From JAX to a 40-qubit hardware circuit

The original QOS paper provides JAX code and numerical simulations. Our next question was simpler but physically concrete: can we execute a recognisable streaming-style single-cell feature map on forty qubits and retrieve enough information for a classifier?

First: a literal QOS building block on four qubits

Before the wide PBMC68k route, we ported the official flat-QOS sampling sketch separately to Qiskit. The 4q toy model uses \(D=16\) positions and \(M=64\) random samples. The samples build literally the same phase vector as q_state_sketch_flat; an additional Hadamard layer converts otherwise invisible phases into measurable interference.

On IBM Fez, 64 random sketch circuits plus two controls ran through Fire Opal action 2334156. Mean Hellinger fidelity with the ideal distributions was 0.990104, the median was 0.991417 and the minimum was 0.980411. This is a literal flat-QOS kernel on hardware. It is not yet a complete QOS classifier: QSVT, the linear solver and the complete readout chain are missing.

Then: a hardware-oriented PBMC68k translation

The circuit processes four feature blocks in the same register. A block is uploaded through single-qubit rotations, after which qubit pairs are connected using a fixed interaction structure. A final rotation layer follows the fourth block.

At logical circuit level, each cell uses:

  • 40 qubits;
  • depth 20 before measurement;
  • 87 two-qubit gates;
  • fully numerical parameters;
  • no mid-circuit measurements or resets.

This is deliberately shallow. The complete theoretical QOS/QSVT protocol requires more complex oracles and error-corrected logical operations. Unlike the 4q sketch above, this 40q circuit is not a literal QOS implementation: its rotation angles are prepared classically and there is no sample-by-sample oracle construction. This variant investigates the next experimental boundary: a physical quantum feature map wide enough to be more difficult to simulate classically, yet shallow enough to survive on current hardware.

Why three measurement circuits per cell?

A quantum state cannot be read out completely in a single measurement. We choose a fixed panel of homogeneous Pauli observables. Each base cell therefore produces three versions:

  • measure every qubit in the X basis;
  • measure every qubit in the Y basis;
  • measure every qubit in the Z basis.

Several single-qubit and two-qubit correlations can be calculated from one global basis measurement. With 64 cells this gives:

64 cells × 3 measurement bases = 192 circuits.

Every circuit received 128 shots, for a total shot budget of 24,576. The readout contained 40 single-qubit supports and 95 predeclared qubit-pair supports per cell, each in X, Y and Z. This produces 405 features.

Validate first, execute later

Because Fire Opal runs are scarce, the workflow used separate safety phases:

  1. reconstruct the dataset, split, encoding, circuit shape, QASM and hashes locally;
  2. pass all 192 payloads through Fire Opal validate without execution;
  3. freeze a hardware plan containing backend, shots and readout;
  4. submit a single batch only after explicit confirmation;
  5. store the action ID and never allow retrieval to resubmit;
  6. perform classification locally only after the hardware file was pinned.

Provider validation accepted every circuit for ibm_fez. Logical depth was always 20 and exported payload depth was 22 before provider compilation. Calibration warnings from validation were retained rather than filtered out.

Fire Opal and IBM Fez

Fire Opal is a performance-management layer from Q-CTRL. It compiles and optimises circuits for the selected device and applies error-suppression or mitigation steps. That does not make the measured result error-free, but it can improve the amount of usable algorithmic information obtained from noisy hardware.

The run received Fire Opal action ID 2334162 and used IBM Fez. The provider reported 26 quantum seconds. This is QPU usage time rather than complete turnaround time: data preparation, compilation, queueing, classical post-processing and model selection are not included.

What came back?

Retrieval returned exactly 192 probability distributions in manifest order. Every value was finite and non-negative. Normalisation differed from one by no more than approximately \(2.2times 10^{-15}\). Each circuit produced between 114 and 128 distinct bit strings.

From these results we reconstructed 64 rows of 405 expectation values. Values ranged from -0.90625 to 1.0. Bit order is explicitly Qiskit little-endian: the rightmost bit corresponds to qubit zero.

This is the main intermediate hardware result: not only were the circuits accepted, but the entire chain from real cell data to usable, ordered quantum features was completed.

Is this the first single-cell QML run?

We should not make such a broad claim. Quantum-kernel studies on biological cell classification and real IBM hardware already existed, including a 2023 study of neuronal M-types. The defensible novelty is narrower: an early and, to the best of our present knowledge, first physical 40-qubit feasibility execution of this specific QOS-inspired coherent PBMC68k route.

Even that wording should be preceded by a systematic literature review in a formal publication. This series therefore primarily uses “from JAX to 40-qubit hardware,” not “the first QML experiment ever.”

In part 5 we examine how the 405 features are used without leaking the test set into model selection.

Sources