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DOE OSTI2020

Materials Data on PrPS by Materials Project

PrPS crystallizes in the orthorhombic Pnma space group. The structure is three-dimensional. there are two inequivalent Pr3+ sites. In the first Pr3+ site, Pr3+ is bonded in a 9-coordinate geometry to four equivalent P1- and five S2- atoms. There are two shorter (3.24 Å) and two longer (3.29 Å) Pr–P bond lengths. There are a spread of Pr–S bond distances ranging from 2.88–3.01 Å. In the second Pr3+ site, Pr3+ is bonded in a 9-coordinate geometry to four equivalent P1- and five S2- atoms. There are two shorter (3.00 Å) and two longer (3.23 Å) Pr–P bond lengths. There are a spread of Pr–S bond distances ranging from 2.86–2.95 Å. P1- is bonded in a distorted hexagonal planar geometry to four Pr3+ and two equivalent P1- atoms. There are one shorter (2.24 Å) and one longer (2.28 Å) P–P bond lengths. There are two inequivalent S2- sites. In the first S2- site, S2- is bonded to five Pr3+ atoms to form a mixture of distorted edge and corner-sharing SPr5 trigonal bipyramids. In the second S2- site, S2- is bonded to five Pr3+ atoms to form a mixture of distorted edge and corner-sharing SPr5 trigonal bipyramids.

36 MATERIALS SCIENCE↗

DOE OSTI2026

PIPS-2025: an updated practical pressure scale for the large-volume presses

In 1997, AIRAPT recommended a set of room-temperature pressure reference points (PRPs) for the large-volume press (LVP) community, known as the Practical International Pressure Scale (PIPS-97). With recent AIRAPT-recommended ruby scale Ruby2020 for diamond-anvil cell (DAC) experiments, it is now necessary to re-examine PIPS-97 for consistency with the DAC pressure scale. Here, we reconstruct equations of state (EOSs) for NaCl and Au that are explicitly tied to Ruby2020 and recalculate the PRPs using these EOSs. The revised PRP values are given. GaAs is removed from the PRP list because of the complexity of its phase transitions. The ZnS value, although retained, requires further investigation. Overall, the revised pressures are systematically higher than PIPS-97 by up to 4% at 35 GPa. We propose that this updated set of PRPs, referred to as PIPS-2025, be adopted for LVP experiments to improve pressure consistency between the LVP and DAC communities.

Large volume press↗

DOE OSTI2024

Efficient Unitary Designs from Random Sums and Permutations

A unitary k-design is an ensemble of unitaries that matches the first k moments of the Haar measure. In this work, we provide two efficient constructions of k-designs on n-qubits using new random matrix theory techniques. Our first construction is based on exponentiating sums of random i.i.d. Hermitian matrices and uses O(k2n2)-many gates. In the spirit of central limit theorems, we show that this random sum approximates the Gaussian Unitary Ensemble (GUE). We then show that the product of just two exponentiated GUE matrices is already approximately Haar random. Our second construction is based on products of exponentiated sums of random permutations and uses Õ(k poly (n)) many gates. The k dependence is optimal (up to polylogarithmic factors) and is inherited from the efficiency of existing k-wise independent permutations. Furthermore, replacing random permutations with quantum-secure pseudorandom permutations (PRPs), we also obtain a pseudorandom unitary (PRU) ensemble that is secure under nonadaptive queries. A central feature of both proofs is a new connection between the polynomial method in quantum query complexity and the large-dimension (N) expansion in random matrix theory. In particular, the first construction uses the polynomial method to control high moments of certain random matrix ensembles without requiring delicate Weingarten calculations. In doing so, we define and solve a moment problem on the unit circle, asking whether a finite number of equally weighted points can reproduce a given set of moments. In our second construction, the key step is to exhibit an orthonormal basis for irreducible representations of the partition algebra that has a low-degree large-N expansion. This allows us to show that the distinguishing probability is a low-degree rational polynomial of the dimension N.

algebra↗