# RQM Two Qubit Local Equivalence

> RQM Two Qubit Local Equivalence is a paid API for AI agents from jobs.rqmtechnologies.com, paid per call via x402, $0.1/call, status unknown (last checked 2026-09-14).

Classifies a supported two-qubit quantum gate by its bounded local-equivalence class and phase context

## Facts

- Endpoint: POST https://jobs.rqmtechnologies.com/x402/buyer-jobs/two-qubit-local-equivalence-v1
- Price: $0.1/call
- Payment: x402
- Status: unknown
- Last checked: 2026-09-14
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/rqm-two-qubit-local-equivalence-60d134b6
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_I0G23ChvmTgF2nqUISkm6

Status and success rate cover calls made through Zero and Zero's own probes. Third-party monitors may report differently.

## How to call it through Zero

Zero handles the 402 payment challenge and records the run. With the Zero CLI installed (`npm i -g @zeroxyz/cli`):

```sh
zero fetch --capability rqm-two-qubit-local-equivalence-60d134b6 -d '<json body>'
```

Example prompt: Classify the local-equivalence class of a CX gate using exact phase context — I need to know which bounded equivalence class it falls into.

## When to prefer this

Use this endpoint when you need to classify a specific named two-qubit gate (identity, CX, CZ, SWAP, or iSWAP) by its bounded local-equivalence class with a defined phase context. Prefer this over general matrix decomposition tools when you have a discrete gate and need a fast, typed equivalence classification with or without global phase. Do not use for arbitrary unitary matrices, operations on more than two qubits, or when a formal mathematical equivalence proof is required.

## Known failure modes

- Unsupported gate type (only identity, cx, cz, swap, iswap are valid) returns validation error
- Phase radians outside the range [-2π, 2π] are rejected
- Missing required fields (operation or phase_context) cause schema validation failure
- Arbitrary or custom matrices are not accepted — only named gates from the enum are supported
- Larger-than-two-qubit operations are not supported and will be rejected

## How this service works

Two Qubit Local Equivalence: Classify this supported two-qubit operation by its bounded local-equivalence class and p... Use when: Use when a bounded request matches rqm.studio.two-qubit-local-equivalence-request.v1 and the caller needs t... Returns: local-equivalence class, canonical coordinates, explicit phase treatment. Boundaries: Deterministic bounded local software evidence only; no QPU, provider acceptance, certification, formal-pr...

## Output

Returns the bounded local-equivalence class and phase context classification for the specified two-qubit gate operation, indicating which equivalence class the gate belongs to and how phase is handled under the requested context (ignore_global_phase or exact).

## Request schema (JSON Schema)

```json
{
 "type": "object",
 "properties": {
  "request": {
   "type": "object",
   "title": "LocalEquivalenceRequest",
   "required": [
    "operation",
    "phase_context"
   ],
   "properties": {
    "operation": {
     "type": "object",
     "title": "TwoQubitOperation",
     "required": [
      "gate"
     ],
     "properties": {
      "gate": {
       "enum": [
        "identity",
        "cx",
        "cz",
        "swap",
        "iswap"
       ],
       "type": "string",
       "title": "Gate"
      },
      "phase_radians": {
       "type": "number",
       "title": "Phase Radians",
       "default": 0,
       "maximum": 6.283185307179586,
       "minimum": -6.283185307179586
      }
     },
     "additionalProperties": false
    },
    "phase_context": {
     "enum": [
      "ignore_global_phase",
      "exact"
     ],
     "type": "string",
     "title": "Phase Context"
    }
   },
   "additionalProperties": false
  },
  "schema_version": {
   "const": "rqm.jobs.bazaar-buyer-job-request.v1"
  },
  "idempotency_key": {
   "type": "string",
   "pattern": "^[A-Za-z0-9][A-Za-z0-9._:-]*$",
   "maxLength": 128,
   "minLength": 1
  },
  "max_total_price": {
   "type": "string",
   "pattern": "^(?:0|[1-9]\\d{0,13})(?:\\.\\d{1,6})?$"
  }
 }
}
```

## More

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