All problems
19 problems, grouped by area. Each problem has its own instances, verifier and leaderboards.
Fault-tolerant arithmetic
6 problemsFewest T gates for field multiplication
Fewer T gates reduce the magic states needed for field multiplication.
Fewest AND gates for field multiplication
Each product can be implemented with a Toffoli gate.
Fewest Toffoli gates for adding a constant
Adding a known constant modulo 2^n is the inner step of modular exponentiation in Shor's algorithm and of many other arithmetic circuits, and spare qubits are expensive, so the Toffoli count at a fixed number of spare qubits decides the cost.
Fewest T gates for a multi-controlled Z with measurements
A controlled NOT with many controls appears in table lookups, comparisons and oracles, and each T gate costs a magic state. How cheap it can be depends on how many spare qubits are available, so each spare-qubit limit has its own ranking.
Fewest Toffoli gates for coherent table lookup
Table lookups are a large part of the cost of fault-tolerant chemistry and simulation algorithms, and Toffoli gates dominate that cost.
Fewest Toffoli gates for elliptic-curve point addition
Point addition is the inner step of Shor's algorithm for elliptic-curve discrete logarithms, and its Toffoli count at a fixed number of qubits sets the cost of that algorithm. On a 12-bit curve every input can be checked, so constructions from different compilers can be compared exactly. The board says nothing about secp256k1 or other cryptographic curves.
Classical simulation
2 problemsFewest stabilizer terms for magic states
Fewer stabilizer terms can reduce the cost of simulating circuits with T, CCZ and other non-Clifford gates.
Fewest multiplications for a random-circuit output amplitude
Find a tensor contraction plan with fewer multiplications under the memory limit.
Error correction
7 problemsMost logical qubits with check weight at most 6
Store more logical qubits within the same physical qubit limit and distance requirement.
Cheapest fault-tolerant preparation of an encoded |0⟩
Cheaper fault-tolerant encoded ancillas reduce the cost of Steane-type error correction and of preparing logical qubits.
Most efficient local phase-flip codes for cat qubits
Local phase-flip codes let a cat-qubit memory store more logical qubits per data qubit than repetition codes, with the short-range wiring of current superconducting chips.
Most efficient weight-6 qLDPC codes with exact distance
A quantum memory needs many logical qubits, each protected by a high distance, from as few physical qubits as possible. The efficiency k·d²/n measures that trade-off for codes whose checks hardware can measure with short circuits.
Fewest CNOTs for a flagged parity check
Error-correcting codes measure their high-weight checks over and over, and every CNOT of a check circuit is a place where a fault can occur. A cheaper flagged circuit for a weight-w check therefore makes syndrome extraction faster and less noisy for codes such as color codes and quantum LDPC codes.
Eight T states per round from the fewest noisy inputs
Magic-state factories take a large share of the cost of a fault-tolerant quantum computer. A protocol that yields eight good T states per round from fewer noisy inputs, at a fixed output error, makes a factory level smaller.
QEC decoder accuracy on fixed circuit-level memory experiments
A decoder decides whether error correction works on real circuits. Fixed shots with hidden labels let decoders be compared on identical circuit-level data.
Photonic resource states
1 problemQuantum simulation
2 problemsLowest-weight fermion-to-qubit encodings for the 2D Hubbard model
Every Pauli factor of a mapped fermionic term costs gates in each Trotter step and in each measurement circuit: synthesizing each term's rotation separately takes 2 (weight - 1) CNOTs, so a lighter encoding needs fewer gates in that standard construction (the board counts weight, not compiled circuits).
Fewest CX gates for a Hubbard Trotter step of Pauli rotations
On current hardware, two-qubit gates take most of the time and cause most of the errors of a Hamiltonian-simulation circuit. A product-formula step is repeated many times, so a CX saved in one step is saved in every step.