QCQIP'2012

The information revolution is largely based on what a physicist would call a classical view of information, assuming that it can be copied freely and is not disturbed by observation. Quantum effects in information processing, which prevent the information in microscopic objects like atoms or photons from being observed or copied accurately, were long regarded as a mere nuisance, but are now known to make possible feats such as quantum cryptography, quantum teleportation and dramatic computational speedups.

Although progress toward a practical quantum computer is slow, other surprising quantum informational effects continue to be discovered, and quantum cryptographic systems are already available commercially. Most importantly, the quantum approach has led to a more coherent and powerful way of thinking about how physical objects interact and influence one another, and how that interaction can be used to compute, communicate, and protect privacy.

This talk will avoid mathematical complications and instead aim to explain central quantum concepts like entanglement, which at first sight seem counterintuitive.

An approximate unitary t-design is a distribution of unitaries which mimic properties of the Haar measure for polynomials (in the entries of the unitaries) of degree up to t. It has been a conjecture in the theory of quantum pseudo-randomness that polynomial sized random quantum circuits form an approximate unitary poly(n)-design. Unfortunately, up to now, the best result known was that polynomial random quantum circuits are unitary 3-designs.

In this talk I'll show that local random quantum circuits acting on n qubits composed of polynomi- ally many nearest neighbour two-qubit gates form an approximate unitary poly(n)-design, settling the conjecture in the affirmative. The proof is based on an interplay of techniques from quantum many-body theory, representation theory, and the theory of Markov chains.

Time permitting I'll also outline a few applications of the result to quantum complexity theory, local equilibration of quantum systems, and topological order. Based on joint work with Aram Harrow and Michal Horodecki.

Asymptotical behavior of non-Markovian dissipative dynamics is not only an issue of fundamental importance to quantum statistics itself, but also a crucial point to understand decoherence of various measures of non-classical correlations in the framework of quantum information theory.

Here we propose an exact approach to resolve the steady behavior of the two-qubit system subjected to a local environment with non-Markovian dissipation. The population on the excited state of the model in the longtime limit is straightforwardly calculated via the function relationship of it with the spectral density function of the reservoir. Consequently, we identify the parameter regimes for various initial states where steady entanglement or steady non-classical correlations without entanglement is linked to the detailed form of the spectral density function.

Quantum effects, besides offering substantial superiority in many tasks over classical methods, are also expected to provide interesting ways to establish secret keys between remote parties. A striking scheme called ‘‘counterfactual quantum cryptography’’ proposed by Noh [Phys. Rev. Lett. 103, 230501 (2009).] allows one to maintain secure key distributions, in which particles carrying secret information are seemingly not being transmitted through quantum channels. We have experimentally demonstrated, for the first time, a faithful implementation for such a scheme with an on-table realization operating at telecom wavelengths. To verify its feasibility for extension over a long distance, we have furthermore reported an illustration on a 1 km fiber. In both cases, high visibilities of more than 98% are achieved through active stabilization of interferometers. Our demonstration is crucial as a direct verification of such a remarkable application, and this procedure can become a key communication module for revealing fundamental physics through counterfactuals.

In collaboration with Yang Liu, Lei Ju, Xiao-Lei Liang, Shi-Biao Tang, Guo-Liang Shen Tu, Lei Zhou, Cheng-Zhi Peng, Teng-Yun Chen, Zeng-Bing Chen, and Jian-Wei Pan.

There are three kind of models for quantum computation: circuit model , cluster state model and adiabatic evolution model. The Hamitonian in the adiabatic quantum computing usually contains the forms of many-body interaction. We should simulate the many-body one using the two-body interaction via some ancilla qubits. We discuss how to simulate the many-body Hamitonian using fewer ancilla, and how to implement adiabatic quantum computaion in ion trap system. We also discuss a new quantum algorithm.

Quantum teleportation enables one to perfectly simulate the direct transfer of a quantum state form a sender to a receiver though the transfer of a finite amount of classical bits and the consumption of a finite amount of shared entanglement. In this context, it is usually assumed that the sender and receiver share the same reference frame, e.g. that their clocks are synchronized or that Cartesian axes x,y,z point in the same directions in space. However, this assumption may not be taken for granted in many situations, for example if the sender and receiver are two units of a quantum computer that is subjected to local noise.

In this talk I will address the task of teleportation in the absence of a shared reference frame, showing a connection with two apparently different topics, namely the no-programming theorem by Nielsen and Chuang and the task of optimal distributed learning of an unknown unitary gate. Using this connection I will discuss optimal approximate teleportation protocols in several interesting situations, showing examples where the optimal protocol does not extract any information about the mismatch between the sender's and receiver's reference frame, as well as examples where the optimal teleportation consists of two-steps, the first being the estimation of the unknown mismatch.

The paradigm of LOCC (local operations and classical communication) plays a fundamental role in some of the most important quantum information tasks such as teleportation and quantum cryptography. However, despite this significance, many open questions still surround the nature of LOCC operations. For instance, does there exist sequences of LOCC protocols that converge to some global map which itself cannot be implemented by LOCC? While examples of such sequences have recently been proven for tripartite systems, hitherto this question has remained unanswered in the bipartite setting.

In this talk, I will discuss some interesting properties concerning the topological closure of LOCC. We will first consider the case of finite round LOCC and I will show how the set of r-round LOCC instruments having no more than n different outcomes is indeed closed. I will then proceed to describe a sequence of bipartite LOCC instruments that converges outside the class of LOCC.

In the past decade, there has been tremendous progress in the development of the quantum computation, especially in solid-state quantum computing. The quantum information storage, the precise manipulation of quantum bits, the transmission of quantum information and quantum bit high efficiency measurement have been a great development. For example, in quantum dots, nuclear magnetic resonance, electron paramagnetic resonance, superconductivity qubits and so on. But most of the systems are still distance from practical quantum computation tasks. Thus it is necessary to research different quantum systems and combine them together to seek a possible way for scalable quantum computation proposal. Spin plays an important role among lots of proposals and is one of the best way for practical quantum computation.

Herein, we mainly focus on the basic theory and experiment fields of quantum computations which base on spins in solid state. We concern on several respects such as decoherence regime, dynamical decoupling methods for suppressing the noise induced by the environment, the initialization of the quantum spin states, high fidelity quantum operations and readout, the entanglement of multiqubits and seek possible methods for scalable quantum computation.

The observation that concepts from quantum information has generated many alternative indicators of quantum phase transitions hints that quantum phase transitions possess operational significance with respect to the processing of quantum information. Yet, studies on whether such transitions lead to quantum phases that differ in their capacity to process information remain limited.

Here We show that there exist quantum phase transitions that cause a distinct qualitative change in our ability to simulate certain quantum systems under perturbation of an external field by local operations and classical communication. In particular, we show that in certain quantum phases of the XY model, adiabatic perturbations of the external magnetic field can be simulated by local spin operations, whereas the resulting effect within other phases results in coherent non-local interactions. We discuss the potential implications to adiabatic quantum computation, where a computational advantage exists only when adiabatic perturbation results in coherent multi-body interactions.

Ref: J.Cui et al. Nature Commun.3, 812 (2012).

The system of trapped ultracold ions is a promising candidate for quantum information processing. I will talk about two proposals using trapped ions for quantum simulation. The first is to simulate Franck-Condon physics with a single trapped ion, in which the Franck-Condon blockade induced by electron-vibron coupling can be used for quantum gating. The second is the simulation of the Mach-Zehnder interferometer with a line of trapped ions based on adiabatic process. The experimental setup for above simulations is under construction.

Although the security of quantum cryptography is provable based on the principles of quantum mechanics, it can be compromised by the flaws in the design of quantum protocols and the noise in their physical implementations. So, it is indispensable to develop techniques of verifying and debugging quantum cryptographic systems. Model-checking has proved to be effective in the verification of classical cryptographic protocols, but an essential difficulty arises when it is applied to quantum systems: the state space of a quantum system is always a continuum even when its dimension is finite.

To overcome this difficulty, we introduce a novel notion of quantum Markov chain, specially suited to model quantum cryptographic protocols, in which quantum effects are entirely encoded into super-operators labelling transitions, leaving the location information (nodes) being classical. Then we define a quantum extension of probabilistic computation tree logic (PCTL) and develop a model-checking algorithm for quantum Markov chains.

In this talk, I will first review Winter's measurement compression theorem, and then move on to prove an extension of this theorem to the case in which the sender is not required to receive the outcomes of the simulated measurement. The total cost of common randomness and classical communication can be lower for such a "non-feedback" simulation, and we prove a single-letter converse theorem demonstrating optimality. We then review the Devetak-Winter theorem on classical data compression with quantum side information, providing new proofs of its achievability and converse parts. From there, we outline a new protocol that we call "measurement compression with quantum side information." Finally, we prove a single-letter theorem characterizing measurement compression with quantum side information when the sender is not required to obtain the measurement outcome.

The dynamics for an open quantum system can be `unravelled' in infinitely many ways, depending on how the environment is monitored, yielding different sorts of conditioned states, evolving stochastically. In the case of ideal monitoring these states are pure, and the set of states for a given monitoring forms a basis (which is overcomplete in general) for the system. It has been argued elsewhere [D. Atkins et al., Europhys. Lett. 69, 163 (2005)] that the `pointer basis' as introduced by Zurek and co-workers [Phys. Rev. Lett. 70, 1187 (1993)], should be identified with the unravelling-induced basis which decoheres most slowly.

Here we show the applicability of this concept of pointer basis to the problem of state stabilization for quantum systems. In particular we prove that for linear Gaussian (LG) quantum systems, if the feedback control is assumed to be strong compared to the decoherence of the pointer basis, then the system can be stabilized in one of the pointer basis states with a fidelity close to one (the infidelity varies inversely with the control strength). Moreover, the optimal unravelling for stabilizing the system (in any state) is that which induces the pointer basis. We illustrate these results with a model system: quantum Brownian motion. We show that even if the feedback control strength is comparable to the decoherence, the optimal unravelling still induces a basis very close to the pointer basis. However, if the feedback control is weak compared to the decoherence, this is not the case.

I will introduce the asymptotic theory of quantum hypothesis testing. This include the formulation of the problem, the quantum Stein's lemma, the quantum Chernoff bound, the quantum Hoeffding bound, the second order asymptotics, and some related issues.

Thermal distribution and quantum fluctuation in environments induce noise on qubits, which leads to the qubit decoherence. The qubit decoherence can act as a probe of dynamics in the environments. Furthermore, controls can be applied on the qubit so that particular processes in the environment can be detected. Under the spin echo control, the thermal noise effect can be removed so that the quantum fluctuation effect is revealed [1,2]. Many-pulse dynamical decoupling control can elongate the qubit coherence time and make the decoherence sensitive to noise at a certain frequency [3,4]. This way the weak signals from single nuclear spins can be greatly amplified such that single-molecule NMR becomes feasible [3]. By removing the thermal noise effect by spin echo, quantum critical points can be identified even at temperature much higher than the interaction energy in the environment [5]. By coupling a probe spin to a ferromagnetic Ising system, the Lee-Yang zeros in the complex plane of magnetic field are mapped to the zeros of the probe spin coherence [6]. In the thermodynamic limit, the probe spin decoherence presents sudden death and sudden rise corresponding to the Lee-Yang edge singularities [6].

This work was supported by Hong Kong RGC and CUHK Focused Investments Scheme.

References:

[1] N. Zhao, Z. Y. Wang & R. B. Liu, Phys. Rev. Lett. 106, 217205 (2011). Anomalous Decoherence Effect in a Quantum Bath.
[2] P. Huang, X. Kong, N. Zhao, F. Shi, P. Wang, X. Rong, R.-B. Liu & J. Du, Nature Communications 2, 570 (2011). Observation of an anomalous decoherence effect in a quantum bath at room temperature.
[3] N. Zhao, J. L. Hu, S. W. Ho, J. T. K. Wan & R. B. Liu, Nature Nanotechnology 6, 242 (2011). Atomic-scale magnetometry of distant nuclear spin clusters via nitrogen-vacancy spin in diamond.
[4] N. Zhao, J. Honert, B. Schmid, J. Isoya, M. Markham, D. Twitchen, F. Jelezko, R.-B. Liu, H. Fedder & J. Wrachtrup, Nature Nanotechnology (in press), arXiv: 1204.6513. Sensing single remote nuclear spins.
[5] S. W. Chen & R. B. Liu, arXiv:1202.4958. Quantum criticality at infinite temperature.
[6] B. B. Wei & R. B. Liu, arXiv:1206.2077. Probing Lee-Yang zeros and coherence sudden death.

I will review our works on quantum information with cold atoms in various external potential with Feshbach resonance, such as harmonic potential, optical lattice and gauge field. Quantum phase transition is one of the most important issues in cold atomic physics, and quantum fidelity is an important concept emerging from quantum information. In this talk, I will describe as simply as possible the role of fidelity and its leading term, i.e. the so called fidelity susceptibility, in quantum phase transitions. The quantum phase transition and the strongly correlated effect of cold atoms in triangular optical lattice, and the interacting Dirac fermions on honeycomb lattice, are investigated by using cluster dynamical mean-field theory and continuous time quantum Monte Carlo method. We also study the quantum spin Hall effect in the kagome optical lattice.

References:
[1] R. Liao, Y. X. Yu, W. M. Liu, Tuning the Tricritical Point with Spin-Orbit Coupling in Polarized Fermionic Condensates, Phys. Rev. Lett. 108, 080406 (2012).
[2] Y. H. Chen, H. S. Tao, D. X. Yao, W. M. Liu, Kondo Metal and Ferrimagnetic Insulator on the Triangular Kagome Lattice, Phys. Rev. Lett. 108, 246402 (2012).

In the parity-time-symmetric (PT-symmetric) Hamiltonian theory, the optimal evolution time can be reduced dramatically and can even be zero. In this talk, we report our experimental simulation of the fast evolution of a PT-symmetric Hamiltonian in a nuclear magnetic resonance quantum system. The experimental results demonstrate that the PT-symmetric Hamiltonian system can indeed evolve much faster than the quantum system, and the evolution time can be arbitrarily close to zero.

Quantum entanglement has been actively sought in optomechanical and electromechanical systems. The simplest system is a mechanical oscillator interacting with a coherent optical field, while the oscillator also suffers from thermal decoherence. With a rigorous functional analysis, we develop a mathematical framework for treating quantum entanglement that involves infinite degrees of freedom. We show that the quantum entanglement is always present between the oscillator and continuous optical field—even when the environmental temperature is high and the oscillator is highly classical. Such an entanglement is also shown to be able to survive more than one mechanical oscillation period if the characteristic frequency of the optomechanical interaction is larger than that of the thermal noise.
Reference: Phys. Rev. A 81, 052307 (2010)

Quantum key distribution (QKD) is a technology that can, in principle, provide cryptographic systems with an unprecedented level of security. Unfortunately, practical QKD schemes often suffer from imperfections and do not achieve the theoretical security. Indeed, quantum hacking against practical QKD systems, particularly via detector side channel attacks, has emerged as a hot topic. Existing counter-measures against this kind of attacks are either highly impractical or may not be fully effective.

Recently, we have proposed (Hoi-Kwong Lo, Marcos Curty, and Bing Qi, Physical Review Letters 108, 130503, 2012) a new solution, measurement-device-independent QKD (MDI-QKD), which can “short-circuit” all detector security loopholes. In other words, the system will be automatically immune to all detector side channel attacks. This is remarkable because it means that commercial QKD detection systems would no longer require any special security certifications and, in fact, they can even be manufactured by a malicious eavesdropper, Eve.

Moreover, unlike previous approaches, MDI-QKD can be implemented with current technologies, standard optical components, realistic detection efficiency, and highly lossy channels. Furthermore, its key generation rate is many orders of magnitude higher than that based on full device-independent QKD. Our simulation results show that long-distance quantum cryptography over 200km will remain secure even with seriously flawed detectors. The feasibility of this protocol is also highlighted by two recent experimental demonstrations (A. Rubenok, et al., A quantum key distribution system immune to detector attacks, arXiv:1204.0738v2; T. Ferreira da Silva, et al., Proof-of-principle demonstration of measurement device independent QKD using polarization qubits, arXiv:1207.6345v1).

As classical computing models, quantum computing models include, from simplicity to complex, quantum finite automata (QFA), quantum pushdown automata, quantum Turing machines, quantum circuits, and others. Due to the expensive quantum resources, the number of states in QFA plays an important role. Therefore, we hope to devise a QFA with the number of states as less as possible, but its computational power is not cut down. To this end, we try to present a state minimization method for various one-way finite automata, such as probabilistic automata, measure-once quantum automata, measure-many quantum automata, measure-once generalized quantum automata, generalized measure-many quantum automata, stochastic sequence machines. With this idea of minimization, one can minimize other one-way (probabilistic and quantum) finite automata.

I will survey some recent observations concerned with the transfer of arbitrary quantum states in a network of spin particles and the preparation of the network in an arbitrary configuration. Among these, I will talk about the recent solution of a problem of Bose about high fidelity state transfer in a spin chain, which originally motivated the study of spin networks as communication nanodevices.

In this talk we consider the quantum communication complexity lower bound for some graph and linear algebra problems including: approximate the clique number, decide the bipartiteness of a graph, and compute the rank/det of a matrix etc. We get some nearly tight quantum lower bound for these problems. The proof of these bound involved the using of reduction from Set-Disjointness problem and inner product problem, the approximate norm method, Fourier analysis on matrix, and Szemeredi regular lemma et al.

This talk is based on the joint works with Chenggu Wang,Wei Yu, Mario Szegedy and Magnus Halldorsson.

The quantum Fourier transform (QFT) is sometimes said to be the source of various exponential quantum speed-ups---most famously, the QFT is a central ingredient in Shor's factoring algorithm. Here we introduce a class of quantum circuits, called normalizer circuits, which cannot outperform classical computers even though the QFT constitutes an essential component. A normalizer circuit over a finite abelian group is any quantum circuit comprising the QFT over this group, gates which compute automorphisms and gates which realize quadratic functions on the group. We prove that all normalizer circuits have polynomial-time classical simulations. This result generalizes the celebrated Gottesman-Knill theorem which states that every stabilizer circuit can be simulated efficiently classically. Finally, we discuss connections between normalizer circuits and Shor's factoring algorithm.

This talk is about the (non-)additivity problems besetting quantum Shannon theory: numerous capacities and entanglement measures are no known to be non-additive, starting with the unpleasant state of the matter that the information-theoretic, operational quantities are only captured as regularisations of "simple" quantities: the Holevo capacity generates the classical capacity of a channel, the entanglement of formation the so-called entanglement cost, etc.

It is unknown how different single-letter quantity and regularisation can be, even in the simplest case of the minimum output entropy of a channel. By way of an analogy with non-local games and their parallel repetition, I want to outline a strategy to delimit the ratio between these numbers, based on the conjectured existence of entanglement measures with certain properties.

Advances in quantum information science have opened new venues for scientific discovery in different fields. In this report, we first discuss recent achievements in quantum simulation. We then introduce an algorithmic quantum cooling method that can be applied to any physical systems, and present its experimental implementation using a quantum optics setup. Considering reliable quantum communication through noisy channels, we further discuss a method that allows perfect quantum communication by encoding pairs of noisy channels. Experimental results on two encoded optical polarization maintaining fibers are presented and the interferometric activation effect on quantum capacity is shown.

We show how multi-walker quantum walks can be implemented in a quantum quincunx created via cavity quantum electrodynamics. The implementation of a quantum walk with a multi-walker opens up the interesting possibility to introduce entanglement and more advanced walks. With different coin tosses and initial states the multi-walker quantum walk shows different probability distributions which deviate strongly from the classical random walks with quadratic enhanced spreadings and localization effects. By introducing decoherence, the transition from quantum walks to the classical versions is observed. We introduce the average fidelity decay as a signature to investigate the decoherence-induced irreversibility of quantum walks.

This talk will introduce the synthesis of binary, ternary and hybrid reversible circuits. In the absence of ancilla qubits, all even binary n-qudit reversible circuits can be constructed by NOT, 1-controlled-NOT and 2-controlled-NOT (Toffoli gate) gates; 2-qudit ternary Swap, NOT and 1-controlled-NOT gates are universal for realization of arbitrary ternary n-qudit reversible circuits; and all even ternary n-qudit reversible circuits can be constructed by ternary NOT and ternary 1-controlled-NOT gates. The results in the synthesis of hybrid reversible circuits are similar to the synthesis of ternary reversible circuits.

We introduce a Markov chain model of concurrent quantum programs. Some characterizations of the reachable space, uniformly repeatedly reachable space and termination of a concurrent quantum program are derived. Based on these characterizations, algorithms for computing the reachable space and uniformly repeatedly reachable space and for deciding the termination are given.

We give a unified characterization of multiparty correlations in a multipartite quantum state based on the maximum entropy principle. Several properties on the correlation measures are presented, which includes a refined example to demonstrate why local operation can create global correlations. Possible relation with an [n,k] secret sharing protocol is discussed.

Quantum Computation and Intelligent Systems

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