Engineering topics

Englert, Berthold-Georg

Publications and source records attributed to Englert, Berthold-Georg.

7 records

DOE OSTI2011

Adaptive schemes for incomplete quantum process tomography

We propose an iterative algorithm for incomplete quantum process tomography with the help of quantum state estimation. The algorithm, which is based on the combined principles of maximum likelihood and maximum entropy, yields a unique estimator for an unknown quantum process when one has less than a complete set of linearly independent measurement data to specify the quantum process uniquely. We apply this iterative algorithm adaptively in various situations and so optimize the amount of resources required to estimate a quantum process with incomplete data.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2011

Quantum state tomography with fully symmetric measurements and product measurements

We introduce random-matrix theory to study the tomographic efficiency of a wide class of measurements constructed out of weighted 2-designs, including symmetric informationally complete (SIC) probability operator measurements (POMs). In particular, we derive analytic formulas for the mean Hilbert-Schmidt distance and the mean trace distance between the estimator and the true state, which clearly show the difference between the scaling behaviors of the two error measures with the dimension of the Hilbert space. We then prove that the product SIC POMs, the multipartite analog of the SIC POMs, are optimal among all product measurements in the same sense as the SIC POMs are optimal among all joint measurements. We further show that, for bipartite systems, there is only a marginal efficiency advantage of the joint SIC POMs over the product SIC POMs. In marked contrast, for multipartite systems, the efficiency advantage of the joint SIC POMs increases exponentially with the number of parties.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2011

Long-lived qubit from three spin-(1/2) atoms

A system of three spin-(1/2) atoms allows the construction of a reference-frame-free (RFF) qubit in the subspace with total angular momentum j=1/2. The RFF qubit stays coherent perfectly as long as the spins of the three atoms are affected homogeneously. The inhomogeneous evolution of the atoms causes decoherence, but this decoherence can be suppressed efficiently by applying a bias magnetic field of modest strength perpendicular to the plane of the atoms. The resulting lifetime of the RFF qubit can be many days, making RFF qubits of this kind promising candidates for quantum information storage units. Specifically, we examine the situation of three {sup 6}Li atoms trapped in a CO{sub 2}-laser-generated optical lattice and find that, with conservatively estimated parameters, a stored qubit maintains a fidelity of 0.9999 for two hours.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2011

Mutually unbiased bases in six dimensions: The four most distant bases

We consider the average distance between four bases in six dimensions. The distance between two orthonormal bases vanishes when the bases are the same, and the distance reaches its maximal value of unity when the bases are unbiased. We perform a numerical search for the maximum average distance and find it to be strictly smaller than unity. This is strong evidence that no four mutually unbiased bases exist in six dimensions. We also provide a two-parameter family of three bases which, together with the canonical basis, reach the numerically found maximum of the average distance, and we conduct a detailed study of the structure of the extremal set of bases.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2011

Test-state approach to the quantum search problem

The search for 'a quantum needle in a quantum haystack' is a metaphor for the problem of finding out which one of a permissible set of unitary mappings - the oracles - is implemented by a given black box. Grover's algorithm solves this problem with quadratic speedup as compared with the analogous search for 'a classical needle in a classical haystack'. Since the outcome of Grover's algorithm is probabilistic - it gives the correct answer with high probability, not with certainty - the answer requires verification. For this purpose we introduce specific test states, one for each oracle. These test states can also be used to realize 'a classical search for the quantum needle' which is deterministic - it always gives a definite answer after a finite number of steps - and 3.41 times as fast as the purely classical search. Since the test-state search and Grover's algorithm look for the same quantum needle, the average number of oracle queries of the test-state search is the classical benchmark for Grover's algorithm.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2011

Density functional of a two-dimensional gas of dipolar atoms: Thomas-Fermi-Dirac treatment

We derive the density functional for the ground-state energy of a two-dimensional, spin-polarized gas of neutral fermionic atoms with magnetic-dipole interaction, in the Thomas-Fermi-Dirac approximation. For many atoms in a harmonic trap, we give analytical solutions for the single-particle spatial density and the ground-state energy, in dependence on the interaction strength, and we discuss the weak-interaction limit that is relevant for experiments. We then lift the restriction of full spin polarization and account for a time-independent inhomogeneous external magnetic field. The field strength necessary to ensure full spin polarization is derived.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2011

Hybrid quantum computation

We present a hybrid model of the unitary-evolution-based quantum computation model and the measurement-based quantum computation model. In the hybrid model, part of a quantum circuit is simulated by unitary evolution and the rest by measurements on star graph states, thereby combining the advantages of the two standard quantum computation models. In the hybrid model, a complicated unitary gate under simulation is decomposed in terms of a sequence of single-qubit operations, the controlled-z gates, and multiqubit rotations around the z axis. Every single-qubit and the controlled-z gate are realized by a respective unitary evolution, and every multiqubit rotation is executed by a single measurement on a required star graph state. The classical information processing in our model requires only an information flow vector and propagation matrices. We provide the implementation of multicontrol gates in the hybrid model. They are very useful for implementing Grover's search algorithm, which is studied as an illustrative example.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗