Decoherence by a nonlinear environment: canonical vs. microcanonical case

We compare decoherence induced in a simple quantum system (qubit) for two different initial states of the environment: canonical (fixed temperature) and microcanonical (fixed energy), for the general case of a fully interacting oscillator environment. We find that even a relatively compact oscillator bath (with the effective number of degrees of freedom of order 10), initially in a microcanonical state, will typically cause decoherence almost indistinguishable from that by a macroscopic, thermal environment, except possibly at singularities of the environment's specific heat (critical points). In the latter case, the precise magnitude of the difference between the canonical and microcanonical results depends on the critical behavior of the dissipative coefficient, characterizing the interaction of the qubit with the environment.Comment: 18 pages, revtex, 2 figures; minor textual changes, corrected typo in eq. (53) (v2); textual changes, mostly in the introduction (v3

A sparse spin qubit array with integrated control electronics

Current implementations of quantum computers suffer from large numbers of control lines per qubit, becoming unmanageable with system scale up. Here, we discuss a sparse spin-qubit architecture featuring integrated control electronics significantly reducing the off-chip wire count. This quantum-classical hardware integration closes the feasibility gap towards a CMOS quantum computer.Comment: Paper accompanying an invited talk at the 2019 IEEE International Electron Devices Meeting (IEDM), December 7-11, 201

Dynamical localization simulated on a few qubits quantum computer

We show that a quantum computer operating with a small number of qubits can simulate the dynamical localization of classical chaos in a system described by the quantum sawtooth map model. The dynamics of the system is computed efficiently up to a time $t\geq \ell$, and then the localization length $\ell$ can be obtained with accuracy $\nu$ by means of order $1/\nu^2$ computer runs, followed by coarse grained projective measurements on the computational basis. We also show that in the presence of static imperfections a reliable computation of the localization length is possible without error correction up to an imperfection threshold which drops polynomially with the number of qubits.Comment: 8 pages, 8 figure

Decoherence of electron spin qubits in Si-based quantum computers

Direct phonon spin-lattice relaxation of an electron qubit bound by a donor impurity or quantum dot in SiGe heterostructures is investigated. The aim is to evaluate the importance of decoherence from this mechanism in several important solid-state quantum computer designs operating at low temperatures. We calculate the relaxation rate $1/T_1$ as a function of [100] uniaxial strain, temperature, magnetic field, and silicon/germanium content for Si:P bound electrons. The quantum dot potential is much smoother, leading to smaller splittings of the valley degeneracies. We have estimated these splittings in order to obtain upper bounds for the relaxation rate. In general, we find that the relaxation rate is strongly decreased by uniaxial compressive strain in a SiGe-Si-SiGe quantum well, making this strain an important positive design feature. Ge in high concentrations (particularly over 85%) increases the rate, making Si-rich materials preferable. We conclude that SiGe bound electron qubits must meet certain conditions to minimize decoherence but that spin-phonon relaxation does not rule out the solid-state implementation of error-tolerant quantum computing.Comment: 8 figures. To appear in PRB-July 2002. Revisions include: some references added/corrected, several typos fixed, a few things clarified. Nothing dramati

Effect of an inhomogeneous external magnetic field on a quantum dot quantum computer

We calculate the effect of an inhomogeneous magnetic field, which is invariably present in an experimental environment, on the exchange energy of a double quantum dot artificial molecule, projected to be used as a 2-qubit quantum gate in the proposed quantum dot quantum computer. We use two different theoretical methods to calculate the Hilbert space structure in the presence of the inhomogeneous field: the Heitler-London method which is carried out analytically and the molecular orbital method which is done computationally. Within these approximations we show that the exchange energy J changes slowly when the coupled dots are subject to a magnetic field with a wide range of inhomogeneity, suggesting swap operations can be performed in such an environment as long as quantum error correction is applied to account for the Zeeman term. We also point out the quantum interference nature of this slow variation in exchange.Comment: 12 pages, 4 figures embedded in tex

Realization of quantum process tomography in NMR

Quantum process tomography is a procedure by which the unknown dynamical evolution of an open quantum system can be fully experimentally characterized. We demonstrate explicitly how this procedure can be implemented with a nuclear magnetic resonance quantum computer. This allows us to measure the fidelity of a controlled-not logic gate and to experimentally investigate the error model for our computer. Based on the latter analysis, we test an important assumption underlying nearly all models of quantum error correction, the independence of errors on different qubits.Comment: 8 pages, 7 EPS figures, REVTe

Tackling Systematic Errors in Quantum Logic Gates with Composite Rotations

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 NMR quantum computing these sequences should be applicable to any implementation of quantum computation.Comment: 6 pages RevTex4 including 4 figures. Will submit to Phys. Rev.

Experimental implementation of a NMR entanglement witness

Entanglement witnesses (EW) allow the detection of entanglement in a quantum system, from the measurement of some few observables. They do not require the complete determination of the quantum state, which is regarded as a main advantage. On this paper it is experimentally analyzed an entanglement witness recently proposed in the context of Nuclear Magnetic Resonance (NMR) experiments to test it in some Bell-diagonal states. We also propose some optimal entanglement witness for Bell-diagonal states. The efficiency of the two types of EW's are compared to a measure of entanglement with tomographic cost, the generalized robustness of entanglement. It is used a GRAPE algorithm to produce an entangled state which is out of the detection region of the EW for Bell-diagonal states. Upon relaxation, the results show that there is a region in which both EW fails, whereas the generalized robustness still shows entanglement, but with the entanglement witness proposed here with a better performance

A scalable quantum computer with an ultranarrow optical transition of ultracold neutral atoms in an optical lattice

We propose a new quantum-computing scheme using ultracold neutral ytterbium atoms in an optical lattice. The nuclear Zeeman sublevels define a qubit. This choice avoids the natural phase evolution due to the magnetic dipole interaction between qubits. The Zeeman sublevels with large magnetic moments in the long-lived metastable state are also exploited to address individual atoms and to construct a controlled-multiqubit gate. Estimated parameters required for this scheme show that this proposal is scalable and experimentally feasible.Comment: 6 pages, 6 figure

Two-particle localization and antiresonance in disordered spin and qubit chains

We show that, in a system with defects, two-particle states may experience destructive quantum interference, or antiresonance. It prevents an excitation localized on a defect from decaying even where the decay is allowed by energy conservation. The system studied is a qubit chain or an equivalent spin chain with an anisotropic ($XXZ$) exchange coupling in a magnetic field. The chain has a defect with an excess on-site energy. It corresponds to a qubit with the level spacing different from other qubits. We show that, because of the interaction between excitations, a single defect may lead to multiple localized states. The energy spectra and localization lengths are found for two-excitation states. The localization of excitations facilitates the operation of a quantum computer. Analytical results for strongly anisotropic coupling are confirmed by numerical studies.Comment: Updated version, 13 pages, 5 figures To appear in Phys. Rev. B (2003