Quantum-error correction on linear-nearest-neighbor qubit arrays

A quantum circuit implementing 5-qubit quantum-error correction on a linear-nearest-neighbor architecture is described. The canonical decomposition is used to construct fast and simple gates that incorporate the necessary swap operations allowing the circuit to achieve the same depth as the current least depth circuit. Simulations of the circuit's performance when subjected to discrete and continuous errors are presented. The relationship between the error rate of a physical qubit and that of a logical qubit is investigated with emphasis on determining the concatenated error correction threshold.

Optimal measurements for relative quantum information

We provide optimal measurement schemes for estimating relative parameters of the quantum state of a pair of spin systems. We prove that the optimal measurements are joint measurements on the pair of systems, meaning that they cannot be achieved by local operations and classical communication. We also demonstrate that in the limit where one of the spins becomes macroscopic, our results reproduce those that are obtained by treating that spin as a classical reference direction.

Optical quantum computation using cluster states

We propose an approach to optical quantum computation in which a deterministic entangling quantum gate may be performed using, on average, a few hundred coherently interacting optical elements (beam splitters, phase shifters, single photon sources, and photodetectors with feedforward). This scheme combines ideas from the optical quantum computing proposal of Knill, Laflamme, and Milburn [Nature (London) 409, 46 (2001)], and the abstract cluster-state model of quantum computation proposed by Raussendorf and Briegel [Phys. Rev. Lett. 86, 5188 (2001)].

Simulating quantum interference in a three-level system with perpendicular transition dipole moments

We consider a three-level V-type atomic system with the ground state coupled by a laser field to only one of the excited states, and with the two excited states coupled together by a dc field. Although the dipole moments of the two dipole-allowed transitions are assumed perpendicular, we demonstrate that this system emulates to a large degree a three-level system with parallel dipole moments-the latter being a system that exhibits quantum interference and displays a number of interesting features. As examples, we show that the system can produce extremely large values for the intensity-intensity correlation function, and that its resonance fluorescence spectrum can display ultranarrow lines. The dressed states for this system are identified, and the spectral features are interpreted in terms of transitions among these dressed states. We also show that this system is capable of exhibiting considerable squeezing.

Energy as an entanglement witness for quantum many-body systems

We investigate quantum many-body systems where all low-energy states are entangled. As a tool for quantifying such systems, we introduce the concept of the entanglement gap, which is the difference in energy between the ground-state energy and the minimum energy that a separable (unentangled) state may attain. If the energy of the system lies within the entanglement gap, the state of the system is guaranteed to be entangled. We find Hamiltonians that have the largest possible entanglement gap; for a system consisting of two interacting spin-1/2 subsystems, the Heisenberg antiferromagnet is one such example. We also introduce a related concept, the entanglement-gap temperature: the temperature below which the thermal state is certainly entangled, as witnessed by its energy. We give an example of a bipartite Hamiltonian with an arbitrarily high entanglement-gap temperature for fixed total energy range. For bipartite spin lattices we prove a theorem demonstrating that the entanglement gap necessarily decreases as the coordination number is increased. We investigate frustrated lattices and quantum phase transitions as physical phenomena that affect the entanglement gap.

Fast simulation of a quantum phase transition in an ion-trap realizable unitary map

We show that a specific implementation of a unitary map on multiple qubits in an ion trap is physically equivalent to a Hamiltonian evolution that belongs to the same universality class as the transverse Ising Hamiltonian. We suggest experimental signatures, and present numerical simulations for the case of four qubits.

Quantum entanglement and fixed-point bifurcations

How does the classical phase-space structure for a composite system relate to the entanglement characteristics of the corresponding quantum system? We demonstrate how the entanglement in nonlinear bipartite systems can be associated with a fixed-point bifurcation in the classical dynamics. Using the example of coupled giant spins we show that when a fixed point undergoes a supercritical pitchfork bifurcation, the corresponding quantum state-the ground state-achieves its maximum amount of entanglement near the critical point. We conjecture that this will be a generic feature of systems whose classical limit exhibits such a bifurcation.

Coherent analysis of quantum optical sideband modes

We demonstrate a device that allows for the coherent analysis of a pair of optical frequency sidebands in an arbitrary basis. We show that our device is quantum noise limited, and hence applications for this scheme may be found in discrete and continuous variable optical quantum information experiments. (c) 2005 Optical Society of America.

Adaptive phase measurements in linear optical quantum computation

Photon counting induces an effective non-linear optical phase shift in certain states derived by linear optics from single photons. Although this non-linearity is non-deterministic, it is sufficient in principle to allow scalable linear optics quantum computation (LOQC). The most obvious way to encode a qubit optically is as a superposition of the vacuum and a single photon in one mode-so-called 'single-rail' logic. Until now this approach was thought to be prohibitively expensive (in resources) compared to 'dual-rail' logic where a qubit is stored by a photon across two modes. Here we attack this problem with real-time feedback control, which can realize a quantum-limited phase measurement on a single mode, as has been recently demonstrated experimentally. We show that with this added measurement resource, the resource requirements for single-rail LOQC are not substantially different from those of dual-rail LOQC. In particular, with adaptive phase measurements an arbitrary qubit state a alpha/0 > + beta/1 > can be prepared deterministically.

Continuous quantum error correction by cooling

We describe an implementation of quantum error correction that operates continuously in time and requires no active interventions such as measurements or gates. The mechanism for carrying away the entropy introduced by errors is a cooling procedure. We evaluate the effectiveness of the scheme by simulation, and remark on its connections to some recently proposed error prevention procedures.

Ion trap transducers for quantum electromechanical oscillators

An enduring challenge for contemporary physics is to experimentally observe and control quantum behavior in macroscopic systems. We show that a single trapped atomic ion could be used to probe the quantum nature of a mesoscopic mechanical oscillator precooled to 4 K, and furthermore, to cool the oscillator with high efficiency to its quantum ground state. The proposed experiment could be performed using currently available technology.

Quantum methods for clock synchronization: Beating the standard quantum limit without entanglement

We introduce methods for clock synchronization that make use of the adiabatic exchange of nondegenerate two-level quantum systems: ticking qubits. Schemes involving the exchange of N independent qubits with frequency omega give a synchronization accuracy that scales as (omega root N)(-1)-i.e., as the standard quantum limit. We introduce a protocol that makes use of N-c coherent exchanges of a single qubit at frequency omega, leading to an accuracy that scales as (omega N-c)(-1) ln N-c. This protocol beats the standard quantum limit without the use of entanglement, and we argue that this scaling is the fundamental limit for clock synchronization allowed by quantum mechanics. We analyze the performance of these protocols when used with a lossy channel.

Distance measures to compare real and ideal quantum processes

With growing success in experimental implementations it is critical to identify a gold standard for quantum information processing, a single measure of distance that can be used to compare and contrast different experiments. We enumerate a set of criteria that such a distance measure must satisfy to be both experimentally and theoretically meaningful. We then assess a wide range of possible measures against these criteria, before making a recommendation as to the best measures to use in characterizing quantum information processing.

Unified derivations of measurement-based schemes for quantum computation

We present unified, systematic derivations of schemes in the two known measurement-based models of quantum computation. The first model (introduced by Raussendorf and Briegel, [Phys. Rev. Lett. 86, 5188 (2001)]) uses a fixed entangled state, adaptive measurements on single qubits, and feedforward of the measurement results. The second model (proposed by Nielsen, [Phys. Lett. A 308, 96 (2003)] and further simplified by Leung, [Int. J. Quant. Inf. 2, 33 (2004)]) uses adaptive two-qubit measurements that can be applied to arbitrary pairs of qubits, and feedforward of the measurement results. The underlying principle of our derivations is a variant of teleportation introduced by Zhou, Leung, and Chuang, [Phys. Rev. A 62, 052316 (2000)]. Our derivations unify these two measurement-based models of quantum computation and provide significantly simpler schemes.

Relativistically invariant quantum information

We show that quantum information can be encoded into entangled states of multiple indistinguishable particles in such a way that any inertial observer can prepare, manipulate, or measure the encoded state independent of their Lorentz reference frame. Such relativistically invariant quantum information is free of the difficulties associated with encoding into spin or other degrees of freedom in a relativistic context.