quantuminformation science explores ways in which quantum physical laws can be harnessed to control the acquisition, transmission, protection, and processing of information. This field has seen explosive growth in th...
quantuminformation science explores ways in which quantum physical laws can be harnessed to control the acquisition, transmission, protection, and processing of information. This field has seen explosive growth in the past several years from progress on both theoretical and experimental fronts. Essential to this endeavor are methods for controlling quantuminformation. In this thesis, I present three new approaches for controlling quantuminformation. First, I present a new protocol for continuously protecting unknown quantum states from noise. This protocol combines and expands ideas from the theories of quantum error correction and quantum feedback control. The result can outperform either approach by itself. I generalize this protocol to all known quantum stabilizer codes, and study its application to the three-qubit repetition code in detail via Monte Carlo simulations. Next, I present several new protocols for controlling quantuminformation that are fault-tolerant. These protocols require only local quantumprocessing due to the topological properties of the quantum error correcting codes upon which they are built. I show that each protocol's fault-dependence behavior exhibits an order-disorder phase transition when mapped onto an associated statistical-mechanical model. I review the critical error rates of these protocols found by numerical study of the associated models, and I present new analytic bounds for them using a self-avoiding random walk argument. Moreover, I discuss fault-tolerant procedures for encoding, error-correction, computing, and decoding quantuminformation using these protocols, and calculate the accuracy threshold of fault-tolerant quantum memory for protocols using them. I end by presenting a new class of quantumalgorithms that solve combinatorial optimization problems solely by measurement. I compute the running times of these algorithms by establishing an explicit dynamical model for the measurement process. This model, the digitize
In this thesis we first give an introduction to the basic aspects of quantum computation followed by an analysis of networks of quantum logic gates where the qubit lines are loops (cyclic). Thus far, investigations in...
In this thesis we first give an introduction to the basic aspects of quantum computation followed by an analysis of networks of quantum logic gates where the qubit lines are loops (cyclic). Thus far, investigations into cyclic networks of quantum logic gates have not been examined (as far as we know) by the quantuminformation community. In our investigations of cyclic quantum networks we have studied simple, one and two qubit systems. The analysis includes: classifying networks into groups, the dynamics of the qubits in a cyclic quantum network, and the perturbation effects of an external qubit acting on a cyclic quantum network. The analysis will be followed by a discussion on quantumalgorithms and quantuminformationprocessing with cyclic quantum networks, a novel implementation of a cyclic network quantum memory and a discussion of quantum sensors via cyclic quantum networks.
We propose a device that meets the physical and quantum mechanical conditions required for the operation of interacting quantum bits. Metal rings embedded in a solid state substrate by means of silicon processing tech...
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ISBN:
(纸本)8890084782
We propose a device that meets the physical and quantum mechanical conditions required for the operation of interacting quantum bits. Metal rings embedded in a solid state substrate by means of silicon processing technology are considered as the basic computing elements. We investigate different set-ups and concepts that are compatible with the topology of the metallic rings. Accessing the rings for in- and output signals as well as achieving the exchange and quantization of information are two essential requirements for a proper operation of an array of communicating quantum bits. In particular, the superposition of the quantum states characterizing the quantum bit array is primordial in order to run quantum computing algorithms. Furthermore, decoherence must be dealt with in a controllable fashion in order to read out the signals before they loose the signature of the quantuminformation. This work reports on the processing and testing of two device configurations.
quantum computation has experienced a steady growth in interest in recent years. With the rapid development of quantum technologies, the quantum mechanical nature of physical systems is becoming an increasingly import...
quantum computation has experienced a steady growth in interest in recent years. With the rapid development of quantum technologies, the quantum mechanical nature of physical systems is becoming an increasingly important part of future industrial technology. The Rydberg atom is one of the best test tubes in which to attempt programmable coherent control because of our in-depth understanding of both atomic physics and ultrafast optics. We demonstrate the use of Rydberg atoms for processingquantuminformation and implementing quantumalgorithms. We adopted N Rydberg energy levels of Cesium atom to store information. The phases of the energy states were each programmed and coherently evolve in time with the encoded information. A coherent manipulation then transferred the information contained in the phases to state amplitudes. The programming and the converting of the information in the data register were both performed by ultrafast optical pulses. We implemented an N-state Rydberg atom data register, with N = 6 and 8. Using half-cycle pulses (HCP), we devised methods which perform unitary operations on this data register. Application of the HCP, or terahertz short pulse, to wave packets prepared with one energy state phase-reversed with respect to the others yields a much simpler wave packet. This interaction forced multi-mode interference which constructively interfered only for the phase-flipped state. An impulsive model calculation as well as direct integration of the time-dependent Schrödinger equation showed good agreement with the experimental data. Related to the quantumalgorithms, the pseudo-unitary operation implemented by the HCP had a similar structural form to the Grover's inversion-about-average operation. For the same reasons that lead to the Grover's quantum state amplification, the state amplitude of the energy state whose phase was reversed robbed atomic population from all other states. Our implementation of the Grover's inversion-about-average op
We have studied the extension of the new field of quantum computing to the multilevel domain, where the information is stored in a coherent superposition of more than two levels. Interference and entanglement, the hal...
We have studied the extension of the new field of quantum computing to the multilevel domain, where the information is stored in a coherent superposition of more than two levels. Interference and entanglement, the hallmarks of quantum mechanics, are more strikingly present in a multilevel system, in the form of wave packets and decoherence. This thesis explores new tools and applications for multilevel quantuminformationprocessing in Rydberg atoms. The quantum equivalent of a classical bit is a qubit, a two-level system. quantum computational logic involves conditional unitary transforms on two qubits, which are the quantum analogs of logic gates in classical computer science. The multilevel extension of a qubit is a qudit, a d-level quantum system. We present several programs for universal quantum logic involving qudits, and physically motivate the formalism with examples from quantum control. Wave packets arise from multilevel quantum interference, and they give an interesting new perspective on quantuminformation stored in a multilevel system. We show that an alternative realization of a qudit in a quantum system is a set of d wave-packet states that are physically separated in time. The wave-packet basis is connected to the energy-level basis by a Fourier transform, a key ingredient of quantumalgorithms. We apply these ideas to Rydberg atoms, and show that an appropriate coupling between such atoms enables a conceptually simpler implementation of the quantum version of the Fast Fourier transform algorithm. Lastly we explore atomic angular momentum as a computational observable. Most of the states in the hydrogen atom are degenerate in energy but differ by discrete units of angular momentum. We show that using Laguerre-Gaussian laser modes, which possess orbital field angular momentum, these internal angular-momentum states in the atom can be entangled with its quantized center-of-mass angular momentum. We propose this entanglement as the building block for m
作者：
Jumpei NiwaKeiji MatsumotoHiroshi ImaiDepartment of Computer Science
Graduate School of Information Science and Technology The University of Tokyo 7-3-1 Hongo Bunkyo-ku Tokyo 113-0033 Japan ERATO
Project Quantum Computation and Information JST Daini Hongo White Building 201 5-28-3 Hongo Bunkyo-ku Tokyo Japan
With current technologies, it seems to be very difficult to implement quantum computers with many qubits. It is therefore of importance to simulate quantumalgorithms and circuits on the existing computers. However, f...
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With current technologies, it seems to be very difficult to implement quantum computers with many qubits. It is therefore of importance to simulate quantumalgorithms and circuits on the existing computers. However, for a large-size problem, the simulation often requires more computational power than is available from sequential processing. Therefore, simulation methods for parallel processors are required. We have developed a general-purpose simulator for quantumalgorithms/circuits on the parallel computer (Sun Enterprise4500). It can simulate algorithms/circuits with up to 30 qubits. In order to test efficiency of our proposed methods, we have simulated Shor’s factorization algorithm and Grover’s database search, and we have analyzed robustness of the corresponding quantum circuits in the presence of both decoherence and operational errors. The corresponding results, statistics, and analyses are presented in this paper.
quantum computing operates in three stages: (i) preparation of the initial states of the n qubits of a register, (ii) step by step transformation of the state of this register by unitary operators which compose the qu...
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ISBN:
(纸本)0780375386
quantum computing operates in three stages: (i) preparation of the initial states of the n qubits of a register, (ii) step by step transformation of the state of this register by unitary operators which compose the quantum program, and (iii), measurement of all or some of the qubits of the register. The existence of quantumalgorithms which are exponentially less complex than their classical counterparts for sonic classes of problems, stems from entangled states established by multi-qubit unitary operators within the quantum program. A register of it qubits is a quantum system composed of n quantum subsystems. The state \psi> of a quantum system composed of two quantum subsystems A and B is said to be entangled when \Psi> is not reducible to a pair composed of a state \Psi(A)> of A and a state \Psi(B)> of B: such situations have no counterpart in the classical world. In quantum theory, such a pair of states is denoted by a tensor product: \Psi> is entangled if it cannot be factorized into the tensor product \Psi(A)>circle times\Psi(B)>. This paper establishes conditions according to which it is possible to tell whether or not the state of a register of it qubits is entangled. The state of a single qubit is a vector a alpha\0> + beta\1> of unit norm in a 2-dimensional vector space, where \0> and \1> are the two basis states and where alpha and beta are complex amplitudes. Then, if both A and B are qubits, the most general form of the state of a register composed of the 2 qubits A and B is also a vector of unit norm, but now in a 4-dimensional space: \Psi>=alpha\00>+beta\01>+gamma\10>+delta\11>. It is straightforward to prove that \Psi>) can be factorized into \Psi(A)>circle times\Psi(B)> if and only if alphadelta=betagamma. In such a case, \Psi>is said to be separable, i.e. not entangled. This paper generalizes this form of condition to registers of it qubits. If \Psi> is the state of a register of n qubits, two different questions about the separability of \Psi>,) a
Time-frequency distributions (TFDs) of Cohen's class often dramatically reveal complex structures that are not evident in the raw signal. Standard linear filters are often not able to separate the underlying signa...
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ISBN:
(纸本)0819445584
Time-frequency distributions (TFDs) of Cohen's class often dramatically reveal complex structures that are not evident in the raw signal. Standard linear filters are often not able to separate the underlying signal from background clutter and noise. The essense of the signal can often be extracted from the TFD by evaluating strategic slices through the TFD for a series of frequencies. However, TFDs are often computationally intense compared to other methods. This paper demonstrates that quadratic filters may be designed to capture the same information as is available in the specific slices through the TFD at a considerably lower computational cost. The outputs of these filters can be combined to provide a robust impulse-like response to the chosen signal. This is particularly useful when the exact time series representation of the signal is unknown, due to variations and background clutter and noise. It is also noted that Teager's method is closely related to TFDs and are an example of a quadratic filter. Results using an ideal matched filter and the TFD motivated quadratic filter are compared to give insight into their relative responses.
In this paper we present the computational model underlying the one-way quantum computer which we introduced recently [Phys. Rev. Lett. 86, 5188 (2001)]. The one-way quantum computer has the property that any quantum ...
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In this paper we present the computational model underlying the one-way quantum computer which we introduced recently [Phys. Rev. Lett. 86, 5188 (2001)]. The one-way quantum computer has the property that any quantum logic network can be simulated on it. Conversely, not all ways of quantuminformationprocessing that are possible with the one-way quantum computer can be understood properly in network model terms. We show that the logical depth is, for certain algorithms, lower than has so far been known for networks. For example, every quantum circuit in the Clifford group can be performed on the one-way quantum computer in a single step.
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