54-Qubit MPS RCS

6×9 grid  �  Depth 6  �  MPS(χ=16)  �  Tier 2 limit (N 21�54, d≤9)

What this benchmark tests

This is the Tier 2 benchmark: 54 qubits at depth 6 using the MPS engine. At depth 6, the mean entanglement entropy is 2.22 bits/qubit across all bonds, indicating the circuit is well into the scrambled regime. With bond dimension χ=16 (capacity: log₂(16) = 4 bits/bond), the MPS represents this circuit with minimal approximation.

The circuit uses a 6×9 nearest-neighbour grid with alternating horizontal and vertical CX layers (Sycamore-style topology), interleaved with random RZ/RX rotations on all qubits. 2,048 distinct bitstring outcomes were produced from 2,048 shots � confirming the distribution is highly spread across the full Hilbert space.

Result summary

Reproduce this result

Install the Qumulator SDK and run the following. Use mode='tensor' with bond_dim=16 to invoke the MPS engine used in this benchmark.

pip install qumulator-sdk

import os, time, math, random
from qumulator import QumulatorClient

client = QumulatorClient(
    api_url=os.environ["QUMULATOR_API_URL"],
    api_key=os.environ["QUMULATOR_API_KEY"],
)

# Tier 2 max: 54-qubit depth-6 RCS on a 6x9 nearest-neighbour grid
N, ROWS, COLS, DEPTH = 54, 6, 9, 6
rng = random.Random(2)

eng = client.circuit.engine(n_qubits=N, mode='tensor', bond_dim=16)

h_even = [(r*COLS+c, r*COLS+c+1) for r in range(ROWS) for c in range(0, COLS-1, 2)]
h_odd  = [(r*COLS+c, r*COLS+c+1) for r in range(ROWS) for c in range(1, COLS-1, 2)]
v_even = [(r*COLS+c, (r+1)*COLS+c) for r in range(0, ROWS-1, 2) for c in range(COLS)]
v_odd  = [(r*COLS+c, (r+1)*COLS+c) for r in range(1, ROWS-1, 2) for c in range(COLS)]
layers = [h_even, v_even, h_odd, v_odd]

for d in range(DEPTH):
    for q in range(N):
        eng.apply('rz', q, params=[rng.uniform(0, 2 * math.pi)])
        eng.apply('rx', q, params=[rng.uniform(0, 2 * math.pi)])
    for q0, q1 in layers[d % 4]:
        eng.apply('cx', [q0, q1])

t0 = time.time()
result = eng.run(shots=2048, seed=2, return_entropy_map=True)
elapsed = time.time() - t0

print(f"Elapsed       : {elapsed:.1f}s")
print(f"Mean S        : {sum(result.entropy_map)/N:.3f} bits/qubit")
print(f"Distinct      : {len(result.counts)} / {result.shots}")

MPS at depth 6: high-entropy near-uniform sampling

At depth 6, the mean entanglement entropy of 2.22 bits/qubit is well within bond dimension χ=16 capacity (log₂(16) = 4 bits/bond). The MPS engine accurately represents the quantum state without significant truncation at this depth.

The output distribution is maximally spread: all 2,048 shots produced distinct bitstrings, indicating the circuit generates near-uniform random sampling across 2⁵⁴ possible outcomes � consistent with a deeply scrambled quantum state.