Winfried Hensinger (Invited Talk)
Title: Quantum computing with trapped ions
Adán Cabello (Invited Talk)
Title: Extreme quantum nonlocality
Abstract
Problem #1: If n qubits were distributed between two parties, which quantum pure states and qubit distributions would allow all-versus-nothing (or Greenberger-Horne-Zeilinger-like) proofs of Bell's theorem using only single-qubit measurements? We show a necessary and sufficient condition for the existence of these proofs and provide all existing proofs up to n=7 qubits.Problem #2: If n qubits were distributed between n parties, which would be the optimal Bell inequalities? We show all optimal n-party Bell inequalities for the perfect correlations of any graph state up to n=6 qubits. Optimal means that the ratio between the quantum violation and the bound for local hidden-variable theories is the maximum over all possible combinations of perfect correlations. This implies that the required detection efficiencies for loophole-free Bell tests are minimal.
The solution of these two problems lead us to a extreme form of bipartite quantum nonlocality robust under decoherence.
Vladimir V. Kisil (Leeds)
Quantum Parallel Computation in the Phase Space
First quantum algorithms inherited the structure of classical computers. The main difference is a replacement of classical bits of information by qubits. Being a quantum states a qubit holds a superposition of 0 and 1 and thus make parallel computations possible. However quantum algorithms are still a linear sequence of transformations of qubit performed in a row.On the other hand quantum computers can be designed from a scratch implementing distinguished features of the quantum world. One of them is the absence of definite paths of objects: a particle is thought to be propagated simultaneously along all possible paths contributing to the final transitional amplitude.
We discuss a possibility of simultaneous (parallel) quantum algorithms based on the path integral technique in the phase space.
Simon Perdrix
Title: Quantum Entanglement Analysis based on Abstract Interpretation
Abstract: Entanglement is a non local property of quantum states which has no classical counterpart and plays a decisive role in quantum information theory. The exact role of the entanglement is nevertheless not well understood. Since an exact analysis of entanglement evolution induces an exponential slowdown, we consider approximative analysis based on the framework of abstract interpretation.A concrete quantum semantics based on super-operators is associated with a simple quantum programming language. The representation of entanglement, i.e. the design of the abstract domain is a key issue. A representation of entanglement as a partition of the memory is chosen. An abstract semantics is introduced, and the soundness of the approximation is proved.
Thorsten Altenkirch & Alexander GreenShor in Haskell
We have implemented a monadic interface to quantum computing in Haskell: the quantum IO monad. Today we are going to report on implementing Shor's algorithm using the quantum IO monad. This raises interesting issues on how to structure reversible and quantum computation, e.g. the introduction of the "unitary let". We will also address issues such as proving properties of quantum algorithms.
Nick PapanikolaouTitle: Model Checking a Quantum Protocol: Theory, Implementation and Issues
Abstract: Numerous protocols have emerged over the past 20-25 years for quantum communication and quantum cryptography. Such protocols pose several challenges not encountered in the study of classical computer science, due to the very nature of the quantum phenomena they involve. This justifies a strong need for languages, methods and tools dedicated to the design and analysis of such protocols. We discuss a high-level, concurrent modelling language for quantum protocols (QMCLang); this language is an essential component of the verification tool QMC, which enables a user to automatically check properties of quantum protocols using model-checking techniques. We will describe and demonstrate QMC, and the temporal logic dEQPL, which is used for specifying protocol properties. The semantics and properties of a substantial quantum protocol will be discussed in this setting. The question of how to generalise the techniques used in QMC to handle protocols involving unitary operators from a universal set will be addressed also, since QMC is currently restricted to the description of those protocols expressible in the quantum stabiliser formalism.
Mehrnoosh SadrzadehAn epistemic measurement system for quantum security
We present a formal system to reason about knowledge properties of quantum security protocols. The formalism is obtained via a marriage of measurement calculus of Danos-Kashefi-Panangaden with the algebra of epistemic updates of Baltag-Coecke-Sadrzadeh.
Our setting consists of a quantale Q of classical and quantum actions and its right module M of classical and quantum data. We endow the pair (M,Q) with a family of appearance maps f_A: (M,Q) --> (M,Q) that represent information of agents A in Ag. The triple (Q, M, f_A) is required to satisfy a set of axioms encoding non-local correlations of quantum mechanics. Reasoning about knowledge of agents after running the protocol is done via unfolding the adjunctions that arise from f_A's and the action of Q on M.
As examples we encode and reason about sharing and secrecy properties of Ekert'91 and BB'84 key distribution and bit-commitment protocols and show we can derive their corresponding attacks.
As future work, we aim to provide this setting with a high level language that has recursive operations and probabilities to be able to also model data screening.
Samson AbramskyComparing Two Approaches to Categorical Quantum Mechanics
We compare the categorical approach to quantum mechanics and quantum information based on monoidal categories with additional structure (dagger-compact etc.), introduced by Abramsky, Coecke et al, with the topos-theoretic approach recently proposed by Isham and Doring.
Bob CoeckeTrue quantumness
What makes QM what it truly is? We discuss some toy models and axiom systems which aim to say something about this, and unify them within one algebraic scheme. Under consideration are the convex schemes tracing back to Ludwig, and including recent work by Barnum, Barrett, Leifer and Wilce and the epistemic Toy models due to Smolin and Spekkens. All of these admit a simple characterisation in terms of categorical structure. The presented results connect the currently ongoing work in computational semantics with ongoing work in the foundations of QM.
J.D. Biamonte (Oxford)Hamiltonian Ground State Classical Spin Logic
An algebraic method to engineer the low-energy subspace of interacting spin systems is presented. To date, all known methods require the introduction of a large spectral gap, where the magnitude of the gap improves only an approximate low-energy effective Hamiltonian. Under suitable restrictions, the presented approach allows k-body interactions to be captured exactly using 2-body Hamiltonians, even if all terms in the Hamiltonian share the same basis and without dependence on perturbation theory or the associated large spectral gap. These methods appear to have several applications in quantum information theory, especially adiabatic quantum computation.
Dan BrownePhase transition of computational power in the resource states for one-way quantum computation
We study how heralded qubit losses during the preparation of a two-dimensional cluster state, a universal resource state for one-way quantum computation, affect its computational power. Above the percolation threshold we present a polynomial-time algorithm that concentrates a universal cluster state, using resources that scale optimally in the size of the original lattice. On the other hand, below the percolation threshold, we show that single qubit measurements on the faulty lattice can be efficiently simulated classically. We observe a phase transition at the threshold when the amount of entanglement in the faulty lattice directly relevant to the computational power changes exponentially.
This is joint work with Matthew B. Elliott, Steven T. Flammia, Seth T. Merkel, Akimasa Miyake, and Anthony J. Short. arXiv:0709.1729
Ross DuncanA Graphical Calculus for Quantum Observables
Alessandra Di Pierro and Herbert WiklickyDeclarative Quantum Programming
Various aspects of quantum processes appear to be rather counter intuitive for human minds or at least extremely difficult to grasp. In order to support (future) quantum programmers we continue to investigate a high level approach towards codifying computational tasks for quantum computers (independently of their concrete physical realisation) in an abstract way. This research is inspired by declarative approaches in classical programming - such as logic and constraint programming. Ideally, the programmer in this setting just specifies a certain number of facts or constraints as givens, and then requests a desired computational result (via some kind of query) from the system, leaving it open how the computational infrastructure may actually obtain the results. We will present work in progress which tries to exploit the ortho-lattice of elementary measurements as a replacement for the the lattice of constraints in the (concurrent) constraint programming paradigm and discuss aspects of the relationship to measurement-based (one-way) quantum computation.
Simon GayQuantum security via process calculus
Stephen BrierleyMaximally entangled pure states
Abstract: An obvious definition for maximal entanglement of n qubit pure states is to require that all one qubit reduced density matrices are maximally mixed. For two and three qubit systems this leads to a unique (up to local unitary operations) state, however this is not true for a system with more than three qubits. We therefore consider all possible bipartitions of the state and ask that they are all maximally mixed. In this talk I will explain the definition of this entanglement measure and examine some examples of interesting states. In light of recent numerical work, I will also discuss the existence of a maximally entangled state in the case of n qubits.