{"openapi":"3.1.0","info":{"title":"AQT Public API","description":"\n## AQT Quantum Gates\n\nThe following quantum gates are natively supported by AQT backends and are defined in terms of the Pauli matrices\n$\n    \\sigma_x =\n    \\begin{pmatrix}\n    0 & 1 \\\\ 1 & 0\n    \\end{pmatrix}\n$, $\n   \\sigma_y =\n    \\begin{pmatrix}\n    0 & -\\mathrm{i} \\\\ \\mathrm{i} & 0\n    \\end{pmatrix}\n$ and $\\sigma_z =\n    \\begin{pmatrix}\n    1 & 0 \\\\ 0 & -1\n    \\end{pmatrix}.\n$\n\n\n<details>\n<summary>\n<span class=\"aqt-details-summary-title\">R-gate:</span>\n<span class=\"aqt-details-summary-description\">\nA single-qubit rotation around an arbitrary axis on the Bloch sphere's equatorial plane `GateR`\n</span>\n</summary>\n\nThe R-gate on qubit j with rotation angles θ and φ, both in units of π, is defined as\n    $$\n    U_{\\mathrm{R}}^j(\\theta,\\varphi) =\n    \\exp\\left( -\\mathrm{i} \\theta \\frac{\\pi}{2}\n    \\left[\\sin(\\varphi \\pi)\\sigma_y^j + \\cos(\\varphi \\pi)\\sigma_x^j \\right] \\right) =\n    \\begin{pmatrix}\n    \\cos(\\theta \\frac{\\pi}{2}) && -\\mathrm{i} e^{-\\mathrm{i} \\varphi \\pi}\\sin(\\theta \\frac{\\pi}{2})\\\\\n    -\\mathrm{i} e^{\\mathrm{i} \\varphi \\pi}\\sin(\\theta \\frac{\\pi}{2}) && \\cos(\\theta \\frac{\\pi}{2})\n    \\end{pmatrix}\n    $$\nwith the Pauli matrices\n    $$\n    \\sigma_x =\n    \\begin{pmatrix}\n    0 & 1 \\\\ 1 & 0\n    \\end{pmatrix} ,\n    \\sigma_y =\n    \\begin{pmatrix}\n    0 & -\\mathrm{i} \\\\ \\mathrm{i} & 0\n    \\end{pmatrix}.\n    $$\n\nθ is the rotation angle in azimuthal direction around the chosen rotation axis and φ is the polar angle\ndefining the direction of the rotation axis in the equatorial plane of the Bloch sphere.\n\n**Examples:**\n    $$\n    \\begin{align*}\n    U_{\\mathrm{R}}^j(0.5, 0) \\ket{0_j} &=\n    \\frac{1}{\\sqrt{2}}\\left (\\ket{0_j} - \\mathrm{i}\\ket{1_j} \\right )\\\\\n    U_{\\mathrm{R}}^j(0.5, 0.5) \\ket{0_j} &=\n    \\frac{1}{\\sqrt{2}}\\left (\\ket{0_j} + \\ket{1_j} \\right )\n    \\end{align*}\n    $$\n\n**Warning:**\n\nSmall $\\theta$ values cannot be implemented natively by the AQT backends.\nSuch instances are thus rewritten as:\n\n$$\nR(\\theta,\\,\\phi)\\to R(\\pi,\\,\\phi+\\pi)\\cdot R(\\theta+\\pi,\\,\\phi)\n$$\n\nThe condition triggering this transformation is an implementation detail,\ntypically $\\theta \\leq \\pi/5$.\n</details>\n\n\n<details>\n<summary>\n<span class=\"aqt-details-summary-title\">Rz-gate:</span>\n<span class=\"aqt-details-summary-description\">\nA single-qubit rotation around the Bloch sphere's z-axis `GateRZ`\n</span>\n</summary>\n\nThe Rz-gate on qubit j with rotation angle φ in units of π is defined as\n    $$\n    U_{\\mathrm{R_z}}^j(\\varphi) =\n    \\exp\\left( -\\mathrm{i} \\varphi \\frac{\\pi}{2} \\sigma_z^j \\right) =\n    \\begin{pmatrix}\n    \\cos(\\varphi \\frac{\\pi}{2}) -\\mathrm{i}\\sin(\\varphi \\frac{\\pi}{2}) && 0 \\\\\n    0 && \\cos(\\varphi \\frac{\\pi}{2}) +\\mathrm{i}\\sin(\\varphi \\frac{\\pi}{2})\n    \\end{pmatrix}\n    $$\nwith the Pauli matrix\n    $$\n    \\sigma_z =\n    \\begin{pmatrix}\n    1 & 0 \\\\ 0 & -1\n    \\end{pmatrix}.\n    $$\n\nφ is the rotation angle in polar direction. The rotation axis is the z-axis of the Bloch sphere.\n\n**Examples:**\n    $$\n    \\begin{align*}\n    U_{\\mathrm{R_z}}^j(1)\\frac{1}{\\sqrt{2}}\\left( \\ket{0_j} + \\ket{1_j}\\right) &=\n    \\frac{1}{\\sqrt{2}}\\left (\\ket{0_j} - \\ket{1_j} \\right ) \\\\\n    U_{\\mathrm{R_z}}^j(0.5)\\frac{1}{\\sqrt{2}}\\left (\\ket{0_j} + \\ket{1_j} \\right) &=\n    \\frac{1}{\\sqrt{2}}\\left (\\ket{0_j} +\\mathrm{i}\\ket{1_j} \\right )\n    \\end{align*}\n    $$\n</details>\n\n\n<details>\n<summary>\n<span class=\"aqt-details-summary-title\">MS-gate:</span>\n<span class=\"aqt-details-summary-description\">\nA two-qubit entangling gate of Mølmer-Sørensen-type `GateRXX`\n</span>\n</summary>\n\nThe MS-gate on qubits j and k with rotation angle θ in units of π is defined as\n    $$\n    \\begin{aligned}\n    U_{\\mathrm{MS}}^{j,k} \\left (\\theta \\right) & =\n    e^{\\mathrm{i}\\theta\\frac{\\pi}{2}}\\exp{\\left(-\\mathrm{i} \\theta \\pi {S_x}^2 \\right) }\n    = \\begin{pmatrix}\n    \\cos(\\theta \\frac{\\pi}{2}) & 0 & 0 && -\\mathrm{i}\\sin(\\theta \\frac{\\pi}{2}) \\\\\n    0 & \\cos(\\theta \\frac{\\pi}{2}) & -\\mathrm{i}\\sin(\\theta \\frac{\\pi}{2}) && 0 \\\\\n    0 & -\\mathrm{i}\\sin(\\theta\\frac{\\pi}{2}) & \\cos(\\theta \\frac{\\pi}{2}) && 0 \\\\\n    -\\mathrm{i}\\sin(\\theta \\frac{\\pi}{2}) & 0 & 0 && \\cos(\\theta \\frac{\\pi}{2})\n    \\end{pmatrix}\n    \\end{aligned}\n    $$\nwith\n    $$\n    S_x =\\frac{1}{2}\\left (\\sigma_x^j + \\sigma_x^k \\right)\n    $$\nand the Pauli matrix\n    $$\n    \\sigma_x =\n    \\begin{pmatrix}\n    0 & 1 \\\\ 1 & 0\n    \\end{pmatrix}.\n    $$\n\nA fully-entangling gate between qubit 0 and qubit 1 therefore is\n    $$\n    U_{\\mathrm{MS}}^{0,1} \\left (0.5 \\right) = \\frac{1}{\\sqrt{2}}\n    \\begin{pmatrix}\n    1 && 0 && 0 && -\\mathrm{i} \\\\ 0 && 1 && -\\mathrm{i} && 0 \\\\\n    0 && -\\mathrm{i} && 1 && 0 \\\\ -\\mathrm{i} && 0 && 0 && 1\n    \\end{pmatrix}\n    $$\n\n**Examples:**\n    $$\n    \\begin{align*}\n    U_{\\mathrm{MS}}^{j,k}(0.5) \\ket{0_j0_k} &=\n    \\frac{1}{\\sqrt{2}}\\left (\\ket{0_j0_k} -\\mathrm{i} \\ket{1_j1_k} \\right ) \\\\\n    U_{\\mathrm{MS}}^{j,k}(0.5) \\ket{1_j1_k} &=\n    \\frac{1}{\\sqrt{2}}\\left ( -\\mathrm{i}\\ket{0_j0_k} + \\ket{1_j1_k} \\right )\n    \\end{align*}\n    $$\n</details>\n\n## AQT Resources\n\n<details>\n<summary>\n<span class=\"aqt-details-summary-title\">Resource characterisation: </span>\n<span class=\"aqt-details-summary-description\">Data describing a resources properties `Characterisation`</span>\n</summary>\n\nResources are characterised by the following set of attributes that describe their\nperformance and capabilities:\n\n<details class=\"aqt-sub-details\">\n<summary>\n<span class=\"aqt-details-summary-title\">Single-qubit gate fidelity </span>\n<span class=\"aqt-details-summary-description\">for each qubit `single_qubit_gate_fidelity`</span>\n</summary>\n\nA set of key-value pairs, where the key represents the index of the\nqubit and the value the fidelity for single-qubit gates.\n\nThe single-qubit gate fidelities are determined following the Randomized\nBenchmarking (RB) protocol. To measure the mean error rate we apply a\nsequence of randomly chosen gates followed by an inverting gate. The decay\nin performance as a function of the sequence length reveals the mean error\nrate per gate.\n\nEach gate fidelity is represented by a value between 0 and 100 and an additional\nuncertainty value. The sum of these two values cannot exceed 100.\n</details>\n\n\n<details class=\"aqt-sub-details\">\n<summary>\n<span class=\"aqt-details-summary-title\">Mean two qubit gate fidelity </span>\n<span class=\"aqt-details-summary-description\">`mean_two_qubit_gate_fidelity`</span>\n</summary>\n\nThe mean two-qubit gate fidelity is determined following the Randomized\nBenchmarking (RB) protocol. To measure the mean error rate we apply a\nsequence of randomly chosen gates followed by an inverting gate. The decay\nin performance as a function of the sequence length reveals the mean error\nrate per gate.\n\nThe mean fidelity is represented by a value between 0 and 100 and an additional\nuncertainty value. The sum of these two values cannot exceed 100.\n</details>\n\n\n<details class=\"aqt-sub-details\">\n<summary>\n<span class=\"aqt-details-summary-title\">SPAM fidelity </span>\n<span class=\"aqt-details-summary-description\">(lower bound) `spam_fidelity_lower_bound`</span>\n</summary>\n\nThe SPAM fidelity or State Preparation and Measurement errors as the name\nindicates describe the errors that occur when the initial quantum state is\nnot prepared as intended or when the readout of the quantum state yields an\nincorrect result. To measure the state preparation errors the qubits are\nprepared in a known state followed by a set of repeated measurements that\nallow to estimate the probability of correctly preparing and measuring that\ngiven state. To estimate the measurement errors, a known gate is applied\nfollowed by a set of repeated measurements that allow to determine the error\nin preparing and measuring incorrectly the final state after that given\noperation.\n</details>\n\n\n<details class=\"aqt-sub-details\">\n<summary>\n<span class=\"aqt-details-summary-title\">T2 coherence time in seconds </span>\n<span class=\"aqt-details-summary-description\">(no Spin Echo) `t2_coherence_time_s`</span>\n</summary>\n\nThe T2 coherence time is estimated by performing Ramsey experiments with a\nvariable waiting time. The amplitude of the contrast of phase scans of Ramsey\nexperiments is measured as a function of the waiting time. The coherence is\nextracted by measuring the exponential decay of the contrast as a function\nof the waiting time.\n\nT2 is represented by a value between 0 and 100 and an additional\nuncertainty value. The sum of these two values cannot exceed 100.\n</details>\n\n\n<details class=\"aqt-sub-details\">\n<summary>\n<span class=\"aqt-details-summary-title\">T1 in seconds </span>\n<span class=\"aqt-details-summary-description\">`t1_s`</span>\n</summary>\n\nLiterature value from <a href=\"https://doi.org/10.1103/PhysRevA.62.032503\"\ntarget=\"_blank\">https://doi.org/10.1103/PhysRevA.62.032503</a>.\n\nT1 is represented by a value between 0 and 100 and an additional\nuncertainty value. The sum of these two values cannot exceed 100.\n</details>\n\n\n<details class=\"aqt-sub-details\">\n<summary>\n<span class=\"aqt-details-summary-title\">Readout time in microseconds </span>\n<span class=\"aqt-details-summary-description\">`readout_time_micros`</span>\n</summary>\n\nThe readout time is the duration of the pulse used to detect the ion state.\n</details>\n\n\n<details class=\"aqt-sub-details\">\n<summary>\n<span class=\"aqt-details-summary-title\">Single-qubit gate duration </span>\n<span class=\"aqt-details-summary-description\">`single_qubit_gate_duration_micros`</span>\n</summary>\n\nThe average duration to execute a single-qubit gate in microseconds.\n</details>\n\n\n<details class=\"aqt-sub-details\">\n<summary>\n<span class=\"aqt-details-summary-title\">Two-qubit gate duration </span>\n<span class=\"aqt-details-summary-description\">`two_qubit_gate_duration_micros`</span>\n</summary>\n\nThe average duration to execute a two-qubit gate in microseconds.\n</details>\n\n\n<details class=\"aqt-sub-details\">\n<summary>\n<span class=\"aqt-details-summary-title\">Last updated at </span>\n<span class=\"aqt-details-summary-description\">`updated_at`</span>\n</summary>\n\nThe timestamp of the last characterisation data update.\n</details>\n\n</details>\n\n","version":"1.2.0"},"servers":[{"url":"/api/v1"}],"paths":{"/result/{job_id}":{"get":{"summary":"Request Result","description":"Request job results.\n\nNB once a job has finished processing and the result is queried, it will only remain available for a period of 24 hours. 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Get"},"examples":[{"summary":"","value":[{"id":"default","accepting_job_submissions":true,"jobs_being_processed":true,"resources":[{"id":"simulator","name":"Simulator without noise","type":"simulator"},{"id":"simulator_noise","name":"Simulator with noise","type":"device"}]}]}]}}},"401":{"description":"Unauthorized"}},"security":[{"Bearer Token":[]}]}},"/submit/{workspace}/{resource}":{"post":{"summary":"Submit Job","description":"Submit a quantum circuit.","operationId":"submit_job_submit__workspace___resource__post","security":[{"Bearer Token":[]}],"parameters":[{"name":"workspace","in":"path","required":true,"schema":{"type":"string","title":"Workspace"}},{"name":"resource","in":"path","required":true,"schema":{"type":"string","title":"Resource"}}],"requestBody":{"required":true,"content":{"application/json":{"schema":{"$ref":"#/components/schemas/SubmitJobRequest"},"examples":{"Default":{"summary":"Default example","value":{"job_type":"quantum_circuit","label":"Example 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This is used to request results."},"job_type":{"type":"string","const":"quantum_circuit","title":"Job Type","default":"quantum_circuit"},"label":{"anyOf":[{"type":"string"},{"type":"null"}],"title":"Label"},"resource_id":{"type":"string","title":"Resource Id"},"workspace_id":{"type":"string","title":"Workspace Id"}},"type":"object","required":["job_id","resource_id","workspace_id"],"title":"BasicJobMetadata","description":"Metadata for a user-submitted job."},"Characterisation":{"properties":{"single_qubit_gate_fidelity":{"additionalProperties":{"$ref":"#/components/schemas/GateFidelity"},"type":"object","title":"Single Qubit Gate Fidelity"},"mean_two_qubit_gate_fidelity":{"$ref":"#/components/schemas/GateFidelity"},"spam_fidelity_lower_bound":{"type":"number","maximum":100.0,"minimum":0.0,"title":"Spam Fidelity Lower Bound"},"t2_coherence_time_s":{"$ref":"#/components/schemas/PositiveFloatValueWithUncertainty"},"t1_s":{"$ref":"#/components/schemas/PositiveFloatValueWithUncertainty"},"readout_time_micros":{"type":"number","minimum":0.0,"title":"Readout Time Micros"},"single_qubit_gate_duration_micros":{"type":"number","minimum":0.0,"title":"Single Qubit Gate Duration Micros"},"two_qubit_gate_duration_micros":{"type":"number","minimum":0.0,"title":"Two Qubit Gate Duration Micros"},"updated_at":{"type":"string","format":"date-time","title":"Updated At"}},"type":"object","required":["single_qubit_gate_fidelity","mean_two_qubit_gate_fidelity","spam_fidelity_lower_bound","t2_coherence_time_s","t1_s","readout_time_micros","single_qubit_gate_duration_micros","two_qubit_gate_duration_micros","updated_at"],"title":"Characterisation","description":"Characterisation data describing a resources properties.\n\nDetails can be found in the description of `Characterisation` in https://arnica.aqt.eu/api/v1/docs\n\nAttributes:\n    single_qubit_gate_fidelity: The single-qubit gate fidelity for each qubit.\n    mean_two_qubit_gate_fidelity: The mean two-qubit gate fidelity.\n    spam_fidelity_lower_bound: The SPAM fidelity (lower bound).\n    t2_coherence_time_s: T2 coherence time (no Spin Echo) in seconds.\n    t1_s: T1 in seconds. Literature value from https://doi.org/10.1103/PhysRevA.62.032503.\n    readout_time_micros: The duration of detecting the ion state in microseconds.\n    single_qubit_gate_duration_micros: Average duration to execute a single-qubit gate in microseconds.\n    two_qubit_gate_duration_micros: Average duration to execute a two-qubit gate in microseconds.\n    updated_at: Timestamp when this was last updated."},"CharacterisationResponse":{"properties":{"single_qubit_gate_fidelity":{"additionalProperties":{"$ref":"#/components/schemas/GateFidelity"},"type":"object","title":"Single Qubit Gate Fidelity"},"mean_two_qubit_gate_fidelity":{"$ref":"#/components/schemas/GateFidelity"},"spam_fidelity_lower_bound":{"type":"number","maximum":100.0,"minimum":0.0,"title":"Spam Fidelity Lower Bound"},"t2_coherence_time_s":{"$ref":"#/components/schemas/PositiveFloatValueWithUncertainty"},"t1_s":{"$ref":"#/components/schemas/PositiveFloatValueWithUncertainty"},"readout_time_micros":{"type":"number","minimum":0.0,"title":"Readout Time Micros"},"single_qubit_gate_duration_micros":{"type":"number","minimum":0.0,"title":"Single Qubit Gate Duration Micros"},"two_qubit_gate_duration_micros":{"type":"number","minimum":0.0,"title":"Two Qubit Gate Duration Micros"},"updated_at":{"type":"string","format":"date-time","title":"Updated At"},"two_qubit_gate_fidelity":{"items":{"$ref":"#/components/schemas/TwoQubitGateFidelity"},"type":"array","title":"Two Qubit Gate Fidelity"}},"type":"object","required":["single_qubit_gate_fidelity","mean_two_qubit_gate_fidelity","spam_fidelity_lower_bound","t2_coherence_time_s","t1_s","readout_time_micros","single_qubit_gate_duration_micros","two_qubit_gate_duration_micros","updated_at"],"title":"CharacterisationResponse","description":"Model for the characterisation of a resource."},"Circuit":{"items":{"$ref":"#/components/schemas/OperationModel"},"type":"array","maxItems":2000,"minItems":1,"title":"Circuit","description":"Json encoding of a quantum circuit."},"GateFidelity":{"properties":{"value":{"type":"number","maximum":100.0,"minimum":0.0,"title":"Value"},"uncertainty":{"type":"number","maximum":100.0,"minimum":0.0,"title":"Uncertainty"}},"type":"object","required":["value","uncertainty"],"title":"GateFidelity","description":"**Gate fidelity**\n\nSpecifies the gate fidelity with a value between 0 and 100 and an additional\nuncertainty value. 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By convention, the lower-indexed\n        qubit comes first.\n    value: The fidelity value for this pair of qubits, between 0 and 100.\n    uncertainty: The uncertainty associated with the fidelity value, between 0 and 100."},"ValidationError":{"properties":{"loc":{"items":{"anyOf":[{"type":"string"},{"type":"integer"}]},"type":"array","title":"Location"},"msg":{"type":"string","title":"Message"},"type":{"type":"string","title":"Error Type"}},"type":"object","required":["loc","msg","type"],"title":"ValidationError"},"Workspace":{"properties":{"id":{"type":"string","title":"Id"},"accepting_job_submissions":{"type":"boolean","title":"Accepting Job Submissions"},"jobs_being_processed":{"type":"boolean","title":"Jobs Being Processed"},"resources":{"items":{"$ref":"#/components/schemas/WorkspaceResource"},"type":"array","title":"Resources"}},"type":"object","required":["id","accepting_job_submissions","jobs_being_processed","resources"],"title":"Workspace","description":"Model for an item in the workspace list response."},"WorkspaceResource":{"properties":{"id":{"type":"string","title":"Id"},"name":{"type":"string","title":"Name"},"type":{"$ref":"#/components/schemas/ResourceType"}},"type":"object","required":["id","name","type"],"title":"WorkspaceResource","description":"Model of a resource within a workspace."}},"securitySchemes":{"Bearer Token":{"type":"http","description":"To authenticate for the API provide a valid token (without 'Bearer')","scheme":"bearer"}}}}