Benchmark AI / Public workspace

CritPt / Tasks

Choose a problem to read its original content, examples and discussion.

Option counts cover the whole public benchmark.

Clear filters

1–50 / 70 tasks

• Default config / train

  Consider a (1+1)-D Lagrangian that consists of a Majorana fermion χ and…

  Answer published by the source

  Identifiers

  upstream_id

  Challenge_11_main

  task_id

  43549b5b-12fb-5540-8faf-06bf7ba110a0

  task_key

  train--Challenge~5f11~5fmain

• Default config / train

  Consider the following spin model on a torus

  Answer published by the source

  Identifiers

  upstream_id

  Challenge_14_main

  task_id

  4b32f00a-e2f7-5424-abc5-434a34fe31f3

  task_key

  train--Challenge~5f14~5fmain

• Default config / train

  The Hamiltonian is

  Answer published by the source

  Identifiers

  upstream_id

  Challenge_15_main

  task_id

  47d9e4aa-1c42-5976-a55c-556b55602b63

  task_key

  train--Challenge~5f15~5fmain

• Default config / train

  Consider the following Hamiltonian in two dimensions on a square lattice:

  Answer published by the source

  Identifiers

  upstream_id

  Challenge_16_main

  task_id

  44768ddb-c30f-5e2f-be38-d96d9fefcb1b

  task_key

  train--Challenge~5f16~5fmain

• Default config / train

  Consider the following Hamiltonian:…

  Answer published by the source

  Identifiers

  upstream_id

  Challenge_17_main

  task_id

  7367714e-8073-56b0-9cbe-5c2ed657958e

  task_key

  train--Challenge~5f17~5fmain

• Default config / train

  Consider two cascaded optical parametric amplifiers (OPAs) pumped by lasers at…

  Answer published by the source

  Identifiers

  upstream_id

  Challenge_19_main

  task_id

  979590b9-1f63-52db-a3c4-cb8a59b03528

  task_key

  train--Challenge~5f19~5fmain

• Default config / train

  Two identical dielectric ellipsoids are confined in two Gaussian optical…

  Answer published by the source

  Identifiers

  upstream_id

  Challenge_20_main

  task_id

  00f3dda1-5be1-5b35-9710-4134f2eb7656

  task_key

  train--Challenge~5f20~5fmain

• Default config / train

  The matching formula in the large-momentum effective theory (LaMET) gives

  Answer published by the source

  Identifiers

  upstream_id

  Challenge_21_main

  task_id

  2c649737-8944-59e9-90b2-c2e5df2b786c

  task_key

  train--Challenge~5f21~5fmain

• Default config / train

  Optimize the Holevo information over cq states …

  Answer published by the source

  Identifiers

  upstream_id

  Challenge_22_main

  task_id

  76ca5c11-31d0-519d-ae55-4443e5a9ff0b

  task_key

  train--Challenge~5f22~5fmain

• Default config / train

  In the framework of large-momentum effective theory (LaMET), the parton…

  Answer published by the source

  Identifiers

  upstream_id

  Challenge_24_main

  task_id

  4a9c932f-668f-5555-8d1c-f149666beae8

  task_key

  train--Challenge~5f24~5fmain

• Default config / train

  A distant energetic astrophysical object contains a single, spherical emission…

  Answer published by the source

  Identifiers

  upstream_id

  Challenge_25_main

  task_id

  b118f446-7ff9-5b5b-93a4-929977b80db3

  task_key

  train--Challenge~5f25~5fmain

• Default config / train

  Consider a one-axis twisting interaction described by the Hamiltonian…

  Answer published by the source

  Identifiers

  upstream_id

  Challenge_27_main

  task_id

  915fb20c-0cc3-51b0-9f3f-6bc118a07775

  task_key

  train--Challenge~5f27~5fmain

• Default config / train

  Consider a four-dimensional hypercubic lattice with lattice spacing a and…

  Answer published by the source

  Identifiers

  upstream_id

  Challenge_28_main

  task_id

  26a20460-a6bc-5854-a421-c9f4df58a2f8

  task_key

  train--Challenge~5f28~5fmain

• Default config / train

  Fermionic atoms trapped in an optical lattice are used to simulate the Hubbard…

  Answer published by the source

  Identifiers

  upstream_id

  Challenge_29_main

  task_id

  0f0a7e02-ffb4-54cd-ae1d-0b7b13d7285b

  task_key

  train--Challenge~5f29~5fmain

• Default config / train

  Consider a population of genetically identical bacterial cells in balanced…

  Answer published by the source

  Identifiers

  upstream_id

  Challenge_2_main

  task_id

  112c22b8-d4b4-5dda-aa61-40533999670d

  task_key

  train--Challenge~5f2~5fmain

• Default config / train

  Consider flow between two parallel plates heated from below and cooled from…

  Answer published by the source

  Identifiers

  upstream_id

  Challenge_31_main

  task_id

  53634481-bef5-5a83-9be9-c3cffe4819f4

  task_key

  train--Challenge~5f31~5fmain

• Default config / train

  Consider natural convection in a porous medium modeled by Darcy's law (i.e.,…

  Answer published by the source

  Identifiers

  upstream_id

  Challenge_32_main

  task_id

  142adaa4-3e48-5f0e-b23c-850e266eb270

  task_key

  train--Challenge~5f32~5fmain

• Default config / train

  Consider the Hamiltonian for three kinds of particles labeled by A, B, C:

  Answer published by the source

  Identifiers

  upstream_id

  Challenge_33_main

  task_id

  1d5de58e-6b53-5db1-aa62-b00cd23784f9

  task_key

  train--Challenge~5f33~5fmain

• Default config / train

  We will explore a simple example of a quantum tensor network, a tensor network…

  Answer published by the source

  Identifiers

  upstream_id

  Challenge_34_main

  task_id

  94ee7dfb-6a27-5e60-abe2-e039051c77eb

  task_key

  train--Challenge~5f34~5fmain

• Default config / train

  In quantum mechanics, we are often interested in solving the problem of finding…

  Answer published by the source

  Identifiers

  upstream_id

  Challenge_35_main

  task_id

  62ceaff2-4985-54b4-9cd6-4d9028d59afb

  task_key

  train--Challenge~5f35~5fmain

• Default config / train

  In the following autocatalytic reaction cycle, each component catalyzes the…

  Answer published by the source

  Identifiers

  upstream_id

  Challenge_36_main

  task_id

  9af1cbe6-92c0-51b0-8314-cec0f36289d8

  task_key

  train--Challenge~5f36~5fmain

• Default config / train

  The Hamiltonian for the Hatsugai-Kohmoto (HK) model is

  Answer published by the source

  Identifiers

  upstream_id

  Challenge_38_main

  task_id

  55985a73-5bf0-5af2-9126-408dfad041b5

  task_key

  train--Challenge~5f38~5fmain

• Default config / train

  Effective field theory is a powerful tool used to construct phenomenological…

  Answer published by the source

  Identifiers

  upstream_id

  Challenge_40_main

  task_id

  2f16bf90-a9e3-5b89-97c9-846da494fe76

  task_key

  train--Challenge~5f40~5fmain

• Default config / train

  In a real-space quantum Monte Carlo simulation of a crystal, only a finite…

  Answer published by the source

  Identifiers

  upstream_id

  Challenge_41_main

  task_id

  9f682704-9d06-5932-a4bd-92a45b23f700

  task_key

  train--Challenge~5f41~5fmain

• Default config / train

  Consider a graphene layer sitting on a 3D substrate. The substrate has charged…

  Answer published by the source

  Identifiers

  upstream_id

  Challenge_42_main

  task_id

  78ee7458-5db5-5e0f-96a7-580d4c29a0c2

  task_key

  train--Challenge~5f42~5fmain

• Default config / train

  Consider the Kitaev honeycomb model at the isotropic limit (assuming…

  Answer published by the source

  Identifiers

  upstream_id

  Challenge_44_main

  task_id

  3d6dcf73-116a-5217-8a0e-e0e4af721133

  task_key

  train--Challenge~5f44~5fmain

• Default config / train

  In goniopolar materials, the thermal power can be n-type in one direction and…

  Answer published by the source

  Identifiers

  upstream_id

  Challenge_45_main

  task_id

  4ae8b035-20b5-5082-af8a-c7b6e94a69ed

  task_key

  train--Challenge~5f45~5fmain

• Default config / train

  Let (m)→(x,t) be a classical spin field defined for xinmathbb R and…

  Answer published by the source

  Identifiers

  upstream_id

  Challenge_47_main

  task_id

  7e3c544c-7278-53eb-ab9c-d810c34d63a2

  task_key

  train--Challenge~5f47~5fmain

• Default config / train

  In a long-range dispersal model, a cluster of species can grow from a single…

  Answer published by the source

  Identifiers

  upstream_id

  Challenge_49_main

  task_id

  aa640307-facc-58b5-b802-2e0182b96568

  task_key

  train--Challenge~5f49~5fmain

• Default config / train

  High-harmonic generation (HHG) is a nonlinear optical process in which intense…

  Answer published by the source

  Identifiers

  upstream_id

  Challenge_4_main

  task_id

  4c319585-7cdc-51d0-a3dd-0ff3dff68989

  task_key

  train--Challenge~5f4~5fmain

• Default config / train

  Consider a composite particle initially (t=0) positioned at x₀=0 on a…

  Answer published by the source

  Identifiers

  upstream_id

  Challenge_51_main

  task_id

  a352fcc1-a923-5811-a5d6-ab59b935b696

  task_key

  train--Challenge~5f51~5fmain

• Default config / train

  The Efimov effect is one of the few examples of a three-body problem that can be…

  Answer published by the source

  Identifiers

  upstream_id

  Challenge_52_main

  task_id

  1eac0cb3-7e5c-5af7-bbab-2affe8f37956

  task_key

  train--Challenge~5f52~5fmain

• Default config / train

  Consider a scalar field ϕ linearly coupled to the standard model…

  Answer published by the source

  Identifiers

  upstream_id

  Challenge_56_main

  task_id

  017ec79f-1e88-584b-8d8b-a6418ec87fcb

  task_key

  train--Challenge~5f56~5fmain

• Default config / train

  Consider a condensed matter system going through a magnetic phase transition.…

  Answer published by the source

  Identifiers

  upstream_id

  Challenge_58_main

  task_id

  766b0cc2-fead-5309-bc39-04f14f1fe8da

  task_key

  train--Challenge~5f58~5fmain

• Default config / train

  Consider a simple cubic crystal with a static periodic strain field of long…

  Answer published by the source

  Identifiers

  upstream_id

  Challenge_59_main

  task_id

  86c86e08-b464-5459-b5b9-23141c16de50

  task_key

  train--Challenge~5f59~5fmain

• Default config / train

  Let α∈[0,1] be a real parameter. Define the function f(n,α)…

  Answer published by the source

  Identifiers

  upstream_id

  Challenge_5_main

  task_id

  0a033e35-140a-5604-84a6-d78e8af0e7a1

  task_key

  train--Challenge~5f5~5fmain

• Default config / train

  In this problem, we want to consider the resolution of single-lens imaging of…

  Answer published by the source

  Identifiers

  upstream_id

  Challenge_60_main

  task_id

  34748c84-167f-566b-99dd-91ef2966844e

  task_key

  train--Challenge~5f60~5fmain

• Default config / train

  We replace each of the M/2+1 vertices of an M/2-simplex with

  Answer published by the source

  Identifiers

  upstream_id

  Challenge_61_main

  task_id

  43c060bd-17bc-5e82-9e7b-4dbf3b490954

  task_key

  train--Challenge~5f61~5fmain

• Default config / train

  Quantum superposition of a single particle can be demonstrated by the…

  Answer published by the source

  Identifiers

  upstream_id

  Challenge_62_main

  task_id

  8d11aa00-f6d3-5de4-a1e0-476676d3ebb1

  task_key

  train--Challenge~5f62~5fmain

• Default config / train

  Quantum contextuality, like Bell nonlocality, is a key signature of…

  Answer published by the source

  Identifiers

  upstream_id

  Challenge_63_main

  task_id

  0fdd6732-8137-5459-9da6-aec30c170683

  task_key

  train--Challenge~5f63~5fmain

• Default config / train

  We consider the two-dimensional Ising conformal field theory.

  Answer published by the source

  Identifiers

  upstream_id

  Challenge_64_main

  task_id

  593a2931-aa62-525b-89dd-42cf9d6c3765

  task_key

  train--Challenge~5f64~5fmain

• Default config / train

  Consider a fermion field ψ that is in the adjoint representations of a…

  Answer published by the source

  Identifiers

  upstream_id

  Challenge_65_main

  task_id

  327718c8-3fba-5242-bcad-f9fcccd8114a

  task_key

  train--Challenge~5f65~5fmain

• Default config / train

  Consider fermion fields that are adjoint representations of a U(N) gauge…

  Answer published by the source

  Identifiers

  upstream_id

  Challenge_66_main

  task_id

  b3d77d3e-865b-56e0-a256-6fdc4d63929c

  task_key

  train--Challenge~5f66~5fmain

• Default config / train

  We study the fundamental limit of a quantum channel called the private channel.…

  Answer published by the source

  Identifiers

  upstream_id

  Challenge_67_main

  task_id

  83217e10-1925-5c4c-8117-a0460804bb70

  task_key

  train--Challenge~5f67~5fmain

• Default config / train

  The quantum f-divergence is defined by …

  Answer published by the source

  Identifiers

  upstream_id

  Challenge_68_main

  task_id

  1220bd73-c482-56b8-b22d-35ffda192359

  task_key

  train--Challenge~5f68~5fmain

• Default config / train

  Suppose the quantum amplitude damping channel acting on a qubit system is…

  Answer published by the source

  Identifiers

  upstream_id

  Challenge_69_main

  task_id

  70e5fa51-5e86-5e0e-a05d-b2d58522e47b

  task_key

  train--Challenge~5f69~5fmain

• Default config / train

  For twisted bilayer MoTe_2, we can build the following simplified continuum…

  Answer published by the source

  Identifiers

  upstream_id

  Challenge_6_main

  task_id

  29f111ff-0ac8-522d-b9d6-de2c03f02c87

  task_key

  train--Challenge~5f6~5fmain

• Default config / train

  Put 4n qubits on a lattice of n rows and 4 columns. Let…

  Answer published by the source

  Identifiers

  upstream_id

  Challenge_70_main

  task_id

  aafd0ef3-cefb-527a-99d2-e82346e74ef8

  task_key

  train--Challenge~5f70~5fmain

• Default config / train

  In order to introduce torsion to the system, one can use the first-order…

  Answer published by the source

  Identifiers

  upstream_id

  Challenge_8_main

  task_id

  757044b3-fd81-5f78-b39a-5d3a709ea62e

  task_key

  train--Challenge~5f8~5fmain

• Default config / train

  In order to introduce torsion to the system, one can use the first-order…

  Answer published by the source

  Identifiers

  upstream_id

  Challenge_9_main

  task_id

  b3161130-e3a1-547a-b6e5-124d59b2de24

  task_key

  train--Challenge~5f9~5fmain