Quantum circuit design & simulation
Build, transpile and simulate quantum circuits to a fidelity or result target.
20 project-authored proposals · taxonomy v1.1 · 0 new benchmark runs. Verifiers and partial-credit rules below are designs, not executed results.
- Typical applications
- Qiskit · Cirq · IBM Quantum Composer
- Class GUI-need label
CL· CLI-sufficient
Task proposals · 20
Expand to inspect the complete original wording and proposed checks. Original proposal text remains English in both interfaces.
R03.07.01.02-T01 Prepare and verify a Bell state
Original instruction
In Qiskit, build a circuit that prepares the Bell state (|00>+|11>)/sqrt(2) from |00>, save the statevector, and also run 4096 shots with measurement. Write the statevector and the measured counts to result.json.
- Platforms
lin· Linuxmac· macOSwin· Windows- Applications
- Qiskit
- Interfaces
term· Terminal- GUI need · task setting
CL· CLI-sufficient- GUI need · ordinary access
CL· CLI-sufficient- Interaction primitives
code· Code & commandstype· Text & forms- Work product
WP07· Simulation result- Conditions
- None declared
- Proposed difficulty
- 2 / 5
Proposed verifier
Statevector fidelity to the target Bell state >= 0.999; measured counts are ~50/50 between 00 and 11 (TVD to ideal < 0.05) with negligible 01/10. Graded by re-running the saved circuit.
Proposed partial credit
50% correct statevector; 50% measurement distribution matches
R03.07.01.02-T02 GHZ state on n qubits
Original instruction
Write a Qiskit function that builds an n-qubit GHZ state (|0..0>+|1..1>)/sqrt(2) for a given n, and generate the circuit for n=5. Save the statevector and 4096-shot counts for n=5 to result.json.
- Platforms
lin· Linuxmac· macOSwin· Windows- Applications
- Qiskit · Cirq
- Interfaces
term· Terminal- GUI need · task setting
CL· CLI-sufficient- GUI need · ordinary access
CL· CLI-sufficient- Interaction primitives
code· Code & commandstype· Text & forms- Work product
WP07· Simulation result- Conditions
- None declared
- Proposed difficulty
- 3 / 5
Proposed verifier
n=5 statevector fidelity to GHZ >= 0.999; counts concentrate on 00000 and 11111 (TVD < 0.05); the function generalizes (checked for n=3,4). Graded by re-running the circuit builder.
Proposed partial credit
40% general builder correct; 30% n=5 statevector; 30% measurement distribution
R03.07.01.02-T03 Prepare a W state
Original instruction
Build a circuit preparing the 3-qubit W state (|100>+|010>+|001>)/sqrt(3). Save the statevector and measured counts (4096 shots) to result.json. Use controlled rotations; no post-selection.
- Platforms
lin· Linuxmac· macOSwin· Windows- Applications
- Qiskit
- Interfaces
term· Terminal- GUI need · task setting
CL· CLI-sufficient- GUI need · ordinary access
CL· CLI-sufficient- Interaction primitives
code· Code & commandstype· Text & forms- Work product
WP07· Simulation result- Conditions
- None declared
- Proposed difficulty
- 3 / 5
Proposed verifier
Statevector fidelity to the W state >= 0.999; counts split ~1/3 each across 100/010/001 (TVD < 0.05), no post-selection. Graded by re-running the circuit.
Proposed partial credit
60% correct statevector (no post-selection); 40% measurement distribution
R03.07.01.02-T04 Quantum Fourier transform
Original instruction
Implement the 4-qubit QFT as a circuit in Qiskit (with the final qubit swaps). Verify it against the exact QFT matrix and output the circuit's unitary and its max elementwise error vs reference to result.json.
- Platforms
lin· Linuxmac· macOSwin· Windows- Applications
- Qiskit
- Interfaces
term· Terminal- GUI need · task setting
CL· CLI-sufficient- GUI need · ordinary access
CL· CLI-sufficient- Interaction primitives
code· Code & commandstype· Text & forms- Work product
WP07· Simulation result- Conditions
- None declared
- Proposed difficulty
- 3 / 5
Proposed verifier
The circuit's unitary matches the exact 4-qubit QFT (max elementwise error < 1e-6 after accounting for the swaps). Graded by comparing unitaries.
Proposed partial credit
40% QFT rotations correct; 30% swaps included; 30% unitary matches within tolerance
R03.07.01.02-T05 Grover search for a marked state
Original instruction
Given the 3-qubit oracle marking state |101> in fixtures/qc/oracle.py, build Grover's algorithm with the optimal number of iterations, run 4096 shots, and write the counts and the most-probable state to result.json.
- Platforms
lin· Linuxmac· macOSwin· Windows- Applications
- Qiskit · Cirq
- Interfaces
term· Terminal- GUI need · task setting
CL· CLI-sufficient- GUI need · ordinary access
CL· CLI-sufficient- Interaction primitives
code· Code & commandstype· Text & forms- Work product
WP07· Simulation result- Conditions
- None declared
- Proposed difficulty
- 3 / 5
Proposed verifier
The marked state 101 is the most frequent outcome with probability >= 0.9; the iteration count matches the optimal for 3 qubits. Graded by re-running the circuit.
Proposed partial credit
30% oracle+diffuser correct; 30% optimal iterations; 40% marked state dominates
R03.07.01.02-T06 Deutsch-Jozsa classification
Original instruction
For each of the two oracles in fixtures/qc/dj_oracles.py (one constant, one balanced over 3 input qubits), build the Deutsch-Jozsa circuit and determine which is which from a single query each. Write the verdicts to result.json.
- Platforms
lin· Linuxmac· macOSwin· Windows- Applications
- Qiskit
- Interfaces
term· Terminal- GUI need · task setting
CL· CLI-sufficient- GUI need · ordinary access
CL· CLI-sufficient- Interaction primitives
code· Code & commandstype· Text & forms- Work product
WP12· Answer/decision- Conditions
- None declared
- Proposed difficulty
- 3 / 5
Proposed verifier
Both oracles correctly classified as constant/balanced from the all-zeros measurement outcome (constant => all zeros, balanced => not). Graded by the reported verdicts.
Proposed partial credit
50% circuit correct; 50% both verdicts correct
R03.07.01.02-T07 Bernstein-Vazirani hidden string
Original instruction
The oracle in fixtures/qc/bv_oracle.py encodes a hidden 5-bit string. Build the Bernstein-Vazirani circuit to recover it in one query and write the recovered string to result.json.
- Platforms
lin· Linuxmac· macOSwin· Windows- Applications
- Qiskit
- Interfaces
term· Terminal- GUI need · task setting
CL· CLI-sufficient- GUI need · ordinary access
CL· CLI-sufficient- Interaction primitives
code· Code & commandstype· Text & forms- Work product
WP12· Answer/decision- Conditions
- None declared
- Proposed difficulty
- 2 / 5
Proposed verifier
The recovered 5-bit string equals the hidden string the oracle encodes. Graded by the reported string.
Proposed partial credit
40% circuit correct; 60% exact hidden string recovered
R03.07.01.02-T08 Quantum teleportation fidelity
Original instruction
Build a teleportation circuit that transfers an arbitrary single-qubit state (prepared by a given Ry(theta),Rz(phi)) from Alice to Bob using an entangled pair and classical correction. For theta=1.1, phi=0.7, report the fidelity of Bob's output to the input state to result.json.
- Platforms
lin· Linuxmac· macOSwin· Windows- Applications
- Qiskit
- Interfaces
term· Terminal- GUI need · task setting
CL· CLI-sufficient- GUI need · ordinary access
CL· CLI-sufficient- Interaction primitives
code· Code & commandstype· Text & forms- Work product
WP07· Simulation result- Conditions
- None declared
- Proposed difficulty
- 4 / 5
Proposed verifier
Bob's reduced state has fidelity >= 0.999 to the prepared input for the given angles (and for two spot-check angle pairs); classical corrections applied. Graded by re-simulation.
Proposed partial credit
30% entanglement+Bell measurement; 30% classical corrections; 40% fidelity >= 0.999
R03.07.01.02-T09 Transpile to a coupling map under CX budget
Original instruction
Transpile the circuit in fixtures/qc/circ.qasm to the linear coupling map in fixtures/qc/coupling.json using only {cx, rz, sx, x} basis, minimizing two-qubit gate count. Save the transpiled QASM and report its CX count and depth to result.json.
- Platforms
lin· Linuxmac· macOSwin· Windows- Applications
- Qiskit
- Interfaces
term· Terminal- GUI need · task setting
CL· CLI-sufficient- GUI need · ordinary access
CL· CLI-sufficient- Interaction primitives
code· Code & commandstype· Text & forms- Work product
WP06· Code/engineering- Conditions
- None declared
- Proposed difficulty
- 5 / 5
Proposed verifier
The transpiled circuit is equivalent to the original (unitary/statevector match within 1e-6), respects the coupling map and basis, and its CX count and depth are <= the stated budget. Graded by equivalence + topology + gate-count checks.
Proposed partial credit
30% equivalent circuit; 30% respects coupling+basis; 40% CX count/depth within budget
R03.07.01.02-T10 VQE ground-state energy of H2
Original instruction
Using the H2 molecular Hamiltonian in fixtures/qc/h2_hamiltonian.json (qubit operator), run VQE with a hardware-efficient ansatz and a classical optimizer to estimate the ground-state energy at the given bond length. Write the energy and optimal parameters to result.json.
- Platforms
lin· Linuxmac· macOSwin· Windows- Applications
- Qiskit · PennyLane
- Interfaces
term· Terminal- GUI need · task setting
CL· CLI-sufficient- GUI need · ordinary access
CL· CLI-sufficient- Interaction primitives
code· Code & commandstype· Text & forms- Work product
WP07· Simulation result- Conditions
long· Long-horizon- Proposed difficulty
- 5 / 5
Proposed verifier
The reported energy is within chemical accuracy (1.6e-3 Hartree) of the exact diagonalization value for the given Hamiltonian. Graded by comparing to the reference eigenvalue.
Proposed partial credit
30% ansatz+expectation wiring; 30% optimization converges; 40% energy within chemical accuracy
R03.07.01.02-T11 QAOA for max-cut
Original instruction
For the 6-node graph in fixtures/qc/maxcut.json, build a depth-p=2 QAOA circuit, optimize the parameters, sample the result, and output the best cut bitstring and its cut value to result.json.
- Platforms
lin· Linuxmac· macOSwin· Windows- Applications
- Qiskit · Cirq
- Interfaces
term· Terminal- GUI need · task setting
CL· CLI-sufficient- GUI need · ordinary access
CL· CLI-sufficient- Interaction primitives
code· Code & commandstype· Text & forms- Work product
WP07· Simulation result- Conditions
long· Long-horizon- Proposed difficulty
- 5 / 5
Proposed verifier
The returned cut value equals the graph's maximum cut (verified by brute force on 6 nodes); the bitstring is a valid partition achieving it. Graded by recomputing the cut.
Proposed partial credit
30% QAOA circuit correct; 30% optimization; 40% max cut achieved
R03.07.01.02-T12 Quantum phase estimation
Original instruction
Estimate the phase of the eigenvalue of a given unitary (a Z-rotation by 2*pi*phi, phi=0.375) using 4 counting qubits of QPE. Output the measured phase estimate and its binary readout to result.json.
- Platforms
lin· Linuxmac· macOSwin· Windows- Applications
- Qiskit
- Interfaces
term· Terminal- GUI need · task setting
CL· CLI-sufficient- GUI need · ordinary access
CL· CLI-sufficient- Interaction primitives
code· Code & commandstype· Text & forms- Work product
WP07· Simulation result- Conditions
- None declared
- Proposed difficulty
- 4 / 5
Proposed verifier
The most-probable readout corresponds to phi=0.375 exactly (0.0110 on 4 bits) with probability >= 0.9. Graded by re-running the QPE circuit.
Proposed partial credit
30% controlled-unitary powers; 30% inverse QFT; 40% correct phase readout
R03.07.01.02-T13 Simon's algorithm period recovery
Original instruction
The oracle in fixtures/qc/simon_oracle.py hides a 3-bit secret s. Build Simon's circuit, collect enough independent measurement outcomes to solve the linear system, and recover s. Write s to result.json.
- Platforms
lin· Linuxmac· macOSwin· Windows- Applications
- Qiskit
- Interfaces
term· Terminal- GUI need · task setting
CL· CLI-sufficient- GUI need · ordinary access
CL· CLI-sufficient- Interaction primitives
code· Code & commandstype· Text & forms- Work product
WP12· Answer/decision- Conditions
- None declared
- Proposed difficulty
- 3 / 5
Proposed verifier
The recovered secret s equals the oracle's hidden string; the solved linear system over GF(2) is consistent with the sampled outcomes. Graded by the reported s.
Proposed partial credit
40% circuit+sampling; 30% GF(2) solve; 30% correct secret
R03.07.01.02-T14 Noisy circuit error estimate
Original instruction
Simulate the GHZ(3) circuit under the depolarizing noise model in fixtures/qc/noise.json (per-gate error rates) for 8192 shots. Report the measured fidelity drop vs the ideal GHZ distribution (TVD) to result.json.
- Platforms
lin· Linuxmac· macOSwin· Windows- Applications
- Qiskit
- Interfaces
term· Terminal- GUI need · task setting
CL· CLI-sufficient- GUI need · ordinary access
CL· CLI-sufficient- Interaction primitives
code· Code & commandstype· Text & forms- Work product
WP07· Simulation result- Conditions
- None declared
- Proposed difficulty
- 4 / 5
Proposed verifier
The reported TVD between the noisy and ideal distributions matches a reference run with the same noise model within +/-0.02. Graded by re-running with the fixed seed/noise model.
Proposed partial credit
40% noise model applied correctly; 30% distribution collected; 30% TVD within tolerance
R03.07.01.02-T15 Repetition-code logical error rate with Stim
Original instruction
Using Stim, build the distance-5 repetition code memory experiment under the circuit-level depolarizing model in fixtures/qc/stim_params.json, simulate 1e5 shots, decode, and report the logical error rate with a confidence interval to result.json.
- Platforms
lin· Linuxmac· macOSwin· Windows- Applications
- Stim
- Interfaces
term· Terminal- GUI need · task setting
CL· CLI-sufficient- GUI need · ordinary access
CL· CLI-sufficient- Interaction primitives
code· Code & commandstype· Text & forms- Work product
WP07· Simulation result- Conditions
long· Long-horizon- Proposed difficulty
- 5 / 5
Proposed verifier
The reported logical error rate falls within the reference confidence interval for the given code distance and error model. Graded by re-running the Stim experiment at the fixed parameters.
Proposed partial credit
30% correct circuit built; 30% simulation+decoding; 40% logical error rate within CI
R03.07.01.02-T16 Superdense coding
Original instruction
Implement superdense coding: encode each of the four 2-bit messages onto one half of a Bell pair and decode to recover the bits. Verify all four messages round-trip and write the per-message decoded bits to result.json.
- Platforms
lin· Linuxmac· macOSwin· Windows- Applications
- Qiskit
- Interfaces
term· Terminal- GUI need · task setting
CL· CLI-sufficient- GUI need · ordinary access
CL· CLI-sufficient- Interaction primitives
code· Code & commandstype· Text & forms- Work product
WP07· Simulation result- Conditions
- None declared
- Proposed difficulty
- 3 / 5
Proposed verifier
All four 2-bit messages are decoded correctly with probability ~1 (TVD < 0.02 each). Graded by re-running the encode/decode for each message.
Proposed partial credit
40% Bell pair + encoding gates; 60% all four messages round-trip
R03.07.01.02-T17 Pauli observable expectation
Original instruction
For the state prepared by fixtures/qc/prep.py, estimate <Z0 Z1> and <X0 X1> by appropriate basis changes and 8192-shot measurement. Write both expectation values to result.json.
- Platforms
lin· Linuxmac· macOSwin· Windows- Applications
- Qiskit · PennyLane
- Interfaces
term· Terminal- GUI need · task setting
CL· CLI-sufficient- GUI need · ordinary access
CL· CLI-sufficient- Interaction primitives
code· Code & commandstype· Text & forms- Work product
WP07· Simulation result- Conditions
- None declared
- Proposed difficulty
- 3 / 5
Proposed verifier
Both estimated expectations are within +/-0.03 of the exact values for the prepared state. Graded by comparing to the analytic expectations.
Proposed partial credit
50% correct basis rotations; 50% both expectations within tolerance
R03.07.01.02-T18 Optimize a parameterized ansatz to a target
Original instruction
Given the target 2-qubit state in fixtures/qc/target.json, build a parameterized ansatz (Ry/CNOT layers) and optimize its parameters to maximize fidelity to the target. Write the final parameters and achieved fidelity to result.json.
- Platforms
lin· Linuxmac· macOSwin· Windows- Applications
- Qiskit · PennyLane
- Interfaces
term· Terminal- GUI need · task setting
CL· CLI-sufficient- GUI need · ordinary access
CL· CLI-sufficient- Interaction primitives
code· Code & commandstype· Text & forms- Work product
WP07· Simulation result- Conditions
- None declared
- Proposed difficulty
- 4 / 5
Proposed verifier
The optimized circuit reaches fidelity >= 0.99 to the target state (verified by re-preparing with the saved parameters). Graded by statevector fidelity.
Proposed partial credit
40% ansatz+cost wiring; 30% optimization runs; 30% fidelity >= 0.99
R03.07.01.02-T19 Build a Bell/GHZ circuit in IBM Quantum Composer (control pair of T01)
Original instruction
Control pair of T01/T02: in the IBM Quantum Composer web GUI, drag gates to build first a Bell state then extend it to a 3-qubit GHZ state, add measurements, and read the probability histogram from the built-in statevector/probabilities view. Export the circuit as QASM.
- Platforms
web· Any OS (web)- Applications
- IBM Quantum Composer
- Interfaces
brow· Browser- GUI need · task setting
G2· GUI-essential- GUI need · ordinary access
G2· GUI-essential- Interaction primitives
drag· Drag & dropclick· Point & clickvis· Visual judgment- Work product
WP06· Code/engineering- Conditions
tutorial· Follow docs/tutorial- Proposed difficulty
- 2 / 5
Proposed verifier
The exported QASM, when simulated, yields the GHZ(3) distribution (TVD < 0.05 to ideal) and the Composer's own probability view shows the 000/111 peaks. Graded on the exported circuit; contrasts with the code-built circuit of T01/T02. No IBM Quantum API token is issued and the VM has no Qiskit or terminal, so the circuit can only be built and exported in the Composer web session.
Proposed partial credit
40% Bell built visually; 40% extended to GHZ(3); 20% exported QASM correct
R03.07.01.02-T20 Quantum counting via amplitude estimation
Original instruction
For the oracle in fixtures/qc/count_oracle.py over 4 qubits marking an unknown number M of states, use quantum counting (QPE on the Grover operator) with 4 counting qubits to estimate M. Write the estimate and the derived angle to result.json.
- Platforms
lin· Linuxmac· macOSwin· Windows- Applications
- Qiskit
- Interfaces
term· Terminal- GUI need · task setting
CL· CLI-sufficient- GUI need · ordinary access
CL· CLI-sufficient- Interaction primitives
code· Code & commandstype· Text & forms- Work product
WP07· Simulation result- Conditions
long· Long-horizon- Proposed difficulty
- 5 / 5
Proposed verifier
The estimated number of marked states M equals the oracle's true count (rounded from the measured phase) and the derived angle matches within tolerance. Graded by comparing to the true M.
Proposed partial credit
30% Grover operator correct; 30% QPE counting; 40% correct M estimate
Mapped research references
Existing benchmark-to-class links from the research catalog. They are not record-level annotations, executions or product endorsements.