A polynomial has saturated Newton polytope (SNP) if every lattice point of the convex hull of its exponent vectors corresponds to a monomial. We compile instances of SNP in algebraic combinatorics (some with proofs, others conjecturally): skew Schur polynomials; symmetric polynomials associated to reduced words, Redfield-Pólya theory, Witt vectors, and totally nonnegative matrices; resultants; discriminants (up to quartics); Macdonald polynomials; key polynomials; Demazure atoms; Schubert polynomials; and Grothendieck polynomials, among others.Our principal construction is the Schubitope. For any subset of [n] 2 , we describe it by linear inequalities. This generalized permutahedron conjecturally has positive Ehrhart polynomial. We conjecture it describes the Newton polytope of Schubert and key polynomials. We also define dominance order on permutations and study its poset-theoretic properties.

No abstract

As with any quantum computing platform, semiconductor quantum dot devices require sophisticated hardware and controls for operation. The increasing complexity of quantum dot devices necessitates the advancement of automated control software and image recognition techniques for rapidly evaluating charge stability diagrams. We use an image analysis toolbox developed in Python to automate the calibration of virtual gates, a process that previously involved a large amount of user intervention. Moreover, we show that straightforward feedback protocols can be used to simultaneously tune multiple tunnel couplings in a triple quantum dot in a computer automated fashion. Finally, we adopt the use of a 'tunnel coupling lever arm' to model the interdot barrier gate response and discuss how it can be used to more rapidly tune interdot tunnel couplings to the GHz values that are compatible with exchange gates.Quantum processors rely on classical hardware and controls in order to prepare, manipulate, and measure qubit states. For this reason, it is advantageous to develop tools to automate the operation of small quantum processors and routinely tune-up single qubit and two-qubit gates to maintain high performance 1-3 . Semiconductor spin qubits are a promising platform for realizing quantum computation largely due to their potential for scaling 4 . To tune up semiconductor quantum dots for operation as spin qubits requires control over the ground state charge occupation and chemical potential of each dot, as well as the interdot tunnel couplings 5 .Following the recent progress in constructing high-fidelity single-qubit and two-qubit gate operations with electron spins 6-11 , there are increasing efforts towards scaling to larger multi-qubit devices 12-15 . One of the key challenges in scaling up spin qubits is developing the software tools necessary to keep pace with increasingly complex devices. To date, approaches to implementing automated control software during tune-up of semiconductor qubits include training neural networks to identify the state of a device 16 , experimentally realizing automated control procedures for tuning double quantum dot (DQD) devices into the single-electron regime 17 , and automatically tuning the interdot tunnel coupling in a DQD [18][19][20] .In this Letter, we use an image analysis toolbox developed at Sandia National Laboratories to accurately analyze charge stability diagrams acquired from a triple quantum dot (TQD) unit cell of a 9-dot linear array 13,21 . Computer automated analysis of charge stability diagrams performs the inversion of the device capacitance matrix and the establishment of 'virtual gates'. Virtual gates compensate for cross-capacitances in the device and allow the chemical potential of each dot in the array to be independently controlled 13,22,23 . Furthermore, we use image analysis to locate interdot charge transitions and automatically perform measurements of the interdot tunnel coupling 24 . Using simple feedback protocols, we demonstrate simultaneous tune-up of the i...

We introduce two new bases of the ring of polynomials and study their relations to known bases. The first basis is the quasiLascoux basis, which is simultaneously both a K-theoretic deformation of the quasikey basis and also a lift of the K-analogue of the quasiSchur basis from quasisymmetric polynomials to general polynomials. We give positive expansions of this quasiLascoux basis into the glide and Lascoux atom bases, as well as a positive expansion of the Lascoux basis into the quasiLascoux basis. As a special case, these expansions give the first proof that the K-analogues of quasiSchur polynomials expand positively in multifundamental quasisymmetric polynomials of T. Lam and P. Pylyavskyy.The second new basis is the kaon basis, a K-theoretic deformation of the fundamental particle basis. We give positive expansions of the glide and Lascoux atom bases into this kaon basis.Throughout, we explore how the relationships among these K-analogues mirror the relationships among their cohomological counterparts. We make several 'alternating sum' conjectures that are suggestive of Euler characteristic calculations.