6 pages, revtex, pedagogical write-up based on talk presented at the National Conference on Quantum Computing (NQC-2002), Gwalior, October 2002 (v2) Possible directions for future development are pointed out. Presented at the First World Congress on Lateral Computing (WCLC 2004), Bangalore, December 2004
Recent developments in quantum computation have made it clear that there is a lot more to computation than the conventional Boolean algebra. Is quantum computation the most general framework for processing information? Having gathered the courage to go beyond the traditional definitions, we are now in a position to answer: Certainly not. The meaning of a message being ``a collection of building blocks'' can be explored in a variety of situations. A generalised framework is proposed based on group theory, and it is illustrated with well-known physical examples. A systematic information theoretical approach is yet to be developed in many of these situations. Some directions for future development are pointed out.
The modeling of natural phenomena via a Markov process --- a process for which the future is independent of the past, given the present--- is ubiquitous in many fields of science. Within this context, it is of foremost importance to develop ways to check from the available empirical data if the underlying mechanism is indeed Markovian. A paradigmatic example is given by data processing inequalities, the violation of which is an unambiguous proof of the non-Markovianity of the process. Here, our aim is twofold. First we show the existence of a monogamy-like type of constraints, beyond data proc…
University of California, Berkeley（加州大学伯克利分校）；Google Quantum AI（谷歌量子人工智能）
Leveraging quantum effects in metrology such as entanglement and coherence allows one to measure parameters with enhanced sensitivity. However, time-dependent noise can disrupt such Heisenberg-limited amplification. We propose a quantum-metrology method based on the quantum-signal-processing framework to overcome these realistic noise-induced limitations in practical quantum metrology. Our algorithm separates the gate parameter $φ$~(single-qubit Z phase) that is susceptible to time-dependent error from the target gate parameter $θ$~(swap-angle between |10> and |01> states) that is largely free…
We present the first instance where post-quantum steering is a stronger-than-quantum resource for information processing -- remote state preparation. In addition, we show that the phenomenon of post-quantum steering is not just a mere mathematical curiosity allowed by the no-signalling principle, but it may arise within compositional theories beyond quantum theory, hence making its study fundamentally relevant. We show these results by formulating a new compositional general probabilistic theory -- which we call Witworld -- with strong post-quantum features, which proves to be a intuitive and …
Quantum coherence allows the computation of an arbitrary number of distinct computational paths in parallel. Based on quantum parallelism it has been conjectured that exponential or even larger speedups of computations are possible. Here it is shown that, although in principle correct, any speedup is accompanied by an associated attenuation of detection rates. Thus, on the average, no effective speedup is obtained relative to classical (nondeterministic) devices.
We clarify the confusion, misunderstanding and misconception that the physical finiteness of the universe, if the universe is indeed finite, would rule out all hypercomputation, the kind of computation that exceeds the Turing computability, while maintaining and defending the validity of Turing computation and the Church-Turing thesis.
The proposal of the optical scheme for holonomic quantum computation is evaluated based on dynamical resolution to the system beyond adiabatic limitation. The time-dependent Schrödinger equation is exactly solved by virtue of the cranking representation and gauge transformation approach. Besides providing rigorous confirmation to holonomies of the geometrical prediction that holds for the ideally adiabatic situation, the dynamical resolution enables one to evaluate elaborately the amplitude of the nonadiabatic deviation, so that the errors induced to the quantum computation can be explicitly e…
We present an architecture of QCPU(Quantum Central Processing Unit), based on the discrete quantum gate set, that can be programmed to approximate any n-qubit computation in a deterministic fashion. It can be built efficiently to implement computations with any required accuracy. QCPU makes it possible to implement universal quantum computation with a fixed, general purpose hardware. Thus the complexity of the quantum computation can be put into the software rather than the hardware.
Quantum error correction in general is experimentally challenging as it requires significant expansion of the size of quantum circuits and accurate performance of quantum gates to fulfill the error threshold requirement. Here we propose a method much simpler for experimental implementation to correct arbitrary detection errors. The method is based on processing of data from repetitive experiments and can correct detection error of any magnitude, as long as the error magnitude is calibrated. The method is illustrated with its application to detection of multipartite entanglement from quantum st…
On the basis of introspective analysis, we establish a crucial requirement for the physical computation basis of consciousness: it should allow processing a significant amount of information together at the same time. Classical computation does not satisfy the requirement. At the fundamental physical level, it is a network of two body interactions, each the input-output transformation of a universal Boolean gate. Thus, it cannot process together at the same time more than the three bit input of this gate - many such gates in parallel do not count since the information is not processed together…
Because the subject of relativistic quantum field theory (QFT) contains all of non-relativistic quantum mechanics, we expect quantum field computation to contain (non-relativistic) quantum computation. Although we do not yet have a quantum theory of the gravitational field, and are far from a practical implementation of a quantum field computer, some pieces of the puzzle (without gravity) are now available. We consider a general model for computation with quantum field theory, and obtain some results for relativistic quantum computation. Moreover, it is possible to see new connections between …
Autonomous Quantum Processing Unit: An Autonomous Thermal Computing Machine & its Physical Limitations
Atominstitut, TU Wien（维也纳工业大学原子研究所）；Vienna Center for Quantum Science and Technology, TU Wien（维也纳量子科学与技术中心）；Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences（奥地利科学院量子光学与量子信息研究所）
In this study, a distinctive feature of quantum computation (QC) is characterized. To this end, a seemingly-powerful classical computing model, called "stochastic ensemble machine (SEnM)," is considered. The SEnM runs with an ensemble consisting of finite copies of a single probabilistic machine, hence is as powerful as a probabilistic Turing machine (PTM). Then the hypothesis--that is, the SEnM can effectively simulate a general circuit model of QC--is tested by introducing an information-theoretic inequality, named readout inequality. The inequality is satisfied by the SEnM and imposes a cri…
It was recently shown that certain subsurface hydrological inverse problems -- here framed as determining the composition of an aquifer from pressure readings -- can be solved on a quantum annealer. However, the quantum annealer performance suffered when solving problems where the aquifer was composed of materials with vastly different permeability, which is often encountered in practice. In this paper, we study why this regime is difficult and use several pre- and post-processing tools to address these issues. This study has three benefits: it improves quantum annealing performance for real-w…
There are quantum solutions for computational problems that make use of interference at some stage in the algorithm. These stages can be mapped into the physical setting of a single particle travelling through a many-armed interferometer. There has been recent foundational interest in theories beyond quantum theory. Here, we present a generalized formulation of computation in the context of a many-armed interferometer, and explore how theories can differ from quantum theory and still perform distributed calculations in this set-up. We shall see that quaternionic quantum theory proves a suitabl…
Quantum information science provides powerful technologies beyond the scope of classical physics. In practice, accurate control of quantum operations is a challenging task with current quantum devices. The implementation of high fidelity and multi-qubit quantum operations consumes massive resources and requires complicated hardware design to fight against noise. An approach to alleviating this problem is to replace quantum operations with classical processing. Despite the common practice of this approach, rigorous criteria to determine whether a given quantum operation is replaceable classical…
We consider a simple model of a Josephson junction phase qubit coupled to a solid-state nanoelectromechanical resonator. This and many related qubit-resonator models are analogous to an atom in an electromagnetic cavity. When the systems are weakly coupled and nearly resonant, the dynamics is accurately described by the rotating-wave approximation (RWA) or the Jaynes-Cummings model of quantum optics. However, the desire to develop faster quantum-information-processing protocols necessitates approximate, yet analytic descriptions that are valid for more strongly coupled qubit-resonator systems.…
Construction of explicit quantum circuits follows the notion of the "standard circuit model" introduced in the solid and profound analysis of elementary gates providing quantum computation. Nevertheless the model is not always optimal (e.g. concerning the number of computational steps) and it neglects physical systems which cannot follow the "standard circuit model" analysis. We propose a computational scheme which overcomes the notion of the transposition from classical circuits providing a computation scheme with the least possible number of Hamiltonians in order to minimize the physical res…
We propose a method to implement cavity QED and quantum information processing in high-Q cavities with a single trapped but non-localized atom. The system is beyond the Lamb-Dick limit due to the atomic thermal motion. Our method is based on adiabatic passages, which make the relevant dynamics insensitive to the randomness of the atom position with an appropriate interaction configuration. The validity of this method is demonstrated from both approximate analytical calculations and exact numerical simulations. We also discuss various applications of this method based on the current experimenta…
The quantum circuit model is the most widely used model of quantum computation. It provides both a framework for formulating quantum algorithms and an architecture for the physical construction of quantum computers. However, several other models of quantum computation exist which provide useful alternative frameworks for both discovering new quantum algorithms and devising new physical implementations of quantum computers. In this thesis, I first present necessary background material for a general physics audience and discuss existing models of quantum computation. Then, I present three result…
Nonadiabatic holonomic quantum computation (NHQC) provides a method to implement error resilient gates and that has attracted considerable attention recently. Since it was proposed, three-level Λ systems have become the typical building block for NHQC and a number of NHQC schemes have been developed based on such systems. In this paper, we investigate the realization of NHQC beyond the standard three-level setting. The central idea of our proposal is to improve NHQC by enlarging the Hilbert space of the building block system and letting it have a bipartite graph structure in order to ensure pu…
