Qubit

About: Qubit is a research topic. Over the lifetime, 29978 publications have been published within this topic receiving 723084 citations. The topic is also known as: quantum bit & qbit.

Perfect Quantum Error Correction Code

Abstract: We present a quantum error correction code which protects a qubit of information against general one qubit errors which maybe caused by the interaction with the environment. To accomplish this, we encode the original state by distributing quantum information over five qubits, the minimal number required for this task. We give a simple circuit which takes the initial state with four extra qubits in the state |0> to the encoded state. The circuit can be converted into a decoding one by simply running it backward. Reading the extra four qubits at the decoder's output we learn which one of the sixteen alternatives (no error plus all fifteen possible 1-bit errors) was realized. The original state of the encoded qubit can then be restored by a simple unitary transformation.

Approaching unit visibility for control of a superconducting qubit with dispersive readout.

Abstract: In a Rabi oscillation experiment with a superconducting qubit we show that a visibility in the qubit excited state population of more than 95% can be attained We perform a dispersive measurement of the qubit state by coupling the qubit non-resonantly to a transmission line resonator and probing the resonator transmission spectrum The measurement process is well characterized and quantitatively understood In a measurement of Ramsey fringes, the qubit coherence time is larger than 500 ns

Quantum codes on a lattice with boundary

Abstract: A new type of local-check additive quantum code is presented. Qubits are associated with edges of a 2-dimensional lattice whereas the stabilizer operators correspond to the faces and the vertices. The boundary of the lattice consists of alternating pieces with two different types of boundary conditions. Logical operators are described in terms of relative homology groups.

The Complexity of the Local Hamiltonian Problem

Abstract: The $k$-{\locHam} problem is a natural complete problem for the complexity class $\QMA$, the quantum analogue of $\NP$. It is similar in spirit to {\sc MAX-$k$-SAT}, which is $\NP$-complete for $k\geq 2$. It was known that the problem is $\QMA$-complete for any $k \geq 3$. On the other hand, 1-{\locHam} is in {\P} and hence not believed to be $\QMA$-complete. The complexity of the 2-{\locHam} problem has long been outstanding. Here we settle the question and show that it is $\QMA$-complete. We provide two independent proofs; our first proof uses only elementary linear algebra. Our second proof uses a powerful technique for analyzing the sum of two Hamiltonians; this technique is based on perturbation theory and we believe that it might prove useful elsewhere. Using our techniques we also show that adiabatic computation with 2-local interactions on qubits is equivalent to standard quantum computation.

Separability of very noisy mixed states and implications for nmr quantum computing

Abstract: We give a constructive proof that all mixed states of N qubits in a sufficiently small neighborhood of the maximally mixed state are separable (unentangled). The construction provides an explicit representation of any such state as a mixture of product states. We give upper and lower bounds on the size of the neighborhood, which show that its extent decreases exponentially with the number of qubits. The bounds show that no entanglement appears in the physical states at any stage of present NMR experiments. Though this result raises questions about NMR quantum computation, further analysis would be necessary to assess the power of the general unitary transformations, which are indeed implemented in these experiments, in their action on separable states.