Showing papers on "Quantum error correction published in 2003"
TL;DR: A two-dimensional quantum system with anyonic excitations can be considered as a quantum computer Unitary transformations can be performed by moving the excitations around each other Unitary transformation can be done by joining excitations in pairs and observing the result of fusion.
4,920 citations
TL;DR: This work gives 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, and proves its universality.
Abstract: 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.
1,370 citations
TL;DR: In this article, the authors proposed an experiment for creating quantum superposition states involving of the order of 10(14) atoms via the interaction of a single photon with a tiny mirror.
Abstract: We propose an experiment for creating quantum superposition states involving of the order of 10(14) atoms via the interaction of a single photon with a tiny mirror. This mirror, mounted on a high-quality mechanical oscillator, is part of a high-finesse optical cavity which forms one arm of a Michelson interferometer. By observing the interference of the photon only, one can study the creation and decoherence of superpositions involving the mirror. A detailed analysis of the requirements shows that the experiment is within reach using a combination of state-of-the-art technologies.
825 citations
TL;DR: This work implements a CNOT quantum gate according to the Cirac–Zoller proposal, which relies on recently developed precise control of atomic phases and the application of composite pulse sequences adapted from nuclear magnetic resonance techniques.
Abstract: Quantum computers have the potential to perform certain computational tasks more efficiently than their classical counterparts. The Cirac–Zoller proposal1 for a scalable quantum computer is based on a string of trapped ions whose electronic states represent the quantum bits of information (or qubits). In this scheme, quantum logical gates involving any subset of ions are realized by coupling the ions through their collective quantized motion. The main experimental step towards realizing the scheme is to implement the controlled-NOT (CNOT) gate operation between two individual ions. The CNOT quantum logical gate corresponds to the XOR gate operation of classical logic that flips the state of a target bit conditioned on the state of a control bit. Here we implement a CNOT quantum gate according to the Cirac–Zoller proposal1. In our experiment, two 40Ca+ ions are held in a linear Paul trap and are individually addressed using focused laser beams2; the qubits3 are represented by superpositions of two long-lived electronic states. Our work relies on recently developed precise control of atomic phases4 and the application of composite pulse sequences adapted from nuclear magnetic resonance techniques5,6.
824 citations
TL;DR: In this article, an unambiguous experimental demonstration and comprehensive characterization of quantum controlled-NOT operation in an optical system was presented. But the experimental results were limited to a single operation condition of the gate.
Abstract: The promise of tremendous computational power, coupled with the development of robust error-correcting schemes, has fuelled extensive efforts to build a quantum computer. The requirements for realizing such a device are confounding: scalable quantum bits (two-level quantum systems, or qubits) that can be well isolated from the environment, but also initialized, measured and made to undergo controllable interactions to implement a universal set of quantum logic gates. The usual set consists of single qubit rotations and a controlled-NOT (CNOT) gate, which flips the state of a target qubit conditional on the control qubit being in the state 1. Here we report an unambiguous experimental demonstration and comprehensive characterization of quantum CNOT operation in an optical system. We produce all four entangled Bell states as a function of only the input qubits' logical values, for a single operating condition of the gate. The gate is probabilistic (the qubits are destroyed upon failure), but with the addition of linear optical quantum non-demolition measurements, it is equivalent to the CNOT gate required for scalable all-optical quantum computation.
804 citations
TL;DR: This work exploits techniques developed for nuclear magnetic resonance to implement the Deutsch–Jozsa algorithm on an ion-trap quantum processor, using as qubits the electronic and motional states of a single calcium ion.
Abstract: Determining classically whether a coin is fair (head on one side, tail on the other) or fake (heads or tails on both sides) requires an examination of each side. However, the analogous quantum procedure (the Deutsch-Jozsa algorithm) requires just one examination step. The Deutsch-Jozsa algorithm has been realized experimentally using bulk nuclear magnetic resonance techniques, employing nuclear spins as quantum bits (qubits). In contrast, the ion trap processor utilises motional and electronic quantum states of individual atoms as qubits, and in principle is easier to scale to many qubits. Experimental advances in the latter area include the realization of a two-qubit quantum gate, the entanglement of four ions, quantum state engineering and entanglement-enhanced phase estimation. Here we exploit techniques developed for nuclear magnetic resonance to implement the Deutsch-Jozsa algorithm on an ion-trap quantum processor, using as qubits the electronic and motional states of a single calcium ion. Our ion-based implementation of a full quantum algorithm serves to demonstrate experimental procedures with the quality and precision required for complex computations, confirming the potential of trapped ions for quantum computation.
474 citations
TL;DR: In this paper, the order rearrangement operation in both parties is controlled by a prior shared control key, which is used repeatedly in a quantum key distribution session, so that Eve cannot steal useful information.
Abstract: A technique is devised to perform orthogonal state quantum key distribution. In this scheme, entangled parts of a quantum information carrier are sent from Alice to Bob through two quantum channels. However, before the transmission, the order of the quantum information carrier in one channel is reordered so that Eve cannot steal useful information. At the receiver's end, the order of the quantum information carrier is restored. The order rearrangement operation in both parties is controlled by a prior shared control key which is used repeatedly in a quantum key distribution session.
452 citations
TL;DR: In these experiments, decoherence is overcome to the extent that the technique would achieve tolerable error rates for quantum repeaters in long-distance quantum communication and the requirement of high-accuracy logic operations in fault-tolerant quantum computation can be considerably relaxed.
Abstract: Distribution of entangled states between distant locations is essential for quantum communication1,2,3 over large distances. But owing to unavoidable decoherence in the quantum communication channel, the quality of entangled states generally decreases exponentially with the channel length. Entanglement purification4,5—a way to extract a subset of states of high entanglement and high purity from a large set of less entangled states—is thus needed to overcome decoherence. Besides its important application in quantum communication, entanglement purification also plays a crucial role in error correction for quantum computation, because it can significantly increase the quality of logic operations between different qubits6. Here we demonstrate entanglement purification for general mixed states of polarization-entangled photons using only linear optics7. Typically, one photon pair of fidelity 92% could be obtained from two pairs, each of fidelity 75%. In our experiments, decoherence is overcome to the extent that the technique would achieve tolerable error rates for quantum repeaters in long-distance quantum communication8. Our results also imply that the requirement of high-accuracy logic operations in fault-tolerant quantum computation can be considerably relaxed6.
414 citations
TL;DR: In this paper, the storage and retrieval of an image in a multi-particle quantum mechanical system was investigated and compared with corresponding classical digital methods, where qubits replaced classical bits in an array of pixels and showed several advantages.
Abstract: We investigate the storage and retrieval of an image in a multi-particle quantum mechanical system. Several models are studied and compared with corresponding classical digital methods. We consider a situation in which qubits replace classical bits in an array of pixels and show several advantages. For example, we consider the situation in which 4 different values are randomly stored in a single qubit and show that quantum mechanical properties allow better reproduction of original stored values compared with classical (even stochastic) methods. The retrieval process is uniquely quantum (involves measurement in more than one bases). The independence and the finiteness of the stored copies of the image play an important role in the quantum protocol being better than the classical one. Other advantages of quantum storage of an image are found in its security.
360 citations
TL;DR: In this article, the authors investigate the quantum dynamics of a Cooper-pair box with a superconducting loop in the presence of a nonclassical microwave field and demonstrate the existence of Rabi oscillations for both single and multiphoton processes.
Abstract: We investigate the quantum dynamics of a Cooper-pair box with a superconducting loop in the presence of a nonclassical microwave field. We demonstrate the existence of Rabi oscillations for both single- and multiphoton processes and, moreover, we propose a new quantum computing scheme (including one-bit and conditional two-bit gates) based on Josephson qubits coupled through microwaves.
347 citations
09 Jan 2003
TL;DR: In this paper, a detailed review of the theory of decoherence-free subspaces and subsystems focusing on their usefulness for preservation of quantum information is provided. But the authors do not consider the decoherent properties of the subsystems.
Abstract: Decoherence is the phenomenon of non-unitary dynamics that arises as a consequence of coupling between a system and its environment. It has important harmful implications for quantum information processing, and various solutions to the problem have been proposed. Here we provide a detailed a review of the theory of decoherence-free subspaces and subsystems, focusing on their usefulness for preservation of quantum information.
TL;DR: The eavesdropping scheme is presented, which reveals that the ping-pong protocol is not secure for transmission efficiencies lower than 60%, but can be hidden in the channel losses if one replaces the original lossy channel with a less lossy one.
Abstract: Security of the "ping-pong" quantum communication protocol recently proposed by Bostrom and Felbinger [Phys. Rev. Lett. 89, 187902 (2002)]] is analyzed in the case of considerable quantum channel losses. The eavesdropping scheme is presented, which reveals that the ping-pong protocol is not secure for transmission efficiencies lower than 60%. Our scheme induces 50% losses, which, however, can be hidden in the channel losses if one replaces the original lossy channel with a less lossy one. Finally, a possible improvement of the ping-pong protocol security is proposed.
TL;DR: In this paper, it was shown that any single-qubit real gate suffices, except those that do not preserve the computational basis, for universal quantum computation, except for Hadamard gates.
Abstract: What additional gates are needed for a set of classical universal gates to do universal quantum computation? We prove that any single-qubit real gate suffices, except those that preserve the computational basis. The Gottesman-Knill Theorem implies that any quantum circuit involving only the Controlled-NOT and Hadamard gates can be efficiently simulated by a classical circuit. In contrast, we prove that Controlled-NOT plus any single-qubit real gate that does not preserve the computational basis and is not Hadamard (or its like) are universal for quantum computing. Previously only a generic gate, namely a rotation by an angle incommensurate with π, is known to be sufficient in both problems, if only one single-qubit gate is added.
TL;DR: In this article, the authors consider whether quantum coherence in the form of mutual entanglement between a pair of qubits is susceptible to decay that may be more rapid than the decay of the coherence of either qubit individually.
Abstract: We consider whether quantum coherence in the form of mutual entanglement between a pair of qubits is susceptible to decay that may be more rapid than the decay of the coherence of either qubit individually. An instance of potential importance for solid-state quantum computing arises if embedded qubits (spins, quantum dots, Cooper pair boxes, etc.) are exposed to global and local noise at the same time. Here we allow separate phase-noisy channels to affect local and nonlocal measures of system coherence. We find that the time for decay of the qubit entanglement can be significantly shorter than the time for local dephasing of the individual qubits.
TL;DR: In this paper, a scalable design for silicon-germanium quantum-dot qubits is presented, which incorporates vertical and lateral tunneling, and simulations of a four-qubit array suggest that the design will enable single electron occupation of each dot of a many-dot array.
Abstract: Spins based in silicon provide one of the most promising architectures for quantum computing. A scalable design for silicon-germanium quantum-dot qubits is presented. The design incorporates vertical and lateral tunneling. Simulations of a four-qubit array suggest that the design will enable single electron occupation of each dot of a many-dot array. Performing two-qubit operations has negligible effect on other qubits in the array. Simulation results are used to translate error correction requirements into specifications for gate-voltage control electronics. This translation is a necessary link between error correction theory and device physics.
TL;DR: It is illustrated in detail that unconventional nontrivial two-qubit geometric gates with built-in fault-tolerant geometric features can be implemented in real physical systems.
Abstract: We propose a new class of unconventional geometric gates involving nonzero dynamic phases, and elucidate that geometric quantum computation can be implemented by using these gates. Comparing with the conventional geometric gate operation, in which the dynamic phase shift must be removed or avoided, the gates proposed here may be operated more simply. We illustrate in detail that unconventional nontrivial two-qubit geometric gates with built-in fault-tolerant geometric features can be implemented in real physical systems.
TL;DR: The high experimental accuracy achieved in the experiment implies that the requirement of tolerable error rate in multistage realization of quantum repeaters can be fulfilled, hence providing a useful toolbox for quantum communication over large distances.
Abstract: We report an experimental realization of entanglement concentration using two polarization-entangled photon pairs produced by pulsed parametric down-conversion In the meantime, our setup also provides a proof-in-principle demonstration of a quantum repeater The quality of our procedure is verified by observing a violation of Bell's inequality by more than 5 standard deviations The high experimental accuracy achieved in the experiment implies that the requirement of tolerable error rate in multistage realization of quantum repeaters can be fulfilled, hence providing a useful toolbox for quantum communication over large distances
TL;DR: Based on a quantum analysis of two capacitively coupled current-biased Josephson junctions, two fundamental two-qubit quantum logic gates are proposed, each of these gates, when supplemented by single-qu bit operations, is sufficient for universal quantum computation.
Abstract: Based on a quantum analysis of two capacitively coupled current-biased Josephson junctions, we propose two fundamental two-qubit quantum logic gates. Each of these gates, when supplemented by single-qubit operations, is sufficient for universal quantum computation. Numerical solutions of the time-dependent Schrodinger equation demonstrate that these operations can be performed with good fidelity.
TL;DR: In this article, a two-qubit gate for the $\mathrm{XY}$ interaction which combines the CNOT and SWAP operations was proposed, which can be implemented efficiently even if only nearest-neighbor coupling between the qubits is available.
Abstract: The two-qubit interaction Hamiltonian of a given physical implementation determines whether or not a two-qubit gate such as the controlled-NOT (CNOT) gate can be realized easily. It can be shown that, e.g., with the $\mathrm{XY}$ interaction more than one two-qubit operation is required in order to realize the CNOT operation. Here we propose a two-qubit gate for the $\mathrm{XY}$ interaction which combines the CNOT and SWAP operations. By using this gate quantum circuits can be implemented efficiently, even if only nearest-neighbor coupling between the qubits is available.
TL;DR: In this paper, the experimental implementation of the quantum random-walk algorithm on a nuclear-magnetic-resonance quantum computer is presented, and it is observed that the quantum walk is in sharp contrast to its classical counterpart.
Abstract: The quantum random walk is a possible approach to construct quantum algorithms. Several groups have investigated the quantum random walk and experimental schemes were proposed. In this paper, we present the experimental implementation of the quantum random-walk algorithm on a nuclear-magnetic-resonance quantum computer. We observe that the quantum walk is in sharp contrast to its classical counterpart. In particular, the properties of the quantum walk strongly depends on the quantum entanglement.
TL;DR: In this paper, an all-optical implementation of quantum computation using semiconductor quantum dots is presented, where quantum memory is represented by the spin of an excess electron stored in each dot.
Abstract: We present an all-optical implementation of quantum computation using semiconductor quantum dots. Quantum memory is represented by the spin of an excess electron stored in each dot. Two-qubit gates are realized by switching on trion-trion interactions between different dots. State selectivity is achieved via conditional laser excitation exploiting Pauli exclusion principle. Read out is performed via a quantum-jump technique. We analyze the effect on our scheme's performance of the main imperfections present in real quantum dots: exciton decay, hole mixing, and phonon decoherence. We introduce an adiabatic gate procedure that allows one to circumvent these effects and evaluate quantitatively its fidelity.
Abstract: We present a study of the effects of decoherence in the operation of a discrete quantum walk on a line, cycle, and hypercube. We find high sensitivity to decoherence, increasing with the number of steps in the walk, as the particle is becoming more delocalized with each step. However, the effect of a small amount of decoherence is to enhance the properties of the quantum walk that are desirable for the development of quantum algorithms. Specifically, we observe a highly uniform distribution on the line, a very fast mixing time on the cycle, and more reliable hitting times across the hypercube.
11 Oct 2003
TL;DR: In this paper, the first superlinear separation between polynomial degree and quantum query complexity was shown by a more general version of the quantum adversary method, and the lower bound was shown to be tight.
Abstract: The degree of a polynomial representing (or approximating) a function f is a lower bound for the quantum query complexity of f. This observation has been a source of many lower bounds on quantum algorithms. It has been an open problem whether this lower bound is tight. We exhibit a function with polynomial degree M and quantum query complexity (M/sup 1.321.../). This is the first superlinear separation between polynomial degree and quantum query complexity. The lower bound is shown by a new, more general version of quantum adversary method.
TL;DR: In this paper, the authors discuss why decoherence has not solved the quantum measurement problem and discuss why, contrary to claims recently made by P.W. Anderson, it is not the solution to the problem.
Abstract: We discuss why, contrary to claims recently made by P.W. Anderson, decoherence has not solved the quantum measurement problem.
TL;DR: In this paper, the use of composite rotations to combat systematic errors in single-qubit quantum logic gates is discussed and three families of compositional rotations which can be used to correct off-resonance and pulse length errors.
Abstract: We describe the use of composite rotations to combat systematic errors in single-qubit quantum logic gates and discuss three families of composite rotations which can be used to correct off-resonance and pulse length errors. Although developed and described within the context of nuclear magnetic resonance quantum computing, these sequences should be applicable to any implementation of quantum computation.
TL;DR: It is demonstrated that two recent innovations in the field of practical quantum key distribution (one-way autocompensation and passive detection) are closely related to the methods developed to protect quantum computations from decoherence.
Abstract: We demonstrate that two recent innovations in the field of practical quantum key distribution (one-way autocompensation and passive detection) are closely related to the methods developed to protect quantum computations from decoherence. We present a new scheme that combines these advantages, and propose a practical implementation of this scheme that is feasible using existing technology.
TL;DR: Detailed control concepts and applications are discussed for quantum systems interacting with a noncommutative noise source and the proposed method reduces the application to a conventional noise reduction problem with feedback.
Abstract: Based on the stochastic differential equation of quantum mechanical feedback obtained in the first part of this paper, detailed control concepts and applications are discussed for quantum systems interacting with a noncommutative noise source. A feedback system in our framework is purely nonclassical in the sense that feedback control is performed via local operation and quantum communication through a quantum channel. The role of the controller is to alter the quantum dynamic characteristics of the plant through entanglement, shared between the plant and controller by sending quantum states, that is modulated by the Hamiltonian on the controller. The input-output relation of quantum systems provides a natural extension of control theory to the quantum domain. This enables one to present a control theoretical interpretation of some fundamental quantum mechanical notions such as the uncertainty principle, but also to find applications of ideas and tools of control theory. One of the most important applications is the production of squeezed states, which has been an important issue of quantum theory in relation to quantum computation and quantum communication. The method proposed here reduces the application to a conventional noise reduction problem with feedback. The H/sub /spl infin// control then leads to complete squeezing.
TL;DR: In this paper, a nuclear magnetic resonance computer with three quantum bits that simulates an adiabatic quantum optimization algorithm is presented, which is made possible by encoding general instances of the given optimization problem into an easily applicable Hamiltonian.
Abstract: We report the realization of a nuclear magnetic resonance computer with three quantum bits that simulates an adiabatic quantum optimization algorithm. Adiabatic quantum algorithms offer new insight into how quantum resources can be used to solve hard problems. This experiment uses a particularly well-suited three quantum bit molecule and was made possible by introducing a technique that encodes general instances of the given optimization problem into an easily applicable Hamiltonian. Our results indicate an optimal run time of the adiabatic algorithm that agrees well with the prediction of a simple decoherence model.
TL;DR: A circuit which uses 2n + 3 qubits and 0(n3lg(n)) elementary quantum gates in a depth of 0( n3) to implement the factorization algorithm using Shor's algorithm on a quantum computer.
Abstract: We try to minimize the number of qubits needed to factor an integer of n bits using Shor's algorithm on a quantum computer. We introduce a circuit which uses 2n + 3 qubits and 0(n3lg(n)) elementary quantum gates in a depth of 0(n3) to implement the factorization algorithm. The circuit is computable in polynomial time on a classical computer and is completely general as it does not rely on any property of the number to be factored.
TL;DR: In this paper, the maximum-likelihood principle is used to unify inference of quantum states and processes from experimental noisy data, and a generic quantum process may be estimated simultaneously with unknown quantum probe states, provided that measurements on probe and transformed probe states are available.
Abstract: The maximum-likelihood principle unifies inference of quantum states and processes from experimental noisy data. Particularly, a generic quantum process may be estimated simultaneously with unknown quantum probe states, provided that measurements on probe and transformed probe states are available. Drawbacks of various approximate treatments are also considered.