of the space of operators. We discuss some applications of this circuit and its relation to known instances of quantum state tomography.Comment: 4 pages, 3 figures include

Quantum computation with phase drift errors

We present results of numerical simulations of the evolution of an ion trap quantum computer made out of 18 ions which are subject to a sequence of nearly 15000 laser pulses in order to find the prime factors of N=15. We analyze the effect of random and systematic phase drift errors arising from inaccuracies in the laser pulses which induce over (under) rotation of the quantum state. Simple analytic estimates of the tolerance for the quality of driving pulses are presented. We examine the use of watchdog stabilization to partially correct phase drift errors concluding that, in the regime investigated, it is rather inefficient.Comment: 5 pages, RevTex, 2 figure

Testing integrability with a single bit of quantum information

We show that deterministic quantum computing with a single bit (DQC1) can determine whether the classical limit of a quantum system is chaotic or integrable using O(N) physical resources, where $N$ is the dimension of the Hilbert space of the system under study. This is a square root improvement over all known classical procedures. Our study relies strictly on the random matrix conjecture. We also present numerical results for the nonlinear kicked top.Comment: Minor changes taking into account Howard Wiseman's comment: quant-ph/0305153. Accepted for publication in Phys. Rev.

Chilean IPNV isolates: Robustness analysis of PCR detection

Background: The genomes of several infectious pancreatic necrosis viruses (IPNVs) isolated in Chile were sequenced with a single amplification approach for both segments A and B. The resulting sequences were then used to determine the conservation of the primer-binding regions used in polymerase chain reaction (PCR)-based diagnostic methods proposed in the literature. Thus, the robustness of each technique was studied, particularly the eventual effect of further mutations within the primer-binding sites. Results: On analysis, most methods currently used to detect Chilean IPNV varieties were deemed adequate. However, the primers were designed to be genogroup specific, implying that most detection methods pose some risk of detecting all strains prevalent in the country, due to the coexistence of genogroups 1 and 5. Conclusions: Negative resultsmust be interpreted carefully given the high genomic variability of IPNVs. Detection techniques (quantitative reverse transcription (qRT)-PCR) based on degenerate primers can be used to minimize the possibilities of false-negative detections

A Method for Modeling Decoherence on a Quantum Information Processor

We develop and implement a method for modeling decoherence processes on an N-dimensional quantum system that requires only an $N^2$-dimensional quantum environment and random classical fields. This model offers the advantage that it may be implemented on small quantum information processors in order to explore the intermediate regime between semiclassical and fully quantum models. We consider in particular $\sigma_z\sigma_z$ system-environment couplings which induce coherence (phase) damping, though the model is directly extendable to other coupling Hamiltonians. Effective, irreversible phase-damping of the system is obtained by applying an additional stochastic Hamiltonian on the environment alone, periodically redressing it and thereby irreversibliy randomizing the system phase information that has leaked into the environment as a result of the coupling. This model is exactly solvable in the case of phase-damping, and we use this solution to describe the model's behavior in some limiting cases. In the limit of small stochastic phase kicks the system's coherence decays exponentially at a rate which increases linearly with the kick frequency. In the case of strong kicks we observe an effective decoupling of the system from the environment. We present a detailed implementation of the method on an nuclear magnetic resonance quantum information processor.Comment: 12 pages, 9 figure

Factoring in a Dissipative Quantum Computer

We describe an array of quantum gates implementing Shor's algorithm for prime factorization in a quantum computer. The array includes a circuit for modular exponentiation with several subcomponents (such as controlled multipliers, adders, etc) which are described in terms of elementary Toffoli gates. We present a simple analysis of the impact of losses and decoherence on the performance of this quantum factoring circuit. For that purpose, we simulate a quantum computer which is running the program to factor N = 15 while interacting with a dissipative environment. As a consequence of this interaction randomly selected qubits may spontaneously decay. Using the results of our numerical simulations we analyze the efficiency of some simple error correction techniques.Comment: plain tex, 18 pages, 8 postscript figure

Decoherence and Initial Correlations in Quantum Brownian Motion

We analyze the evolution of a quantum Brownian particle starting from an initial state that contains correlations between this system and its environment. Using a path integral approach, we obtain a master equation for the reduced density matrix of the system finding relatively simple expressions for its time dependent coefficients. We examine the evolution of delocalized initial states (Schr\"odinger's cats) investigating the effectiveness of the decoherence process. Analytic results are obtained for an ohmic environment (Drude's model) at zero temperature.Comment: 15 pages, RevTex, 5 figures included. Submitted to Phys. Rev.

Discrete Wigner functions and the phase space representation of quantum teleportation

We present a phase space description of the process of quantum teleportation for a system with an $N$ dimensional space of states. For this purpose we define a discrete Wigner function which is a minor variation of previously existing ones. This function is useful to represent composite quantum system in phase space and to analyze situations where entanglement between subsystems is relevant (dimensionality of the space of states of each subsystem is arbitrary). We also describe how a direct tomographic measurement of this Wigner function can be performed.Comment: 8 pages, 1 figure, to appear in Phys Rev