Showing papers on "Qubit published in 2002"
TL;DR: In this paper, the authors studied the entanglement in the transverse Ising model, a special case of the one-dimensional infinite-lattice anisotropic XY model, which exhibits a quantum phase transition.
Abstract: What entanglement is present in naturally occurring physical systems at thermal equilibrium? Most such systems are intractable and it is desirable to study simple but realistic systems that can be solved. An example of such a system is the one-dimensional infinite-lattice anisotropic XY model. This model is exactly solvable using the Jordan-Wigner transform, and it is possible to calculate the two-site reduced density matrix for all pairs of sites. Using the two-site density matrix, the entanglement of formation between any two sites is calculated for all parameter values and temperatures. We also study the entanglement in the transverse Ising model, a special case of the XY model, which exhibits a quantum phase transition. It is found that the next-nearest-neighbor entanglement (though not the nearest-neighbor entanglement) is a maximum at the critical point. Furthermore, we show that the critical point in the transverse Ising model corresponds to a transition in the behavior of the entanglement between a single site and the remainder of the lattice.
1,274 citations
TL;DR: In this article, the authors studied the topological quantum error-correcting surface codes (surface codes) introduced by Kitaev, where qubits are arranged in a two-dimensional array on a surface of nontrivial topology.
Abstract: We analyze surface codes, the topological quantum error-correcting codes introduced by Kitaev. In these codes, qubits are arranged in a two-dimensional array on a surface of nontrivial topology, and encoded quantum operations are associated with nontrivial homology cycles of the surface. We formulate protocols for error recovery, and study the efficacy of these protocols. An order-disorder phase transition occurs in this system at a nonzero critical value of the error rate; if the error rate is below the critical value (the accuracy threshold), encoded information can be protected arbitrarily well in the limit of a large code block. This phase transition can be accurately modeled by a three-dimensional Z(2) lattice gauge theory with quenched disorder. We estimate the accuracy threshold, assuming that all quantum gates are local, that qubits can be measured rapidly, and that polynomial-size classical computations can be executed instantaneously. We also devise a robust recovery procedure that does not require measurement or fast classical processing; however, for this procedure the quantum gates are local only if the qubits are arranged in four or more spatial dimensions. We discuss procedures for encoding, measurement, and performing fault-tolerant universal quantum computation with surface codes, and argue that these codes provide a promising framework for quantum computing architectures.
1,176 citations
TL;DR: A circuit based on a large-area current-biased Josephson junction whose two lowest energy quantum levels are used to implement a solid-state qubit is designed and operated and is the basis of a scalable quantum computer.
Abstract: We have designed and operated a circuit based on a large-area current-biased Josephson junction whose two lowest energy quantum levels are used to implement a solid-state qubit. The circuit allows measurement of the qubit states with a fidelity of 85% while providing sufficient decoupling from external sources of relaxation and decoherence to allow coherent manipulation of the qubit state, as demonstrated by the observation of Rabi oscillations. This qubit circuit is the basis of a scalable quantum computer.
882 citations
TL;DR: In this paper, a model of quantum computation with local fermionic modes (LFMs), sites which can be either empty or occupied by a fermion, was defined and the simulation cost was reduced to O(log m) and a constant.
756 citations
TL;DR: In this article, a simple formula for the average fidelity between a unitary quantum gate and a general quantum operation on a qudit was presented, generalizing the formula for qubits found by Bowdrey et al.
571 citations
TL;DR: The full implementation of a quantum cryptography protocol using a stream of single photon pulses generated by a stable and efficient source operating at room temperature reaches a domain where single photons have a measurable advantage over an equivalent system based on attenuated light pulses.
Abstract: We report the full implementation of a quantum cryptography protocol using a stream of single photon pulses generated by a stable and efficient source operating at room temperature. The single photon pulses are emitted on demand by a single nitrogen-vacancy color center in a diamond nanocrystal. The quantum bit error rate is less that 4.6% and the secure bit rate is 7700 bits/s. The overall performances of our system reaches a domain where single photons have a measurable advantage over an equivalent system based on attenuated light pulses.
558 citations
TL;DR: A general Bell inequality is derived which is a sufficient and necessary condition for the correlation function for N particles to be describable in a local and realistic picture, for the case in which measurements on each particle can be chosen between two arbitrary dichotomic observables.
Abstract: We derive a single general Bell inequality which is a sufficient and necessary condition for the correlation function for N particles to be describable in a local and realistic picture, for the case in which measurements on each particle can be chosen between two arbitrary dichotomic observables. We also derive a necessary and sufficient condition for an arbitrary N-qubit mixed state to violate this inequality. This condition is a generalization and reformulation of the Horodecki family condition for two qubits.
381 citations
TL;DR: In this article, a teleportation scheme for a coherent-state qubit is developed and applied to gate operations, which is shown to be robust to detection inefficiency and can be used for universal quantum computation using optical coherent states.
Abstract: We study universal quantum computation using optical coherent states. A teleportation scheme for a coherent-state qubit is developed and applied to gate operations. This scheme is shown to be robust to detection inefficiency.
356 citations
TL;DR: An efficient and intuitive framework for universal quantum computation is presented that uses pairs of spin-1/2 particles to form logical qubits and a single physical interaction, Heisenberg exchange, to produce all gate operations.
Abstract: An efficient and intuitive framework for universal quantum computation is presented that uses pairs of spin-1/2 particles to form logical qubits and a single physical interaction, Heisenberg exchange, to produce all gate operations. Only two Heisenberg gate operations are required to produce a controlled $\ensuremath{\pi}$-phase shift, compared to nineteen for exchange-only proposals employing three spins. Evolved from well-studied decoherence-free subspaces, this architecture inherits immunity from collective decoherence mechanisms. The simplicity and adaptability of this approach should make it attractive for spin-based quantum computing architectures.
331 citations
TL;DR: It is proved that one of two mixed states can be transformed into the other by single-qubit operations if and only if these states have equal values of all 18 invariants, which provides a complete description of nonlocal properties.
Abstract: Entanglement of two parts of a quantum system is a nonlocal property unaffected by local manipulations of these parts. It can be described by quantities invariant under local unitary transformations. Here we present, for a system of two qubits, a set of invariants which provides a complete description of nonlocal properties. The set contains 18 real polynomials of the entries of the density matrix. We prove that one of two mixed states can be transformed into the other by single-qubit operations if and only if these states have equal values of all 18 invariants. Corresponding local operations can be found efficiently. Without any of these 18 invariants the set is incomplete. Similarly, nonlocal, entangling properties of two-qubit unitary gates are invariant under single-qubit operations. We present a complete set of 3 real polynomial invariants of unitary gates. Our results are useful for optimization of quantum computations since they provide an effective tool to verify if and how a given two-qubit operation can be performed using exactly one elementary two-qubit gate, implemented by a basic physical manipulation (and arbitrarily many single-qubit gates).
PACS: 03.67-a; 03.67.Lx
323 citations
TL;DR: In this article, an alternative concept for a scalable spin quantum computer that combines aspects of other proposals with the advantageous features of endohedral fullerenes was proposed, where electron spins instead of nuclear spins are used and that the manipulation of fullerene molecules is fairly easy.
Abstract: We propose an alternative concept for a scalable spin quantum computer that combines aspects of other proposals with the advantageous features of endohedral fullerenes. The key advantages are that electron spins instead of nuclear spins are used and that the manipulation of fullerene molecules is fairly easy. Qubits are set and read out via pulsed electron-spin resonance. Addressing is provided by local magnetic fields or field gradients $(A$ gate). The qubit-qubit interaction is mediated by magnetic dipolar coupling and can be controlled via the direction of the magnetic field with respect to the distance vector of the qubits $(J$ gate). Molecular as well as solid-state architectures are discussed.
TL;DR: The results show that the behavior of quantum random walk is striking different from that of the classical ramdom walk.
Abstract: This letter treats the quantum random walk on the line determined by a 2 × 2 unitary matrix U. A combinatorial expression for the mth moment of the quantum random walk is presented by using 4 matrices, P, Q, R and S given by U. The dependence of the mth moment on U and initial qubit state p is clarified. A new type of limit theorems for the quantum walk is given. Furthermore necessary and sufficient conditions for symmetry of distribution for the quantum walk is presented. Our results show that the behavior of quantum random walk is striking different from that of the classical ramdom walk.
PACS: 03.67.Lx; 05.40.Fb; 02.50.Cw
TL;DR: In this article, the authors extend the tomographic reconstruction technique to two new regimes: one-and two-qutrit systems, and show how quantum-state tomography can be performed for multiqudits with a specific example illustrating how to achieve this in one- and two-qubit systems.
Abstract: Recently quantum tomography has been proposed as a fundamental tool for prototyping a few qubit quantum device. It allows the complete reconstruction of the state produced from a given input into the device. From this reconstructed density matrix, relevant quantum information quantities such as the degree of entanglement and entropy can be calculated. Generally, orthogonal measurements have been discussed for this tomographic reconstruction. In this paper, we extend the tomographic reconstruction technique to two new regimes. First, we show how nonorthogonal measurements allow the reconstruction of the state of the system provided the measurements span the Hilbert space. We then detail how quantum-state tomography can be performed for multiqudits with a specific example illustrating how to achieve this in one- and two-qutrit systems.
TL;DR: This work considers a model in which the system is a qubit, and reaches equilibrium after several successive two-qubit interactions (thermalizing machines) with qubits of a reservoir, and characterize completely the family of thermalizing machines.
Abstract: We study the relaxation of a quantum system towards the thermal equilibrium using tools developed within the context of quantum information theory. We consider a model in which the system is a qubit, and reaches equilibrium after several successive two-qubit interactions (thermalizing machines) with qubits of a reservoir. We characterize completely the family of thermalizing machines. The model shows a tight link between dissipation, fluctuations, and the maximal entanglement that can be generated by the machines. The interplay of quantum and classical information processes that give rise to practical irreversibility is discussed.
TL;DR: The quadrupole S(1/2)-D(5/2) optical transition of a single trapped Ca+ ion is coherently coupled to the standing wave field of a high finesse cavity and deterministic coupling of the cavity mode to the ion's vibrational state is achieved.
Abstract: The quadrupole S(1/2)-D(5/2) optical transition of a single trapped Ca+ ion, well suited for encoding a quantum bit of information, is coherently coupled to the standing wave field of a high finesse cavity. The coupling is verified by observing the ion's response to both spatial and temporal variations of the intracavity field. We also achieve deterministic coupling of the cavity mode to the ion's vibrational state by selectively exciting vibrational state-changing transitions and by controlling the position of the ion in the standing wave field with nanometer precision.
TL;DR: Experimental realization shows that the structural resolution of today's pulse shapers is easily sufficient for pulse formation and the scaling of the system is favorable; sources for decoherence can be eliminated.
Abstract: A new physical implementation for quantum computation is proposed. The vibrational modes of molecules are used to encode qubit systems. Global quantum logic gates are realized using shaped femtosecond laser pulses which are calculated applying optimal control theory. The scaling of the system is favorable; sources for decoherence can be eliminated. A complete set of one- and two-quantum gates is presented for a specific molecule. Detailed analysis regarding experimental realization shows that the structural resolution of today's pulse shapers is easily sufficient for pulse formation.
TL;DR: In this article, a pair of non-degenerate time-bin entangled photons at telecom wavelengths with ultrashort pump pulses was created and shown to be entangled by performing Bell kind tests of the Franson type with visibilities of up to 91%.
Abstract: We create pairs of nondegenerate time-bin entangled photons at telecom wavelengths with ultrashort pump pulses. Entanglement is shown by performing Bell kind tests of the Franson type with visibilities of up to 91%. As time-bin entanglement can easily be protected from decoherence as encountered in optical fibers, this experiment opens the road for complex quantum communication protocols over long distances. We also investigate the creation of more than one photon pair in a laser pulse and present a simple tool to quantify the probability of such events to happen.
TL;DR: A fundamental asymmetry to nonlocality is revealed, which is the origin of "nonlocality without entanglement," and a very simple proof of this phenomenon is presented.
Abstract: Entanglement is a useful resource because some global operations cannot be locally implemented using classical communication. We prove a number of results about what is and what is not locally possible. We focus on orthogonal states, which can always be globally distinguished. We establish the necessary and sufficient conditions for a general set of $2\ifmmode\times\else\texttimes\fi{}2$ quantum states to be locally distinguishable, and for a general set of $2\ifmmode\times\else\texttimes\fi{}n$ quantum states to be distinguished given an initial measurement of the qubit. These results reveal a fundamental asymmetry to nonlocality, which is the origin of ``nonlocality without entanglement,'' and we present a very simple proof of this phenomenon.
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TL;DR: In this paper, a combinatorial expression for the mth moment of the quantum random walk is presented by using four matrices, P, Q, R and S given by U. The dependence of the mst moment on U and initial qubit state phi is clarified.
Abstract: This letter treats the quantum random walk on the line determined by a 2 times 2 unitary matrix U. A combinatorial expression for the mth moment of the quantum random walk is presented by using 4 matrices, P, Q, R and S given by U. The dependence of the mth moment on U and initial qubit state phi is clarified. A new type of limit theorems for the quantum walk is given. Furthermore necessary and sufficient conditions for symmetry of distribution for the quantum walk is presented. Our results show that the behavior of quantum random walk is striking different from that of the classical ramdom walk.
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TL;DR: In this paper, the authors studied the authentication of messages composed of quantum states and gave a formal definition of authentication in the quantum setting, and proposed a non-interactive scheme that enables A to both encrypt and authenticate an m qubit message by encoding it into m+s qubits, where the error probability decreases exponentially in the security parameter s.
Abstract: Authentication is a well-studied area of classical cryptography: a sender A and a receiver B sharing a classical secret key want to exchange a classical message with the guarantee that the message has not been modified or replaced by a dishonest party with control of the communication line. In this paper we study the authentication of messages composed of quantum states. We give a formal definition of authentication in the quantum setting. Assuming A and B have access to an insecure quantum channel and share a secret, classical random key, we provide a non-interactive scheme that enables A to both encrypt and authenticate an m qubit message by encoding it into m+s qubits, where the error probability decreases exponentially in the security parameter s. The scheme requires a secret key of size 2m+O(s). To achieve this, we give a highly efficient protocol for testing the purity of shared EPR pairs. It has long been known that learning information about a general quantum state will necessarily disturb it. We refine this result to show that such a disturbance can be done with few side effects, allowing it to circumvent cryptographic protections. Consequently, any scheme to authenticate quantum messages must also encrypt them. In contrast, no such constraint exists classically. This reasoning has two important consequences: It allows us to give a lower bound of 2m key bits for authenticating m qubits, which makes our protocol asymptotically optimal. Moreover, we use it to show that digitally signing quantum states is impossible.
TL;DR: In this article, it was shown that the Holevo bound is the classical information capacity of unital qubit channels, and an explicit formula for this capacity was given for product channels.
Abstract: Additivity of the Holevo capacity is proved for product channels, under the condition that one of the channels is a unital qubit channel, with the other completely arbitrary. As a byproduct this proves that the Holevo bound is the classical information capacity of such qubit channels, and provides an explicit formula for this classical capacity. Additivity of minimal entropy and multiplicativity of p-norms are also proved under the same assumptions. The proof relies on a new bound for the p-norm of an output state from the half-noisy phase-damping channel.
TL;DR: In this article, the authors implemented remote state preparation (RSP) of a qubit from a hydrogen to a carbon nucleus in molecules of carbon-13 labeled chloroform ${13}$CHCl${3}$ using liquid-state nuclear magnetic resonance (NMR) technique.
Abstract: We have experimentally implemented remote state preparation (RSP) of a qubit from a hydrogen to a carbon nucleus in molecules of carbon-13 labeled chloroform $^{13}$CHCl$_{3}$ over interatomic distances using liquid-state nuclear magnetic resonance (NMR) technique. Full RSP of a special ensemble of qubits, i.e., a qubit chosen from equatorial and polar great circles on a Bloch sphere with Pati's scheme, was achieved with one cbit communication. Such a RSP scheme can be generalized to prepare a large number of qubit states and may be used in other quantum information processing and quantum computing.
TL;DR: The Penrose-Hameroff 'Orch OR' model of consciousness is reviewed as an example of the possible utility of quantum computation in MTs, and pathways for electron mobility and possible quantum tunneling and superconductivity among aromatic amino acids in tubulins are shown.
Abstract: Technological computation is entering the quantum realm, focusing attention on biomolecular information processing systems such as proteins, as presaged by the work of Michael Conrad. Protein conformational dynamics and pharmacological evidence suggest that protein conformational states-fundamental information units ('bits') in biological systems-are governed by quantum events, and are thus perhaps akin to quantum bits ('qubits') as utilized in quantum computation. 'Real time' dynamic activities within cells are regulated by the cell cytoskeleton, particularly microtubules (MTs) which are cylindrical lattice polymers of the protein tubulin. Recent evidence shows signaling, communication and conductivity in MTs, and theoretical models have predicted both classical and quantum information processing in MTs. In this paper we show conduction pathways for electron mobility and possible quantum tunneling and superconductivity among aromatic amino acids in tubulins. The pathways within tubulin match helical patterns in the microtubule lattice structure, which lend themselves to topological quantum effects resistant to decoherence. The Penrose-Hameroff 'Orch OR' model of consciousness is reviewed as an example of the possible utility of quantum computation in MTs.
TL;DR: In this paper, a scheme for generating multiple strongly interacting qubits in rare-earth ion-doped inorganic crystals at cryogenic temperatures is presented, based on existing material data and established measurement techniques and should therefore be straightforward to realise in practice.
TL;DR: In this article, higher-dimensional versions of qubits, or qudits, can be encoded into spin systems and into harmonic oscillators, yielding important advantages for quantum computation.
Abstract: We show that higher-dimensional versions of qubits, or qudits, can be encoded into spin systems and into harmonic oscillators, yielding important advantages for quantum computation. Whereas qubit-based quantum computation is adequate for analyses of quantum vs classical computation, in practice qubits are often realized in higher-dimensional systems by truncating all but two levels, thereby reducing the size of the precious Hilbert space. We develop natural qudit gates for universal quantum computation, and exploit the entire accessible Hilbert space. Mathematically, we give representations of the generalized Pauli group for qudits in coupled spin systems and harmonic oscillators, and include analyses of the qubit and the infinite-dimensional limits.
TL;DR: An unprecedented large value of the teleportation "fidelity" has been attained: F = (95.3 +/- 0.6)%.
Abstract: We report the experimental realization of teleporting a one-particle entangled qubit. The qubit is physically implemented by a two-dimensional subspace of states of a mode of the electromagnetic field, specifically, the space spanned by the vacuum and the one-photon state. Our experiment follows the line suggested by Lee and Kim [Phys. Rev. A 63, 012305 (2000)] and Knill, Laflamme, and Milburn [Nature (London) 409, 46 (2001)]. An unprecedented large value of the teleportation ``fidelity'' has been attained: $F\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}(95.3\ifmmode\pm\else\textpm\fi{}0.6)%$.
TL;DR: In this paper, the authors studied the entanglement of thermal and ground states in the Heisenberg qubit rings with a magnetic field and showed that the ground state is a four-body maximally entangled state measured by the square N-bit concurrence.
Abstract: We study the entanglement of thermal and ground states in the Heisenberg $\mathrm{XX}$ qubit rings with a magnetic field. A general result is found that for even-number rings, pairwise entanglement between nearest-neighbor qubits is independent of both the sign of exchange interaction constants and the sign of magnetic fields. As an example we study the entanglement in the four-qubit model and find that the ground state of this model without magnetic fields is shown to be a four-body maximally entangled state measured by the square N-bit concurrence.
TL;DR: In this article, a simple way of characterizing the average fidelity between a unitary operator and a general operation on a single qubit is described, which only involves calculating the fidelities for a few pure input states, and discuss possible applications to experimental techniques including nuclear magnetic resonance (NMR).
TL;DR: The universal quantum homogenizer as mentioned in this paper is a quantum machine that takes as an input a system qubit initially in the state r and a set of N reservoir qubits initially prepared in the same state j.
Abstract: We design a universal quantum homogenizer, which is a quantum machine that takes as an input a system qubit initially in the state r and a set of N reservoir qubits initially prepared in the same state j .I n the homogenizer the system qubit sequentially interacts with the reservoir qubits via the partial swap transformation. The homogenizer realizes, in the limit sense, the transformation such that at the output each qubit is in an arbitrarily small neighborhood of the state j irrespective of the initial states of the system and the reservoir qubits. This means that the system qubit undergoes an evolution that has a fixed point, which is the reservoir state j. We also study approximate homogenization when the reservoir is composed of a finite set of identically prepared qubits. The homogenizer allows us to understand various aspects of the dynamics of open systems interacting with environments in nonequilibrium states. In particular, the reversibility vs irreversibility of the dynamics of the open system is directly linked to specific ~classical! information about the order in which the reservoir qubits interacted with the system qubit. This aspect of the homogenizer leads to a model of a quantum safe with a classical combination. We analyze in detail how entanglement between the reservoir and the system is created during the process of quantum homogenization. We show that the information about the initial state of the system qubit is stored in the entanglement between the homogenized qubits.
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TL;DR: In this paper, the authors presented a quantum circuit that uses 2n+3 qubits and O(n^3 lg(n)) elementary quantum gates in a depth of O( n^3) to implement the factorization algorithm.
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 O(n^3 lg(n)) elementary quantum gates in a depth of O(n^3) 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.
Keywords: Factorization, quantum circuits, modular arithmetics