Effective fault-tolerant quantum computation with slow measurements

How important is fast measurement for fault-tolerant quantum computation? Using a combination of existing and new ideas, we argue that measurement times as long as even 1000 gate times or more have a very minimal effect on the quantum accuracy threshold. This shows that slow measurement, which appears to be unavoidable in many implementations of quantum computing, poses no essential obstacle to scalability.     

Single-spin measurements for quantum computation using magnetic resonance force microscopy

The quantum theory of a single-spin measurement using magnetic resonance force microscopy is presented. We use an oscillating cantilever-driven adiabatic reversal technique. The frequency shift of the cantilever vibrations is estimated. We show that the frequency shift causes the formation of a Schrödinger cat state for the cantilever. The interaction between the cantilever and the environment quickly destroys the coherence between the two cantilever trajectories. It is shown that using partial adiabatic reversals one can obtain a significant increase in the frequency shift. We discuss the possibility of sub-magneton spin density detection in molecules using magnetic resonance force microscopy.     

Dynamical localization effect in a coupled quantum dot array driven by an AC magnetic field

We have studied the transport properties of a ring-coupled quantum dot array driven by an AC magnetic field, which is connected to two leads, and we give the response of the transport current to the dynamical localization. We found that when the ratio of the magnetic flux to the total quantum dots number is a root of the zeroth order Bessel function, dynamical localization and collapse of quasi-energy occurs and importantly, the transport current displays a dip which is the signal of dynamical localization. The dynamical localization effect is strengthened as a result of the increase of the quantum dot number, and it is weakened on account of the increase of the dots-lead hopping rate.     

Knill-laflamme-milburn linear optics quantum computation as a measurement-based computation

We show that the Knill Lafllame Milburn method of quantum computation with linear optics gates can be interpreted as a one-way, measurement-based quantum computation of the type introduced by Briegel and Raussendorf. We also show that the permanent state of n n-dimensional systems is a universal state for quantum computation.     

Dynamical localization and eigenstate localization in trap models

The one-dimensional random trap model with a power-law distribution of mean sojourn times exhibits a phenomenon of dynamical localization in the case where diffusion is anomalous: the probability to find two independent walkers at the same site, as given by the participation ratio, stays constant and high in a broad domain of intermediate times. This phenomenon is absent in dimensions two and higher. In finite lattices of all dimensions the participation ratio finally equilibrates to a different final value. We numerically investigate two-particle properties in a random trap model in one and in three dimensions, using a method based on spectral decomposition of the transition rate matrix. The method delivers a very effective computational scheme producing numerically exact results for the averages over thermal histories and initial conditions in a given landscape realization. Only a single averaging procedure over disorder realizations is necessary. The behavior of the participation ratio is compared to other measures of localization, as for example to the states’ gyration radius, according to which the dynamically localized states are extended. This means that although the particles are found at the same site with a high probability, the typical distance between them grows. Moreover the final equilibrium state is extended both with respect to its gyration radius and to its Lyapunov exponent. In addition, we show that the phenomenon of dynamical localization is only marginally connected with the spectrum of the transition rate matrix, and is dominated by the properties of its eigenfunctions which differ significantly in dimensions one and three.     

Multibosons in quantum computation

The role of the three-boson algebra in the theoretical construction of both logical states and operators for quantum computing is investigated. The computational basis consists of three orthonormal codewords obtained from the coherent states of the algebra. The gate and phase operators acting on the codewords are found, and the relation between their matrix representations in the Fock space and the fundamental representation of su(3) is discussed.     

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.     

Resilient quantum computation in correlated environments: a quantum phase transition perspective

We analyze the problem of a quantum computer in a correlated environment protected from decoherence by quantum error correction using a perturbative renormalization group approach. The scaling equation obtained reflects the competition between the dimension of the computer and the scaling dimension of the correlations. For an irrelevant flow, the error probability is reduced to a stochastic form for a long time and/or a large number of qubits; thus, the traditional derivation of the threshold theorem holds for these error models. In this way, the "threshold theorem" of quantum computing is rephrased as a dimensional criterion.     

Low-temperature environments for quantum computation and quantum simulation

This review summarizes the requirement of low temperature conditions in existing experimental approaches to quantum computation and quantum simulation.     

约瑟夫森器件中的宏观量子现象及超导量子计算

超导体中的电子结成库珀对，凝聚到可以用一个宏观波函数来描绘的能量基态，该波函数的位相是代表了成百万库珀对集体运动的宏观变量．以约瑟夫森结为基础元件的超导约瑟夫森器件，使人们能够控制并测量一个超导体的位相和库珀对数目，因此是研究宏观量子现象的理想系统．文章回顾了约瑟夫森器件中的宏观量子现象研究的发展历程，介绍了当前超导约瑟夫森器件在量子计算中的重要应用，并对它们的未来作了简要的展望．     

Quantum entanglement formation by repeated spin blockade measurements in a spin field-effect transistor structure embedded with quantum dots

We propose a method of operating a quantum state machine made of stacked quantum dots buried in adjacent to the channel of a spin field-effect transistor (FET) [S. Datta, B. Das, Appl. Phys. Lett. 56 (1990) 665; K. Yoh, et al., Proceedings of the 23rd International Conference on Physics of Semiconductors (ICPS) 2004; H. Ohno, K. Yoh et al., Jpn. J. Appl. Phys. 42 (2003) L87; K. Yoh, J. Konda, S. Shiina, N. Nishiguchi, Jpn. J. Appl. Phys. 36 (1997) 4134]. In this method, a spin blockade measurement extracts the quantum state of a nearest quantum dot through Coulomb blockade [K. Yoh, J. Konda, S. Shiina, N. Nishiguchi, Jpn. J. Appl. Phys. 36 (1997) 4134; K. Yoh, H. Kazama, Physica E 7 (2000) 440] of the adjacent channel conductance. Repeated quantum Zeno-like (QZ) measurements [H. Nakazato, et al., Phys. Rev. Lett. 90 (2003) 060401] of the spin blockade is shown to purify the quantum dot states within several repetitions. The growth constraints of the stacked InAs quantum dots are shown to provide an exchange interaction energy in the range of 0.01–1 meV [S. Itoh, et al., Jpn. J. Appl. Phys. 38 (1999) L917; A. Tackeuchi, et al., Jpn. J. Appl. Phys. 42 (2003) 4278]. We have verified that one can reach the fidelity of 90% by repeating the measurement twice, and that of 99.9% by repeating only eleven QZ measurements. Entangled states with two and three vertically stacked dots are achieved with the sampling frequency of the order of 100 MHz.     

Dynamical initial conditions in quantum cosmology

Loop quantum cosmology is shown to provide both the dynamical law and initial conditions for the wave function of a universe by one discrete evolution equation. Accompanied by the condition that semiclassical behavior is obtained at large volume, a unique wave function is predicted.     

Unstable systems and repeated measurements

In this part of the paper we treat two examples. In the first one the chamber structure is assumed only to be periodic andP(t) is an exponential. In the second example no specific assumption is made about the primary decay law and the measuring device is structured as an idealized spark chamber. This example contains results ofBeskow andNilsson as a special case.We follow the program formulated in the first part of this paper (referred hereafter as [I]). In the introduction of [I] we mentioned three examples; here we give two of them.     

Quantum algorithms in one-way quantum computation

Cluster states are the fundamental resource for the one-way model of quantum computation. In this paper we show the realization of a two-photon four-qubit cluster state. The qubits are encoded in the polarization and the linear momentum of the particles. By using this state we realized two important quantum algorithms, namely the Grover’s search and the Deutsch’s algorithm.     

Pseudospin quantum computation in semiconductor nanostructures

We theoretically show that spontaneously interlayer-coherent bilayer quantum Hall droplets should allow robust and fault-tolerant pseudospin quantum computation in semiconductor nanostructures with voltage-tuned external gates providing qubit control and a quantum Ising Hamiltonian providing qubit entanglement. Using a spin-boson model, we estimate decoherence to be small (approximately 10(-5)).