Quantum Codes for Simplifying Design and Suppressing Decoherence in Superconducting Phase-Qubits

We introduce simple qubit-encodings and logic gates which eliminate the need for certain difficult single-qubit operations in superconducting phase-qubits, while preserving universality. The simplest encoding uses two physical qubits per logical qubit. Two architectures for its implementation are proposed: one employing N physical qubits out of which N/2 are ancillas fixed in the |1 state, the other employing N/2+1 physical qubits, one of which is a bus qubit connected to all others. Details of a minimal set of universal encoded logic operations are given, together with recoupling schemes, that require nanosecond pulses. A generalization to codes with higher ratio of number of logical qubits per physical qubits is presented. Compatible decoherence and noise suppression strategies are also discussed. PACS: 03.67.Lx; 85.25.Hv; 03.67.-a; 89.70.+c     

Quantum Information Processing in Cavity-QED

We give a brief overview of cavity-QED and its roles in quantum information science. In particular, we discuss setups in optical cavity-QED, where either atoms serve as stationary qubits, or photons serve as flying qubits. PACS: 42.50.Pq, 03.67.Lx, 03.67.Hk, 32.80.Pj     

Data Compression Limit for an Information Source of Interacting Qubits

A system of interacting qubits can be viewed as a non-i.i.d quantum information source. A possible model of such a source is provided by a quantum spin system, in which spin-1/2 particles located at sites of a lattice interact with each other. We establish the limit for the compression of information from such a source and show that asymptotically it is given by the von Neumann entropy rate. Our result can be viewed as a quantum ana-logue of Shannon's noiseless coding theorem for a class of non-i.i.d. quantum informa-tion sources. From the probabilistic point of view it is an analog of the Shannon-McMillan-Breiman theorem considered as a cornerstone of modern Information Theory. PACS: 03.67-a; 03.67.Lx     

Generation of Inequivalent Generalized Bell Bases

The notion of equivalence of maximally entangled bases of bipartite d–dimensional Hilbert spaces _{d d} is introduced. An explicit method of inequivalent bases construction is presented. PACS: 03.67.-a     

Spin-Based Quantum Dot Quantum Computing in Silicon

The spins of localized electrons in silicon are strong candidates for quantum information processing because of their extremely long coherence times and the integrability of Si within the present microelectronics infrastructure. This paper reviews a strategy for fabricating single electron spin qubits in gated quantum dots in Si/SiGe heterostructures. We discuss the pros and cons of using silicon, present recent advances, and outline challenges. PACS: 03.67.Pp, 03.67.Lx, 85.35.Be, 73.21.La     

Controlling Spin Qubits in Quantum Dots

We review progress on the spintronics proposal for quantum computing where the quantum bits (qubits) are implemented with electron spins. We calculate the exchange interaction of coupled quantum dots and present experiments, where the exchange coupling is measured via transport. Then, experiments on single spins on dots are described, where long spin relaxation times, on the order of a millisecond, are observed. We consider spin-orbit interaction as sources of spin decoherence and find theoretically that also long decoherence times are expected. Further, we describe the concept of spin filtering using quantum dots and show data of successful experiments. We also show an implementation of a read out scheme for spin qubits and define how qubits can be measured with high precision. Then, we propose new experiments, where the spin decoherence time and the Rabi oscillations of single electrons can be measured via charge transport through quantum dots. Finally, all these achievements have promising applications both in conventional and quantum information processing. PACS: 03.67.Lx, 03.67.Mn, 73.23.Hk, 85.35.Be     

Ion Trap Quantum Computing with Ca+ Ions

The scheme of an ion trap quantum computer is described and the implementation of quantum gate operations with trapped Ca⁺ ions is discussed. Quantum information processing with Ca⁺ ions is exemplified with several recent experiments investigating entanglement of ions. PACS: 03.67.Lx, 03.67.Mn, 32.80.Pj     

Scaling and Renormalization in Fault-Tolerant Quantum Computers

This work is concerned with phrasing the concepts of fault-tolerant quantum computation within the framework of disordered systems, Bernoulli site percolation in particular. We show how the so-called threshold theorems on the possibility of fault-tolerant quantum computation with constant error rate can be cast as a renormalization (coarse-graining) of the site percolation process describing the occurrence of errors during computation. We also use percolation techniques to derive a trade-off between the complexity overhead of the fault-tolerant circuit and the threshold error rate. PACS: 03.67.Pp; 03.67.Lx     

Quantum Algorithms for Highly Structured Search Problems

We consider the problem of identifying a base k string given an oracle which returns information about the number of correct components in a query, specifically, the Hamming distance between the query and the solution, modulo r = max{2, 6 – k}. Classically this problem requires (nlog _r k) queries. For k {2, 3, 4}, we construct quantum algorithms requiring only a single quantum query. For k > 4, we show that O(k) quantum queries suffice. In both cases the quantum algorithms are optimal. PACS: 03.67.Lx     

Quantum Computing with Trapped Ion Hyperfine Qubits

We discuss the basic aspects of quantum information processing with trapped ions, including the principles of ion trapping, preparation and detection of hyperfine qubits, single-qubit operations and multi-qubit entanglement protocols. Recent experimental advances and future research directions are outlined. PACS: 03.67.Lx, 32.80.Pj, 32.80.Qk, 42.50.Vk     

Qubitless Quantum Logic

We discuss the implementation of quantum logic in a system of strongly interacting particles. The implementation is qubitless since logical qubits do not correspond to any well-defined physical substates. As an illustration, we present the results of simulations of the quantum controlled-NOT gate and Shor's algorithm for a chain of spin-1/2 particles with Heisenberg coupling. Our proposal extends quantum information processing theory to systems with permanent strong coupling between the two-state subsystems. PACS: 03.67.Lx; 03.65.Ta     

Ergodic Quantum Computing

We propose a (theoretical) model for quantum computation where the result can be read out from the time average of the Hamiltonian dynamics of a 2-dimensional crystal on a cylinder.The Hamiltonian is a spatially local interaction among Wigner–Seitz cells containing six qubits. The quantum circuit that is simulated is specified by the initialization of program qubits. As in Margolus Hamiltonian cellular automaton (implementing classical circuits), a propagating wave in a clock register controls asynchronously the application of the gates. However, in our approach all required initializations are basis states. After a while the synchronizing wave is essentially spread around the whole crystal. The circuit is designed such that the result is available with probability about 1/4 despite of the completely undefined computation step. This model reduces quantum computing to preparing basis states for some qubits, waiting, and measuring in the computational basis. Even though it may be unlikely to find our specific Hamiltonian in real solids, it is possible that also more natural interactions allow ergodic quantum computing.PACS:03.67.Lx     

Securing QKD Links in the Full Hilbert Space

Many quantum key distribution QKD analyses examine the link security in a subset of the full Hilbert space that is available to describe the system. In reality, information about the photon state can be embedded in correlations between the polarization space and other dimensions of the full Hilbert space in such a way that Eve can determine the polarization of a photon without affecting it. This paper uses the concept of suitability Hockney et al. Suitability versus Fidelity for Rating Single Photon Guns to quantify the available information for Eve to exploit, and demonstrate how it is possible for Alice and Bob to fool themselves into thinking they have a highly secure link.PACS:03.67.Dd; 03.67.HK; 42.50.-p.     

Visualization of the Quantum Fourier Transform Using a Quantum Computer Simulator

The quantum Fourier transform (QFT) is a key subroutine of quantum algorithms for factoring and simulation and is the heart of the hidden-subgroup problem, the solution of which is expected to lead to the development of new quantum algorithms. The QFT acts on the Hilbert space and alters the quantum mechanical phases and probability amplitudes. Unlike its classical counterpart its schematic representation and visualization are very dif.cult. The aim of this work is to develop a schematic representation and visualization of the QFT by running it on a quantum computer simulator which has been constructed in the framework of this research. Base states, superpositions of base states and entangled states are transformed and the corresponding schematic representations are presented. The visualization of the QFT presented here and the quantum computer simulator developed for this purpose may become a useful tool for introducing the QFT to students and researches without a strong background in quantum mechanics or Fourier analysis. PACS: 03.67.-a, 03.67.Lx     

Qubit Geometry and Conformal Mapping

Identifying the Bloch sphere with the Riemann sphere (the extended complex plane), we obtain relations between single qubit unitary operations and Möbius transformations on the extended complex plane. PACS: 03.67.-a, 03.67.Lx, 03.67.Hk     

Liouville Invariance in Quantum and Classical Mechanics

The density-matrix and Heisenberg formulations of quantum mechanics follow—for unitary evolution—directly from the Schrödinger equation. Nevertheless, the symmetries of the corresponding evolution operator, the Liouvillian L = i[, H], need not be limited to those of the Hamiltonian H. This is due to L only involving eigenenergy differences, which can be degenerate even if the energies themselves are not. Remarkably, this possibility has rarely been mentioned in the literature, and never pursued more generally. We consider an example involving mesoscopic Josephson devices, but the analysis only assumes familiarity with basic quantum mechanics. Subsequently, such L-symmetries are shown to occur more widely, in particular also in classical mechanics. The symmetry's relevance to dissipative systems and quantum-information processing is briefly discussed. PACS: 03.65.-w, 03.67.-a, 45.20.Jj, 74.50.+r     

Implementing a Quantum Algorithm with Exchange-Coupled Quantum Dots: A Feasibility Study

We present Monte Carlo wavefunction simulations for quantum computations employing an exchange-coupled array of quantum dots. Employing a combination of experimentally and theoretically available parameters, we find that gate fidelities greater than 98% may be obtained with current experimental and technological capabilities. Application to an encoded 3 qubit (nine physical qubits) Deutsch-Josza computation indicates that the algorithmic fidelity is more a question of the total time to implement the gates than of the physical complexity of those gates. PACS: 81.07.Ta, 02.70.Ss, 03.67.Lx, 03.65.Yz