On Computability of Decaying and Nondecaying States in Quantum Systems with Cantor Spectra

We study Hamiltonians with singular spectra of Cantor type with a constant ratio of dissection. The decay properties of the states in such systems depend on the nature of the dissection rate that can be characterized in terms of the algebraic number theory. We show that in spite of simplicity of the considered model the computational modeling of nondecaying states is in general impossible.     

Quantum Algorithm for Hilbert's Tenth Problem

We explore in the framework of Quantum Computation the notion of Computability, which holds a central position in Mathematics and Theoretical Computer Science. A quantum algorithm for Hilbert's tenth problem, which is equivalent to the Turing halting problem and is known to be mathematically noncomputable, is proposed where quantum continuous variables and quantum adiabatic evolution are employed. If this algorithm could be physically implemented, as much as it is valid in principle—that is, if certain Hamiltonian and its ground state can be physically constructed according to the proposal—quantum computability would surpass classical computability as delimited by the Church—Turing thesis. It is thus argued that computability, and with it the limits of Mathematics, ought to be determined not solely by Mathematics itself but also by Physical Principles.     

Qubit Semantics and Quantum Trees

In the qubit semantics the meaning of any sentence α is represented by a quregister: a unit vector of the n–fold tensor product ⊗ⁿ ℂ², where n depends on the number of occurrences of atomic sentences in α (see Cattaneo et al.). The logic characterized by this semantics, called quantum computational logic (QCL), is unsharp, because the noncontradiction principle is violated. We show that QCL does not admit any logical truth. In this framework, any sentence α gives rise to a quantum tree, consisting of a sequence of unitary operators. The quantum tree of α can be regarded as a quantum circuit that transforms the quregister associated to the occurrences of atomic subformulas of α into the quregister associated to α.     

An Alternative Adiabatic Quantum Algorithm for the Hamiltonian Cycle Problem

We put forward an alternative quantum algorithm for finding Hamiltonian cycles in any N-vertex graph based on adiabatic quantum computing. With a von Neumann measurement on the final state, one may determine whether there is a Hamiltonian cycle in the graph and pick out a cycle if there is any. Although the proposed algorithm provides a quadratic speedup, it gives an alternative algorithm based on adiabatic quantum computation, which is of interest because of its inherent robustness.     

Adiabatic Quantum Gates

We discuss the logic implementation of quantum gates in the framework of the quantum adiabatic method, which uses the language of ground states, spectral gaps and Hamiltonians instead of the standard unitary transformation language.     

Quantum Computational Logic

A quantum computational logic is constructed by employing density operators on spaces of qubits and quantum gates represented by unitary operators. It is shown that this quantum computational logic is isomorphic to the basic sequential effect algebra [0, 1].     

A Quantum Protocol for Millionaire Problem with Continuous Variables

In this paper, a protocol for quantum millionaire problem with continuous variables is proposed. In the protocol, two participants can compare the values of their fortune with the assistance of a semi-trusted third party （STTP）. Only EPR states are exploited in our protocol while most other protocols exploited d-dimensional Bell states. Two participants are just required to perform single particle operations, which makes our protocol more efficiently. Our protocol can ensure fairness, correctness, security and high efficiency as well. In our protocol, only the two participants can deduce the results of comparisons, others include STTP will learn no information. Our protocol can resist various kinds of attacks from both the outside eavesdroppers and the inside participants, even the STTP.     

量子计算与量子模拟

量子计算和量子模拟在过去的几年里发展迅速,今后涉及多量子比特的量子计算和量子模拟将是一个发展的重点.本文回顾了该领域的主要进展,包括量子多体模拟、量子计算、量子计算模拟器、量子计算云平台、量子软件等内容,其中量子多体模拟又涵盖量子多体动力学、时间晶体及多体局域化、量子统计和量子化学等的模拟.这些研究方向的回顾是基于对现阶段量子计算和量子模拟研究特点的考虑,即量子比特数处于中等规模而量子操控精度还不具有大规模逻辑门实现的能力,研究处于基础科研和实用化的过渡阶段,因此综述的内容主要还是希望管窥今后的发展.     

Unstructured Adiabatic Quantum Search

In the adiabatic quantum computation model, a computational procedure is described by the continuous time evolution of a time dependent Hamiltonian. We apply this method to the Grover's problem, i.e., searching a marked item in an unstructured database. Classically, the problem can be solved only in a running time of order O(N) (where N is the number of items in the database), whereas in the quantum model a speed up of order has been obtained. We show that in the adiabatic quantum model, by a suitable choice of the time-dependent Hamiltonian, it is possible to do the calculation in constant time, independent of the the number of items in the database. However, in this case the initial time-complexity of is replaced by the complexity of implementing the driving Hamiltonian.     

Quantum demonstration of a bio-molecular solution of the satisfiability problem on spin-based ensemble

DNA computation (DNAC) has been proposed to solve the satisfiability (SAT) problem due to operations in parallel on extremely large numbers of strands. This paper attempts to treat the DNA-based bio-molecular solution for the SAT problem from the quantum mechanical perspective with a purpose to explore the relationship between DNAC and quantum computation (QC). To achieve this goal, it first builds up the correspondence of operations between QC and DNAC. Then it gives an example for the case of two variables and three clauses for details of this theory. It also demonstrates a three-qubit experiment for solving the simplest SAT problem with a single variable on a liquid-state nuclear magnetic resonance ensemble to verify this theory. Some discussions are made for the potential application and for further exploration of the present work.     

Maximum Speed of Quantum Evolution

In this paper, we discuss the question of the minimum time needed for any state of a given quantum system to evolve into a distinct (orthogonal) state. This problem is relevant to deriving physical limits in quantum computation and quantum information processing. Here, we consider both cases of nonadiabatic and adiabatic evolution and we derive the Hamiltonians corresponding to the minimum time evolution predicted by the Margolus–Levitin theorem.     

Measurement-Based Interference in Quantum Computation

The interference has been measured by the visibility in two-level systems,which,however,does not work for multi-level systems.We generalize a measure of the interference based on decoherence process,consistent with the visibility in qubit systems.By taking cluster states as examples,we show in the one-way quantum computation that the gate fidelity is proportional to the interference of the measured qubit and is inversely proportional to the interference of all register qubits.We also find that the interference increases with the number of the computing steps.So we conjecture that the interference may be the source of the speedup of the one-way quantum computation.     

Quantum Density Peak Clustering Algorithm

A widely used clustering algorithm, density peak clustering (DPC), assigns different attribute values to data points through the distance between data points, and then determines the number and range of clustering by attribute values. However, DPC is inefficient when dealing with scenes with a large amount of data, and the range of parameters is not easy to determine. To fix these problems, we propose a quantum DPC (QDPC) algorithm based on a quantum DistCalc circuit and a Grover circuit. The time complexity is reduced to O(log(N2)+6N+N), whereas that of the traditional algorithm is O(N2). The space complexity is also decreased from O(N·⌈logN⌉) to O(⌈logN⌉).     

Measurement-Based Interference in Quantum Computation

The interference has been measured by the visibility in two-level systems, which, however, does not work for multi-level systems. We generalize a measure of the interference based on decoherence process, consistent with the visibility in qubit systems. By taking cluster states as examples, we show in the one-way quantum computation that the gate fidelity is proportional to the interference of the measured qubit and is inversely proportional to the interference of all register qubits. We also find that the interference increases with the number of the computing steps. So we conjecture that the interference may be the source of the speedup of the one-way quantum computation.     

Efficient State Preparation via Ion Trap Quantum Computing and Quantum Searching Algorithm

We present a scheme to-prepare a quantum state in an ion trap with probability approaching to one by means of ion trap quantum computing and Grover's quantum search algorithm acting on trapped ions.     

Quantum computation with Turaev-Viro codes

For a 3-manifold with triangulated boundary, the Turaev-Viro topological invariant can be interpreted as a quantum error-correcting code. The code has local stabilizers, identified by Levin and Wen, on a qudit lattice. Kitaev’s toric code arises as a special case. The toric code corresponds to an abelian anyon model, and therefore requires out-of-code operations to obtain universal quantum computation. In contrast, for many categories, such as the Fibonacci category, the Turaev-Viro code realizes a non-abelian anyon model. A universal set of fault-tolerant operations can be implemented by deforming the code with local gates, in order to implement anyon braiding. We identify the anyons in the code space, and present schemes for initialization, computation and measurement. This provides a family of constructions for fault-tolerant quantum computation that are closely related to topological quantum computation, but for which the fault tolerance is implemented in software rather than coming from a physical medium.     

Quantum computation and simulation with superconducting qubits

Superconducting circuits based on Josephson junctions are regarded as one of the most promising technologies for the implementation of scalable quantum computers. This review presents the basic principles of superconducting qubits and shows the progress of quantum computing and quantum simulation based on superconducting qubits in recent years.The experimental realization of gate operations, readout, error correction codes, as well as some quantum algorithms are summarized, followed by an introduction of quantum simulation. And then some important applications in fields including condensed matter physics, quantum annealing, and quantum chemistry are discussed.     

基于超导量子器件的量子计算

超导量子器件能够展现宏观量子相干性.基于超导量子器件的量子计算是量子信息领域中的一个重要研究方向,同时,超导量子器件物理特性的研究也是目前凝聚态物理和量子光学领域的交叉前沿课题.文章简述了近年来在超导量子计算方面的一些重要结果和进展,并讨论了其研究现状和发展趋势.     

Robust Quantum Search with Uncertain Number of Target States

The quantum search algorithm is one of the milestones of quantum algorithms. Compared with classical algorithms, it shows quadratic speed-up when searching marked states in an unsorted database. However, the success rates of quantum search algorithms are sensitive to the number of marked states. In this paper, we study the relation between the success rate and the number of iterations in a quantum search algorithm of given λ=M/N, where M is the number of marked state and N is the number of items in the dataset. We develop a robust quantum search algorithm based on Grover–Long algorithm with some uncertainty in the number of marked states. The proposed algorithm has the same query complexity ON as the Grover’s algorithm, and shows high tolerance of the uncertainty in the ratio M/N. In particular, for a database with an uncertainty in the ratio M±MN, our algorithm will find the target states with a success rate no less than 96%.     

Quantum Computational Semantics on Fock Space

In the Fock space semantics, meanings of sentences are identified with density operators of the (unsymmetrized) Fock space based on the Hilbert space ℂ². Generally, the meaning of a sentence is smeared over different sectors of . The standard quantum computational semantics is a limit case of the Fock space semantics, where the meaning of any sentence α only “lives” in one sector of , which is determined by the logical complexity of α. We prove that the global Fock space semantics and the standard quantum computational semantics characterize the same logic. PACS: 03.67.Lx.