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MgIn2 crystallizes in the tetragonal I4/mmm space group. The structure is two-dimensional and consists of two MgIn2 sheets oriented in the (0, 0, 1) direction. Mg is bonded in a distorted body-centered cubic geometry to eight equivalent In atoms. All Mg–In bond lengths are 3.19 Å. In is bonded to four equivalent Mg atoms to form a mixture of distorted edge, corner, and face-sharing InMg4 cuboctahedra.
SrO10 crystallizes in the tetragonal P4/mcc space group. The structure is two-dimensional and consists of two hydrogen peroxide molecules and two SrO8 sheets oriented in the (0, 0, 1) direction. In each SrO8 sheet, Sr is bonded in a distorted body-centered cubic geometry to eight equivalent O atoms. All Sr–O bond lengths are 2.64 Å. O is bonded in a distorted bent 120 degrees geometry to one Sr and one O atom. The O–O bond length is 1.28 Å.
MgNd2 crystallizes in the monoclinic C2/m space group. The structure is two-dimensional and consists of two MgNd2 sheets oriented in the (1, 0, 0) direction. Mg is bonded in a body-centered cubic geometry to eight Nd atoms. There are a spread of Mg–Nd bond distances ranging from 3.36–3.43 Å. There are two inequivalent Nd sites. In the first Nd site, Nd is bonded in a 4-coordinate geometry to four equivalent Mg atoms. In the second Nd site, Nd is bonded in a 12-coordinate geometry to four equivalent Mg atoms.
MgSm2 crystallizes in the monoclinic C2/m space group. The structure is two-dimensional and consists of two MgSm2 sheets oriented in the (1, 0, 0) direction. Mg is bonded in a body-centered cubic geometry to eight Sm atoms. There are a spread of Mg–Sm bond distances ranging from 3.35–3.38 Å. There are two inequivalent Sm sites. In the first Sm site, Sm is bonded in a 12-coordinate geometry to four equivalent Mg atoms. In the second Sm site, Sm is bonded in a 12-coordinate geometry to four equivalent Mg atoms.
MoBi3 crystallizes in the monoclinic P2_1/m space group. The structure is two-dimensional and consists of one MoBi3 sheet oriented in the (1, 0, 0) direction. there are two inequivalent Mo sites. In the first Mo site, Mo is bonded in a body-centered cubic geometry to eight Bi atoms. There are a spread of Mo–Bi bond distances ranging from 2.83–3.00 Å. In the second Mo site, Mo is bonded in a 12-coordinate geometry to ten Bi atoms. There are a spread of Mo–Bi bond distances ranging from 2.84–3.45 Å. There are six inequivalent Bi sites. In the first Bi site, Bi is bonded in a 1-coordinate geometry to three equivalent Mo and one Bi atom. The Bi–Bi bond length is 3.38 Å. In the second Bi site, Bi is bonded in a 3-coordinate geometry to three Mo atoms. In the third Bi site, Bi is bonded in a 4-coordinate geometry to four Mo atoms. In the fourth Bi site, Bi is bonded in a 9-coordinate geometry to four Mo and two equivalent Bi atoms. Both Bi–Bi bond lengths are 3.28 Å. In the fifth Bi site, Bi is bonded in a 1-coordinate geometry to three Mo and five Bi atoms. Both Bi–Bi bond lengths are 3.32 Å. In the sixth Bi site, Bi is bonded in a distorted single-bond geometry to one Mo and two equivalent Bi atoms.
NiS2 crystallizes in the tetragonal I4/mmm space group. The structure is two-dimensional and consists of two NiS2 sheets oriented in the (0, 0, 1) direction. Ni4+ is bonded in a body-centered cubic geometry to eight equivalent S2- atoms. All Ni–S bond lengths are 2.46 Å. S2- is bonded in a 5-coordinate geometry to four equivalent Ni4+ and one S2- atom. The S–S bond length is 2.13 Å.
Mg2Ag crystallizes in the orthorhombic Cmcm space group. The structure is two-dimensional and consists of two Mg2Ag sheets oriented in the (0, 1, 0) direction. Mg is bonded in a 4-coordinate geometry to four equivalent Ag atoms. There are a spread of Mg–Ag bond distances ranging from 2.87–2.92 Å. Ag is bonded in a body-centered cubic geometry to eight equivalent Mg atoms.
Mg2Ga crystallizes in the orthorhombic Cmcm space group. The structure is two-dimensional and consists of two Mg2Ga sheets oriented in the (0, 1, 0) direction. Mg is bonded in a 4-coordinate geometry to four equivalent Ga atoms. There are a spread of Mg–Ga bond distances ranging from 2.95–3.01 Å. Ga is bonded in a distorted body-centered cubic geometry to eight equivalent Mg atoms.
CaO10 crystallizes in the tetragonal P4/mcc space group. The structure is two-dimensional and consists of two molecular oxygen molecules and two CaO8 sheets oriented in the (0, 0, 1) direction. In each CaO8 sheet, Ca is bonded in a body-centered cubic geometry to eight equivalent O atoms. All Ca–O bond lengths are 2.47 Å. O is bonded in a distorted bent 120 degrees geometry to one Ca and one O atom. The O–O bond length is 1.28 Å.
Ca2Mg crystallizes in the monoclinic C2/m space group. The structure is two-dimensional and consists of two Ca2Mg sheets oriented in the (1, 0, 0) direction. there are two inequivalent Ca sites. In the first Ca site, Ca is bonded in a 11-coordinate geometry to four equivalent Mg atoms. There are two shorter (3.40 Å) and two longer (3.46 Å) Ca–Mg bond lengths. In the second Ca site, Ca is bonded in a 12-coordinate geometry to four equivalent Mg atoms. There are two shorter (3.45 Å) and two longer (3.51 Å) Ca–Mg bond lengths. Mg is bonded in a body-centered cubic geometry to eight Ca atoms.
Bi2Sr2CaCu2O8 crystallizes in the orthorhombic Ccc2 space group. The structure is two-dimensional and consists of two Bi2Sr2CaCu2O8 sheets oriented in the (0, 1, 0) direction. Sr2+ is bonded in a 9-coordinate geometry to nine O2- atoms. There are a spread of Sr–O bond distances ranging from 2.58–2.94 Å. Ca2+ is bonded in a body-centered cubic geometry to eight O2- atoms. There are two shorter (2.51 Å) and six longer (2.52 Å) Ca–O bond lengths. Cu2+ is bonded in a distorted square co-planar geometry to five O2- atoms. There are four shorter (1.93 Å) and one longer (2.72 Å) Cu–O bond lengths. Bi3+ is bonded in a distorted T-shaped geometry to three O2- atoms. There are a spread of Bi–O bond distances ranging from 2.06–2.21 Å. There are four inequivalent O2- sites. In the first O2- site, O2- is bonded to two equivalent Sr2+, two equivalent Ca2+, and two equivalent Cu2+ atoms to form a mixture of distorted corner, edge, and face-sharing OSr2Ca2Cu2 octahedra. The corner-sharing octahedra tilt angles range from 0–66°. In the second O2- site, O2- is bonded in a 3-coordinate geometry to one Sr2+ and two equivalent Bi3+ atoms. In the third O2- site, O2- is bonded to two equivalent Sr2+, two equivalent Ca2+, and two equivalent Cu2+ atoms to form a mixture of distorted corner, edge, and face-sharing OSr2Ca2Cu2 octahedra. The corner-sharing octahedra tilt angles range from 0–66°. In the fourth O2- site, O2- is bonded in a 1-coordinate geometry to four equivalent Sr2+, one Cu2+, and one Bi3+ atom.
MgPr2 crystallizes in the orthorhombic Cmcm space group. The structure is two-dimensional and consists of two MgPr2 sheets oriented in the (0, 1, 0) direction. Mg is bonded in a body-centered cubic geometry to eight equivalent Pr atoms. There are four shorter (3.37 Å) and four longer (3.38 Å) Mg–Pr bond lengths. Pr is bonded in a 8-coordinate geometry to four equivalent Mg atoms.
Sc13Os3Br16 crystallizes in the orthorhombic Pnnm space group. The structure is two-dimensional and consists of two Sc13Os3Br16 sheets oriented in the (0, 0, 1) direction. there are five inequivalent Sc sites. In the first Sc site, Sc is bonded in a 6-coordinate geometry to two Os and four Br atoms. There are one shorter (2.69 Å) and one longer (2.80 Å) Sc–Os bond lengths. There are a spread of Sc–Br bond distances ranging from 2.70–3.31 Å. In the second Sc site, Sc is bonded in a 6-coordinate geometry to two Os and four Br atoms. There are one shorter (2.64 Å) and one longer (2.77 Å) Sc–Os bond lengths. There are a spread of Sc–Br bond distances ranging from 2.80–3.31 Å. In the third Sc site, Sc is bonded to two equivalent Os and four Br atoms to form distorted ScOs2Br4 octahedra that share corners with two equivalent ScBr6 octahedra, an edgeedge with one ScOs2Br4 octahedra, and faces with two equivalent ScOs2Br4 pentagonal pyramids. The corner-sharing octahedral tilt angles are 29°. Both Sc–Os bond lengths are 2.68 Å. There are a spread of Sc–Br bond distances ranging from 2.75–3.02 Å. In the fourth Sc site, Sc is bonded to two equivalent Os and four Br atoms to form a mixture of distorted edge and face-sharing ScOs2Br4 pentagonal pyramids. Both Sc–Os bond lengths are 2.76 Å. There are a spread of Sc–Br bond distances ranging from 2.80–2.84 Å. In the fifth Sc site, Sc is bonded to six Br atoms to form corner-sharing ScBr6 octahedra. The corner-sharing octahedral tilt angles are 29°. There are two shorter (2.69 Å) and four longer (2.73 Å) Sc–Br bond lengths. There are two inequivalent Os sites. In the first Os site, Os is bonded in a 8-coordinate geometry to eight Sc atoms. In the second Os site, Os is bonded in a body-centered cubic geometry to eight Sc atoms. There are six inequivalent Br sites. In the first Br site, Br is bonded in a distorted T-shaped geometry to three Sc atoms. In the second Br site, Br is bonded in a 4-coordinate geometry to four Sc atoms. In the third Br site, Br is bonded in a 3-coordinate geometry to three Sc atoms. In the fourth Br site, Br is bonded in a 4-coordinate geometry to four Sc atoms. In the fifth Br site, Br is bonded in a 2-coordinate geometry to two equivalent Sc atoms. In the sixth Br site, Br is bonded in a 2-coordinate geometry to four Sc atoms.
Sr2YbCu2(BiO4)2 crystallizes in the tetragonal I4/mmm space group. The structure is two-dimensional and consists of two Sr2YbCu2(BiO4)2 sheets oriented in the (0, 0, 1) direction. Sr2+ is bonded in a 9-coordinate geometry to nine O2- atoms. There are a spread of Sr–O bond distances ranging from 2.62–2.85 Å. Yb3+ is bonded in a body-centered cubic geometry to eight equivalent O2- atoms. All Yb–O bond lengths are 2.43 Å. Cu+1.50+ is bonded in a square co-planar geometry to five O2- atoms. There are four shorter (1.87 Å) and one longer (2.79 Å) Cu–O bond lengths. Bi3+ is bonded to five O2- atoms to form a mixture of distorted corner and edge-sharing BiO5 square pyramids. There are one shorter (2.06 Å) and four longer (2.64 Å) Bi–O bond lengths. There are three inequivalent O2- sites. In the first O2- site, O2- is bonded to two equivalent Sr2+, two equivalent Yb3+, and two equivalent Cu+1.50+ atoms to form distorted OSr2Yb2Cu2 octahedra that share corners with eight equivalent OSr2Yb2Cu2 octahedra, corners with two equivalent OSrBi4 square pyramids, edges with three equivalent OSr2Yb2Cu2 octahedra, and faces with four equivalent OSr2Yb2Cu2 octahedra. The corner-sharing octahedra tilt angles range from 0–66°. In the second O2- site, O2- is bonded to one Sr2+ and four equivalent Bi3+ atoms to form distorted OSrBi4 square pyramids that share corners with four equivalent OSr2Yb2Cu2 octahedra, corners with four equivalent OSrBi4 square pyramids, and edges with four equivalent OSrBi4 square pyramids. The corner-sharing octahedral tilt angles are 45°. In the third O2- site, O2- is bonded in a 1-coordinate geometry to four equivalent Sr2+, one Cu+1.50+, and one Bi3+ atom.
Sr2Mg1 crystallizes in the monoclinic C2/m space group. The structure is two-dimensional and consists of two Sr2Mg1 sheets oriented in the (1, 0, 0) direction. there are two inequivalent Sr sites. In the first Sr site, Sr is bonded in a 4-coordinate geometry to four equivalent Mg atoms. All Sr–Mg bond lengths are 3.63 Å. In the second Sr site, Sr is bonded in a 4-coordinate geometry to four equivalent Mg atoms. All Sr–Mg bond lengths are 3.62 Å. Mg is bonded in a body-centered cubic geometry to eight Sr atoms.
BaO10 crystallizes in the tetragonal P4/mcc space group. The structure is two-dimensional and consists of two oxygen molecules and two BaO8 sheets oriented in the (0, 0, 1) direction. In each BaO8 sheet, Ba is bonded in a body-centered cubic geometry to eight equivalent O atoms. All Ba–O bond lengths are 2.82 Å. O is bonded in a bent 120 degrees geometry to one Ba and one O atom. The O–O bond length is 1.29 Å.
MgPr2 crystallizes in the monoclinic C2/m space group. The structure is two-dimensional and consists of two MgPr2 sheets oriented in the (1, 0, 0) direction. Mg is bonded in a body-centered cubic geometry to eight Pr atoms. There are a spread of Mg–Pr bond distances ranging from 3.40–3.43 Å. There are two inequivalent Pr sites. In the first Pr site, Pr is bonded in a 4-coordinate geometry to four equivalent Mg atoms. In the second Pr site, Pr is bonded in a 12-coordinate geometry to four equivalent Mg atoms.
Scalable quantum algorithms for the simulation of quantum many-body systems in thermal equilibrium are important for predicting properties of quantum matter at finite temperatures. Here we describe and benchmark a quantum computing version of the minimally entangled typical thermal states (METTS) algorithm for which we adopt an adaptive variational approach to perform the required quantum imaginary time evolution. The algorithm, which we name AVQMETTS, dynamically generates compact and problem-specific quantum circuits, which are suitable for noisy intermediate-scale quantum (NISQ) hardware. We benchmark AVQMETTS on statevector simulators and perform thermal energy calculations of integrable and nonintegrable quantum spin models in one and two dimensions and demonstrate an approximately linear system-size scaling of the circuit complexity. We further map out the finite-temperature phase transition line of the two-dimensional transverse field Ising model. Finally, we study the impact of noise on AVQMETTS calculations using a phenomenological noise model.