7,619 research outputs found
Measurement-based quantum computation on cluster states
We give a detailed account of the one-way quantum computer, a scheme of quantum computation that consists entirely of one-qubit measurements on a particular class of entangled states, the cluster states. We prove its universality, describe why its underlying computational model is different from the network model of quantum computation, and relate quantum algorithms to mathematical graphs. Further we investigate the scaling of required resources and give a number of examples for circuits of practical interest such as the circuit for quantum Fourier transformation and for the quantum adder. Finally, we describe computation with clusters of finite size
Finding Optimal Flows Efficiently
Among the models of quantum computation, the One-way Quantum Computer is one
of the most promising proposals of physical realization, and opens new
perspectives for parallelization by taking advantage of quantum entanglement.
Since a one-way quantum computation is based on quantum measurement, which is a
fundamentally nondeterministic evolution, a sufficient condition of global
determinism has been introduced as the existence of a causal flow in a graph
that underlies the computation. A O(n^3)-algorithm has been introduced for
finding such a causal flow when the numbers of output and input vertices in the
graph are equal, otherwise no polynomial time algorithm was known for deciding
whether a graph has a causal flow or not. Our main contribution is to introduce
a O(n^2)-algorithm for finding a causal flow, if any, whatever the numbers of
input and output vertices are. This answers the open question stated by Danos
and Kashefi and by de Beaudrap. Moreover, we prove that our algorithm produces
an optimal flow (flow of minimal depth.)
Whereas the existence of a causal flow is a sufficient condition for
determinism, it is not a necessary condition. A weaker version of the causal
flow, called gflow (generalized flow) has been introduced and has been proved
to be a necessary and sufficient condition for a family of deterministic
computations. Moreover the depth of the quantum computation is upper bounded by
the depth of the gflow. However, the existence of a polynomial time algorithm
that finds a gflow has been stated as an open question. In this paper we answer
this positively with a polynomial time algorithm that outputs an optimal gflow
of a given graph and thus finds an optimal correction strategy to the
nondeterministic evolution due to measurements.Comment: 10 pages, 3 figure
Spekkens' toy model in all dimensions and its relationship with stabiliser quantum mechanics
Spekkens' toy model is a non-contextual hidden variable model with an epistemic restriction, a constraint on what an observer can know about reality. The aim of the model, developed for continuous and discrete prime degrees of freedom, is to advocate the epistemic view of quantum theory, where quantum states are states of incomplete knowledge about a deeper underlying reality. Many aspects of quantum mechanics and protocols from quantum information can be reproduced in the model. In spite of its significance, a number of aspects of Spekkens' model remained incomplete. Formal rules for the update of states after measurement had not been written down, and the theory had only been constructed for prime-dimensional and infinite dimensional systems. In this work, we remedy this, by deriving measurement update rules and extending the framework to derive models in all dimensions, both prime and non-prime. Stabiliser quantum mechanics (SQM) is a sub-theory of quantum mechanics with restricted states, transformations and measurements. First derived for the purpose of constructing error correcting codes, it now plays a role in many areas of quantum information theory. Previously, it had been shown that Spekkens' model was operationally equivalent to SQM in the case of odd prime dimensions. Here, exploiting known results on Wigner functions, we extend this to show that Spekkens' model is equivalent to SQM in all odd dimensions, prime and non-prime. This equivalence provides new technical tools for the study of technically difficult compound-dimensional SQM
Modulation of internuclear communication in multinuclear Ruthenium(II) polypyridyl complexes
The syntheses and characterisation of a series of mononuclear and dinuclear ruthenium polypyridyl complexes based on the bridging ligands 1,3-bis-[5-(2-pyridyl)-1H-1,2,4-triazol-3-yl]benzene, 1,4-bis-[5-(2-pyridyl)-1H-1,2,4-triazol-3-yl]benzene, 2,5-bis-[5-(2-pyridyl)-1H-1,2,4-triazol-3-yl]thiophene, 2,5-bis-[5-pyrazinyl-1H-1,2,4-triazol-3-yl]thiophene are reported. Electrochemical studies indicate that in these systems, the ground state interaction is critically dependent on the nature of the bridging ligand and its protonation state, with strong and weak interactions being observed for thiophene- and phenylene-bridged complexes, respectively
2QAN: A quantum compiler for 2-local qubit Hamiltonian simulation algorithms
Simulating quantum systems is one of the most important potential applications of quantum computers. The high-level circuit defning the simulation needs to be compiled into one that complies with hardware limitations such as qubit architecture (connectivity) and instruction (gate) set. General-purpose quantum compilers work at the gate level and have little knowledge of the mathematical properties of quantum applications, missing further optimization opportunities. Existing application-specifc compilers only apply advanced optimizations in the scheduling procedure and are restricted to the CNOT or CZ gate set. In this work, we develop a compiler, named 2QAN, to optimize quantum circuits for 2-local qubit Hamiltonian simulation problems, a framework which includes the important quantum approximate optimization algorithm (QAOA). In particular, we exploit the flexibility of permuting different operators in the Hamiltonian (no matter whether they commute) and propose permutation-aware techniques for qubit routing, gate optimization and scheduling to minimize compilation overhead. 2QAN can target different architectures and different instruction sets. Compilation results on four applications (up to 50 qubits) and three quantum computers (namely, Google Sycamore, IBMQ Montreal and Rigetti Aspen) show that 2QAN outperforms state-of-theart general-purpose compilers and application-specifc compilers. Specifcally, 2QAN can reduce the number of inserted SWAP gates by 11.5X, reduce overhead in hardware gate count by 68.5X, and reduce overhead in circuit depth by 21X. Experimental results on the Montreal device demonstrate that benchmarks compiled by 2QAN achieve the highest fdelity
The Multilingual Times: Breaking the Language Barrier Between Journalism and Science
This paper recounts and reflects upon the first two years of a project of transdisciplinary online collaboration involving a group of students studying journalism at Dublin Institute of Technology (DIT), who are paired one-to-one with a group studying linguistics at Trinity College Dublin. Taking as its starting point the idea that most journalism urgently needs to improve the accuracy and depth of its science coverage, and the equally urgent idea that scientists need to improve their capacity to communicate clearly to a wide public, the project has seen the students working together to produce an accessibly written blog, The Multilingual Times, reporting on the latest peer-reviewed research in the field of multilingualism. By using a series of Google Drive folders and files to host the collaborative work, the instructors (the paperâs co-authors) are able to monitor studentsâ progress, address issues as they arise, and assess the contributions of each student to the finished blog-posts. The project is therefore, in additional to its other pedagogical facets, something of an experiment in using Google Apps and its online synchronous and asynchronous capacities to facilitate collaboration
Folk Theorems on the Correspondence between State-Based and Event-Based Systems
Kripke Structures and Labelled Transition Systems are the two most prominent
semantic models used in concurrency theory. Both models are commonly believed
to be equi-expressive. One can find many ad-hoc embeddings of one of these
models into the other. We build upon the seminal work of De Nicola and
Vaandrager that firmly established the correspondence between stuttering
equivalence in Kripke Structures and divergence-sensitive branching
bisimulation in Labelled Transition Systems. We show that their embeddings can
also be used for a range of other equivalences of interest, such as strong
bisimilarity, simulation equivalence, and trace equivalence. Furthermore, we
extend the results by De Nicola and Vaandrager by showing that there are
additional translations that allow one to use minimisation techniques in one
semantic domain to obtain minimal representatives in the other semantic domain
for these equivalences.Comment: Full version of SOFSEM 2011 pape
Nonunitary quantum computation in the ground space of local Hamiltonians
A central result in the study of quantum Hamiltonian complexity is that the k-local Hamiltonian problem is
quantum-Merlin-Arthurâcomplete. In that problem, we must decide if the lowest eigenvalue of a Hamiltonian
is bounded below some value, or above another, promised one of these is true. Given the ground state of the
Hamiltonian, a quantum computer can determine this question, even if the ground state itself may not be efficiently
quantum preparable. Kitaevâs proof of QMA-completeness encodes a unitary quantum circuit in QMA into the
ground space of a Hamiltonian. However, we now have quantum computing models based on measurement
instead of unitary evolution; furthermore, we can use postselected measurement as an additional computational
tool. In this work, we generalize Kitaevâs construction to allow for nonunitary evolution including postselection.
Furthermore, we consider a type of postselection under which the construction is consistent, which we call tame
postselection. We consider the computational complexity consequences of this construction and then consider
how the probability of an event upon which we are postselecting affects the gap between the ground-state energy
and the energy of the first excited state of its corresponding Hamiltonian. We provide numerical evidence that the
two are not immediately related by giving a family of circuits where the probability of an event upon which we
postselect is exponentially small, but the gap in the energy levels of the Hamiltonian decreases as a polynomial
Cellular automaton decoders for topological quantum codes with noisy measurements and beyond
We propose an error correction procedure based on a cellular automaton, the sweep rule, which is applicable to a broad range of codes beyond topological quantum codes. For simplicity, however, we focus on the three-dimensional toric code on the rhombic dodecahedral lattice with boundaries and prove that the resulting local decoder has a non-zero error threshold. We also numerically benchmark the performance of the decoder in the setting with measurement errors using various noise models. We find that this error correction procedure is remarkably robust against measurement errors and is also essentially insensitive to the details of the lattice and noise model. Our work constitutes a step towards finding simple and high-performance decoding strategies for a wide range of quantum low-density parity-check codes
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