Secure Multi-Party Quantum Computation Based on Blind Quantum Computation

International Journal of Theoretical Physics - Blind quantum computation (BQC) allows quantum-limited clients to delegate their quantum-computing tasks to a remote quantum server while keep their...     

Quantum Computation Toward Quantum Gravity

The aim of this paper is to enlighten the emerging relevance of Quantum Information Theory in the field of Quantum Gravity. As it was suggested by J. A. Wheeler, information theory must play a relevant role in understanding the foundations of Quantum Mechanics (the "It from bit" proposal). Here we suggest that quantum information must play a relevant role in Quantum Gravity (the "It from qubit" proposal). The conjecture is that Quantum Gravity, the theory which will reconcile Quantum Mechanics with General Relativity, can be formulated in terms of quantum bits of information (qubits) stored in space at the Planck scale. This conjecture is based on the following arguments: a) The holographic principle, b) The loop quantum gravity approach and spin networks, c) Quantum geometry and black hole entropy. From the above arguments, as they stand in the literature, it follows that the edges of spin networks pierce the black hole horizon and excite curvature degrees of freedom on the surface. These excitations are micro-states of Chern-Simons theory and account of the black hole entropy which turns out to be a quarter of the area of the horizon, (in units of Planck area), in accordance with the holographic principle. Moreover, the states which dominate the counting correspond to punctures of spin j = 1/2 and one can in fact visualize each micro-state as a bit of information. The obvious generalization of this result is to consider open spin networks with edges labeled by the spin –1/ 2 representation of SU(2) in a superposed state of spin "on" and spin "down." The micro-state corresponding to such a puncture will be a pixel of area which is "on" and "off" at the same time, and it will encode a qubit of information. This picture, when applied to quantum cosmology, describes an early inflationary universe which is a discrete version of the de Sitter universe.     

Quantum Nondeterministic Computation

We investigate the possible contribution of quantum measurement in yieldingthe quantum computation speedup appearing in a modified version of Simon'salgorithm.     

Quantum Interference Computation

Quantum speed-up has been conjectured but not proven for a general computation. Quantum interference computation (QUIC) provides a general speed-up. It is a form of ground-mode computation that reinforces the ground mode in a beam of mostly non-ground modes by quantum superposition. It solves the general Boolean problem in the square root of the number of operations that a classical computer would need for the same problem. For example a typical 80-bit problem would take about 10²⁴ cycles (10⁷ years at 1 GHz) of classical computation and about 10¹² cycles (20 minutes at 1 GHz) of QUIC.     

Fermionic Quantum Computation

We define a model of quantum computation with local fermionic modes (LFMs)—sites which can be either empty or occupied by a fermion. With the standard correspondence between the Foch space of m LFMs and the Hilbert space of m qubits, simulation of one fermionic gate takes O(m) qubit gates and vice versa. We show that using different encodings, the simulation cost can be reduced to O(log m) and a constant, respectively. Nearest neighbors fermionic gates on a graph of bounded degree can be simulated at a constant cost. A universal set of fermionic gates is found. We also study computation with Majorana fermions which are basically halves of LFMs. Some connection to qubit quantum codes is made.     

Blind Quantum Signature with Blind Quantum Computation

Blind quantum computation allows a client without quantum abilities to interact with a quantum server to perform a unconditional secure computing protocol, while protecting client’s privacy. Motivated by confidentiality of blind quantum computation, a blind quantum signature scheme is designed with laconic structure. Different from the traditional signature schemes, the signing and verifying operations are performed through measurement-based quantum computation. Inputs of blind quantum computation are securely controlled with multi-qubit entangled states. The unique signature of the transmitted message is generated by the signer without leaking information in imperfect channels. Whereas, the receiver can verify the validity of the signature using the quantum matching algorithm. The security is guaranteed by entanglement of quantum system for blind quantum computation. It provides a potential practical application for e-commerce in the cloud computing and first-generation quantum computation.     

Arbitrated Quantum Signature with Hamiltonian Algorithm Based on Blind Quantum Computation

A novel arbitrated quantum signature (AQS) scheme is proposed motivated by the Hamiltonian algorithm (HA) and blind quantum computation (BQC). The generation and verification of signature algorithm is designed based on HA, which enables the scheme to rely less on computational complexity. It is unnecessary to recover original messages when verifying signatures since the blind quantum computation is applied, which can improve the simplicity and operability of our scheme. It is proved that the scheme can be deployed securely, and the extended AQS has some extensive applications in E-payment system, E-government, E-business, etc.     

Quantum Computation with Nonlinear Optics

We propose a scheme of quantum computation with nonlinear quantum optics. Polarization states of photons are used for qubits. Photons with different frequencies represent different qubits. Single qubit rotation operation is implemented through optical elements like the Faraday polarization rotator. Photons are separated into different optical paths, or merged into a single optical path using dichromatic mirrors. The controlled-NOT gate between two qubits is implemented by the proper combination of parametric up and down conversions. This scheme has the following features： （1） No auxiliary qubits are required in the controlled-NOT gate operation; （2） No measurement is required in the course of the computation; （3） It is resource efficient and conceptually simple.     

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 Computation of Fuzzy Numbers

We study the possibility of performing fuzzy set operations on a quantum computer. After giving a brief overview of the necessary quantum computational and fuzzy set theoretical concepts we demonstrate how to encode the membership function of a digitized fuzzy number in the state space of a quantum register by using a suitable superposition of tensor product states that form a computational basis. We show that a standard quantum adder is capable to perform Kaufmann's addition of fuzzy numbers in the course of only one run by acting at once on all states in the superposition, which leads to a considerable gain in the number of required operations with respect to performing such addition on a classical computer.     

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.     

Interferometric Computation Beyond Quantum Theory

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 suitable candidate, whereas box-world does not. We also find that a classical hidden variable model first presented by Spekkens (Phys Rev A 75(3): 32100, 2007) can also be used for this type of computation due to the epistemic restriction placed on the hidden variable.     

Observable-Geometric Phases and Quantum Computation

This paper presents an alternative approach to geometric phases from the observable point of view. Precisely, we introduce the notion of observable-geometric phases, which is defined as a sequence of phases associated with a complete set of eigenstates of the observable. The observable-geometric phases are shown to be connected with the quantum geometry of the observable space evolving according to the Heisenberg equation. They are indeed distinct from Berry’s phase (Berry Proc. R. Soc. London Series A 392:45–57, 1984; Simon Phys. Rev. Lett. 51:2167–2170, 1983) as the system evolves adiabatically. It is shown that the observable-geometric phases can be used to realize a universal set of quantum gates in quantum computation. This scheme leads to the same gates as the Abelian geometric gates of Zhu and Wang (Phys. Rev. Lett. 89: 097902: 1–4, 2002, Phys. Rev. A 67: 022319: 1–9, 2003), but based on the quantum geometry of the observable space beyond the state space.

     

Numerical Computation of Quantum Capacity

Quantum capacity is an important tool to analysethe performance of information transmission for quantumchannels. In this paper, the quantum capacities of theattenuation channel for PSK and OOK arediscussed.     

量子环上粒子体系的计算

对于量子环上带电粒子体系,组成本征函数的基矢数及哈密顿矩阵元素数都极大,数值计算量庞大.本文介绍在处理此问题时按轨道总角动量分类从基矢集中选择子基矢集的方法和技巧.应用计算机进行数值计算时,此方法比以往节省90%以上的时间.     

中国科学院物理研究所固态量子信息与计算实验室

以场效应晶体管为代表的传统电子技术已经把人类社会带入了信息时代。但是,随着全球信息化的不断发展,传统信息技术在运算能力、存储量和安全性等多个方面固有的发展瓶颈正逐步显现出来。