HS-Bloch

Surface-Aware Phase Coordination for Noisy Quantum Systems.

Status: Active Research (v1.1)

Implementation: Fujitsu QARP Module (In Progress)

1. The Core Problem: Phase is not enough

In the standard Quantum HS° framework, we treat time as a phase on a circle (S¹). This is perfect for ideal clocks. However, real quantum processors suffer from decoherence: the state "shrinks" inside the Bloch sphere.

Ideal State: Radius r=1 (On the surface).
Noisy State: Radius r<1 (In the interior).

A system can be perfectly aligned in phase (angle is correct) but be completely useless if its coherence has collapsed (radius ≈ 0).

2. The Solution: HS-Bloch Gating

HS-Bloch extends the coordination vector from 1D (Phase) to 2D (Phase + Coherence Proxy). An execution is authorized only if both conditions are met. This logic is deterministic and uses fixed-point integers to prevent ambiguity.

2.1. Gating Logic (Tick-Canonical)

An execution is authorized IF AND ONLY IF:

The temporal phase, φ_tick, is inside the target phase window [start, end].
The quality metric, c_u16 (Coherence Proxy), is ≥ the minimum required threshold.

2.2. The `c_u16` Metric

We encode coherence magnitude as a u16 fixed-point integer (0-65535). This ensures deterministic, signable verification without the risks of floating-point arithmetic.

2.3. Vector Policies (v1.1)

HS-Bloch v1.1 allows for multi-dimensional quality requirements. Instead of a single threshold, you can define a vector of named thresholds and an evaluation policy.

Policy Operator	Description
"AND" (default)	All required quality dimensions must meet their respective thresholds.
"MIN"	The worst-case observed value must be greater than or equal to the highest required threshold.
"K_OF_N"	At least `k` of the `N` required dimensions must meet their thresholds.

3. Freshness Constraint (v1.1)

A quality measurement is only useful if it's recent. HS-Bloch v1.1 introduces a tick-canonical freshness constraint to prevent decisions based on stale data.

A requirement can include max_delta_ticks, an integer defining the maximum allowed time difference (in ticks) between the execution context and the quality measurement context. The check uses a wrap-safe circular distance calculation, making it robust across cycle boundaries.

If the measurement is older than max_delta_ticks, the evaluation fails with FAIL_STALE.

4. Application: The Fujitsu Pilot

Selected for the Quantum Simulator Challenge 2025-26.

We are deploying HS-Bloch on Fujitsu's 40-qubit simulator to solve the "Quantum Weather" problem in variational algorithms (QAOA).

Architecture

We implement a custom QARP Block (HSBlochGate) that acts as a temporal firewall.

Sensing: The block probes the simulator's noise model (via the Pytket interface) to estimate the instantaneous coherence proxy.
Decision: It compares the proxy against the c_u16 threshold and policy.
Action:
- Good Weather: Trigger the expensive QAOA circuit.
- Bad Weather: Skip/Wait the shot, saving resources.

Preliminary Results

In small-scale tests (10 qubits), this gating logic improved the Mean Solution Quality by +12.1% by filtering out decoherence spikes. We are now scaling this to industrial MO-MAXCUT instances.

5. Developer Specs (v1.1)

Vector Requirement Example (K_OF_N)

A signed requirement object specifying a 2-of-3 policy and a freshness constraint of 1500 ticks.

{
  "quality_req": {
    "hsbloch_schema_id": "TV-HSBLOCH-2026-02",
    "coherence_meter_id": "TV-COH-RAMSEY-Z-VIS-2026-01",
    "coh_encoding": "u16",
    "policy_op": "K_OF_N",
    "k": 2,
    "max_delta_ticks": 1500,
    "coh_min_vec_u16": {
      "ramsey_vis": 42000,
      "readout_fid": 50000,
      "prep_fid": 45000
    }
  }
}

Metering Report (HS-bits)

When measuring alignment cost, we report two distinct values:

H_align: The entropy cost of phase synchronization.
H_coh: The entropy cost of coherence maintenance (work done while waiting for good "weather").

Failure Codes

The verifier derives one of these codes upon evaluation.

Code	Meaning
PASS	All conditions met.
FAIL_BELOW_THRESHOLD	Quality metric did not meet the required threshold(s).
FAIL_METER_MISMATCH	The observation's meter ID does not match the requirement's.
FAIL_STALE	The observation is older than `max_delta_ticks`.
FAIL_MALFORMED	A required field is missing or incorrectly formatted.
FAIL_POLICY	The policy operator or its parameters are invalid or unrecognized.