MIT iQuHack 2026 — Solutions

Challenge overview (Peak Bitstring Recovery)

Task: For each OpenQASM 2 circuit, recover the peak bitstring (the computational-basis outcome with maximum amplitude / probability).
Note: The platform accepts the bitstring or its reverse (bit-order agnostic).

Problem list

Problem	Name	Qubits	Points	Recommended strategy	Files
P1	Little Dimple 🫧	4	10	Visual inspection (gate structure)	Files/P1_little_peak.qasm
P2	Small Bump 🪨	20	20	Full statevector simulation (CPU)	Files/P2_small_bump.qasm, Solutions/P2.ipynb
P3	Tiny Ripple 🌊	30	30	Full statevector simulation + argmax probability	Files/P3_tiny_ripple.qasm, Solutions/P3.ipynb
P4	Gentle Mound 🌿	40	40	MPS simulation (tuned bond/truncation)	Files/P4_gentle_mound.qasm, Solutions/P4.ipynb
P5	Soft Rise 🌄	50	50	Higher bond MPS + multi-run sampling + aggregation	Files/P5_soft_rise.qasm, Solutions/P5.ipynb
P6	Low Hill ⛰️	60	60	Circuit simplification + approximate transpilation	Files/P6_low_hill.qasm
P7	Rolling Ridge 🏞️	46	70	Decompose via interaction graph; solve subcircuits	Files/P7_rolling_ridge.qasm
P8	Bold Peak 🏜️	72	80	Decomposition + iterative refinement	Files/P8_bold_peak.qasm
P9	Grand Summit 🏔️	56	90	Combine simplification + partial sim + decomposition	Files/P9_grand_summit.qasm
P10	Eternal Mountain 🗻	56	100	Full toolbox: simplification + decomposition + search	Files/P10_eternal_mountain.qasm

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Results

• P1: DONE
• P2: DONE
• P3: DONE
• P4: DONE
• P5: DONE
• P6: TODO
• P7: TODO
• P8: TODO
• P9: TODO
• P10: TODO

P1 — Little Dimple 🫧 (4 qubits, 10 pts)

Strategy: Visual inspection
This circuit is intentionally simple. By inspecting the gate sequence and its effect on the computational basis, the peak bitstring can be inferred directly without running a simulator.

Files

• QASM: Files/P1_little_peak.qasm

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P2 — Small Bump 🪨 (20 qubits, 20 pts)

Strategy: Full statevector simulation (CPU)
The circuit size is small enough to allow exact classical simulation. I simulate the full statevector and directly identify the basis state with the maximum probability amplitude.

Files

• QASM: Files/P2_small_bump.qasm
• Notebook: Solutions/P2.ipynb

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P3 — Tiny Ripple 🌊 (30 qubits, 30 pts)

Strategy: Full statevector simulation with probability extraction
Although larger, the circuit remains within feasible limits for classical simulation. I compute the final statevector and extract the dominant outcome by ranking probabilities.

Files

• QASM: Files/P3_tiny_ripple.qasm
• Notebook: Solutions/P3.ipynb

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P4 — Gentle Mound 🌿 (40 qubits, 40 pts)

Strategy: Matrix Product State (MPS) simulation
At this size, full statevector simulation becomes expensive. I switch to an MPS-based simulator with controlled bond dimension and truncation, which efficiently approximates the output distribution and reveals the peak bitstring.

Files

• QASM: Files/P4_gentle_mound.qasm
• Notebook: Solutions/P4.ipynb

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P5 — Soft Rise 🌄 (50 qubits, 50 pts)

Strategy: High-bond MPS + repeated sampling and aggregation
The circuit is highly entangling and can appear nearly uniform under naive simulation. I increase the bond dimension, run multiple sampling passes, and aggregate results to uncover the hidden bias toward the peak bitstring.

Files

• QASM: Files/P5_soft_rise.qasm
• Notebook: Solutions/P5.ipynb

Solutions — Recovered Peak Bitstrings

The following peak bitstrings were recovered for the solved challenges.
(The submission platform accepts each bitstring or its reverse.)

Problem	Qubits	Peak Bitstring	Notes
P1	4	1001	Inferred directly from circuit structure
P2	20	11000001000100011000	Exact statevector simulation
P3	30	001110001111101100001101010001	Exact statevector simulation
P4	40	1011011000101000010011001110100001010110	MPS simulation
P5	50	01101000100100001010101011100000010111100011111110	High-bond MPS + sampling aggregation

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Additional recovered solutions (not fully documented)

These solutions were recovered during the event but are not yet fully written up in this repository.

P7 — Rolling Ridge (46 qubits)
Peak bitstring:

0000011101100100001000111100111111111101000110

Estimated probability: 0.36032951062222224

P8 — Bold Peak (72 qubits)
Peak bitstring:

010100010010111001000011110001110011101110100011010001000111101001111101

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Contributors

• Joven Sekhon (JSekhon)
• Elena Yu (yxele)

REQUIREMENTS

pip install -r requirements.txt