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Performance Management: A Qiskit Function by Q-CTRL Fire Opal

Note

Qiskit Functions are an experimental feature available only to IBM Quantum® Premium Plan, Flex Plan, and On-Prem (via IBM Quantum Platform API) Plan users. They are in preview release status and subject to change.

Overview

Fire Opal Performance Management makes it simple for anyone to achieve meaningful results from quantum computers at scale without needing to be quantum hardware experts. When running circuits with Fire Opal Performance Management, AI-driven error suppression techniques are automatically applied, enabling the scaling of larger problems with more gates and qubits. This approach reduces the number of shots required to reach the correct answer, with no added overhead — resulting in significant savings in both compute time and cost.

Performance Management suppresses errors and increases the probability of getting the correct answer on noisy hardware. In other words, it increases the signal-to-noise ratio. The following image shows how increased accuracy enabled by Performance Management can reduce the need for additional shots in the case of a 10-qubit Quantum Fourier Transform algorithm. With only 30 shots, Q-CTRL reaches the 99% confidence threshold, whereas the default (QiskitRuntime Sampler, optimization_level=3 and resilience_level=1, ibm_sherbrooke) requires 170,000 shots. By getting the right answer faster, you save significant compute runtime.

The Performance Management function can be used with any algorithm, and you can easily use it in place of the standard Qiskit Runtime primitives. Behind the scenes, multiple error suppression techniques work together to prevent errors from happening at runtime. All Fire Opal pipeline methods are pre-configured and algorithm-agnostic, meaning you always get the best performance out of the box.

To get access to Performance Management, contact Q-CTRL.

Description

Fire Opal Performance Management has two options for execution that are similar to the Qiskit Runtime primitives, so you can easily swap in the Q-CTRL Sampler and Estimator. The general workflow for using the Performance Management function is:

1. Define your circuit (and operators in the case of the Estimator).
2. Run the circuit.
3. Retrieve the results.

To reduce hardware noise, Fire Opal employs a range of AI-driven error suppression techniques depicted in the following image. With Fire Opal, the entire pipeline is completely automated with zero need for configuration.

Fire Opal's pipeline eliminates the need for additional overhead, such as increased quantum runtime or extra physical qubits. Note that classical processing time remains a factor (refer to the Benchmarks section for estimates, where "Total time" reflects both classical and quantum processing). In contrast to error mitigation, which requires overhead in the form of sampling, Fire Opal's error suppression works at both the gate and pulse levels to address various sources of noise and to prevent the likelihood of an error occurring. By preventing errors, the need for expensive post-processing is eliminated.

The following image depicts the error suppression methods automated by Fire Opal Performance Management.

The function offers two primitives, Sampler and Estimator, and the inputs and outputs of both extend the implemented spec for Qiskit Runtime V2 primitives.

Benchmarks

Published algorithmic benchmarking results demonstrate significant performance improvement across various algorithms, including Bernstein-Vazirani, quantum Fourier transform, Grover’s search, quantum approximate optimization algorithm, and variational quantum eigensolver. The rest of this section provides more details about types of algorithms you can run, as well as the expected performance and runtimes.

The following independent studies demonstrate how Q-CTRL's Performance Management enables algorithmic research at record-breaking scale:

• Parametrized Energy-Efficient Quantum Kernels for Network Service Fault Diagnosis - up to 50-qubit quantum kernel learning
• Tensor-based quantum phase difference estimation for large-scale demonstration - up to 33-qubit quantum phase estimation
• Hierarchical Learning for Quantum ML: Novel Training Technique for Large-Scale Variational Quantum Circuits - up to 21-qubit quantum data loading

The following table provides a rough guide on accuracy and runtimes from prior benchmarking runs on ibm_fez. Performance on other devices may vary. The usage time is based on an assumption of 10,000 shots per circuit. The "Number of qubits" indicated is not a hard limitation but represents rough thresholds where you can expect extremely consistent solution accuracy. Larger problem sizes have been successfully solved, and testing beyond these limits is encouraged.

Example	Number of qubits	Accuracy	Measure of accuracy	Total time (s)	Runtime usage (s)	Primitive (Mode)
Bernstein–Vazirani	50Q	100%	Success Rate (Percentage of runs where the correct answer is the highest count bitstring)	10	8	Sampler
Quantum Fourier Transform	30Q	100%	Success Rate (Percentage of runs where the correct answer is the highest count bitstring)	10	8	Sampler
Quantum Phase Estimation	30Q	99.9998%	Accuracy of the angle found: 1- abs(real_angle - angle_found)/pi	10	8	Sampler
Quantum simulation: Ising model (15 steps)	20Q	99.775%	$A$ (defined below)	60 (per step)	15 (per step)	Estimator
Quantum simulation 2: molecular dynamics (20 time points)	34Q	96.78%	$A_{mean}$ (defined below)	10 (per time point)	6 (per time point)	Estimator

Defining the accuracy of the measurement of an expectation value - the metric $A$ is defined as follows:

$$A = 1 - \frac{|\epsilon^{ideal} - \epsilon^{meas}|}{\epsilon^{ideal}_{max} - \epsilon^{ideal}_{min}},$$

where $\epsilon^{ideal}$ = ideal expectation value, $\epsilon^{meas}$ = measured expectation value, $\epsilon^{ideal}_{max}$ = ideal maximum value, and $\epsilon^{ideal}_{min}$ = ideal minimum value. $A_{mean}$ is simply the average of the value of $A$ across multiple measurements.

This metric is used because it is invariant to global shifts and scaling in the range of attainable values. In other words, regardless of whether you shift the range of possible expectation values higher or lower or increase the spread, the value of $A$ should remain consistent.

Get started

Fire Opal Performance Management uses Qiskit v2.0.0, which is the recommended version. Supported versions are Qiskit >=v2.0.0. Authenticate using your IBM Quantum Platform API key, and select the Qiskit Function as follows. (This snippet assumes you've already saved your account to your local environment.)

# Added by doQumentation — required packages for this notebook
!pip install -q matplotlib numpy qiskit qiskit-ibm-catalog qiskit-ibm-runtime

from qiskit_ibm_catalog import QiskitFunctionsCatalog

catalog = QiskitFunctionsCatalog(channel="ibm_quantum_platform")

# Access Function
perf_mgmt = catalog.load("q-ctrl/performance-management")

Estimator primitive

Estimator example

Use Fire Opal Performance Management's Estimator primitive to determine the expectation value of a single circuit-observable pair. In addition to the qiskit-ibm-catalog and qiskit packages, you will also use the numpy package to run this example. You can install this package by uncommenting the following cell if you are running this example in a notebook using the IPython kernel.

# %pip install numpy

1. Create the circuit

As an example, generate a random Hermitian operator and an observable to input to the Performance Management function.

import numpy as np
from qiskit.circuit.library import iqp
from qiskit.quantum_info import random_hermitian, SparsePauliOp

n_qubits = 50

# Generate a random circuit
mat = np.real(random_hermitian(n_qubits, seed=1234))
circuit = iqp(mat)
circuit.measure_all()

# Define observables as a string
observable = SparsePauliOp("Z" * n_qubits)

# Create PUB tuple
estimator_pubs = [(circuit, observable)]

2. Run the circuit

Run the circuit and optionally define the backend and number of shots.

# This cell is hidden from users
from qiskit_ibm_runtime import QiskitRuntimeService

service = QiskitRuntimeService()
backend_name = service.least_busy().name

# Run the circuit using the estimator
qctrl_estimator_job = perf_mgmt.run(
    primitive="estimator",
    pubs=estimator_pubs,
    backend_name=backend_name,
)

You can use the familiar Qiskit Serverless APIs to check your Qiskit Function workload's status:

qctrl_estimator_job.status()

'QUEUED'

3. Retrieve the result

# Retrieve the counts from the result list
result = qctrl_estimator_job.result()

The results have the same format as an Estimator result:

print(
    f"The result of the submitted job had {len(result)} PUB and has a value:\n {result}\n"
)
print(
    f"The associated PubResult of this job has the following DataBins:\n {result[0].data}\n"
)
print(f"And this DataBin has attributes: {result[0].data.keys()}")
print(
    f"The expectation values measured from this PUB are: \n{result[0].data.evs}"
)

The result of the submitted job had 1 PUB and has a value:
 PrimitiveResult([PubResult(data=DataBin(evs=-0.0035, stds=0.999993874981242), metadata={'precision': None})], metadata={})

The associated PubResult of this job has the following DataBins:
 DataBin(evs=-0.0035, stds=0.999993874981242)

And this DataBin has attributes: dict_keys(['evs', 'stds'])
The expectation values measured from this PUB are: 
-0.0035

Estimator inputs

vorsicht

Fire Opal Performance Management accepts abstract circuits, in contrast to the native Qiskit Runtime primitives, which only accept circuits that are written in the target backend’s Instruction Set Architecture (ISA). For best results, do not transpile circuits before submitting via the Performance Management function.

Name	Type	Description	Required	Default	Example
pubs	QctrlEstimatorPubLike or list[QctrlEstimatorPubLike]	One or more tuples containing the inputs listed under EstimatorPubLike components	Yes	N/A	(circuit, observables, parameter_values)
backend_name	str	The name of the backend	No	The least busy backend that your instance has access to	"ibm_fez"
options	dict	Input options; see Options section for more details	No	See the Options section for details	{"default_shots": 2048}

QctrlEstimatorPubLike components (derived from the Qiskit Runtime PUB definition):

• A single circuit defined as a QuantumCircuit or in OpenQASM 2.0 or 3.0 string format.
• One or more observables that specify the expectation values to estimate, in any of the formats denoted in the list "Supported observables formats".
• (Optional) A collection of parameter values to bind the circuit against, which follow the same array broadcasting rules as the QiskitRuntime primitives.
• (Optional) A target precision for expectation values to estimate.
• (Optional) A real number representing the precision, or a dictionary of run options containing the shot count. For example: {"shots": <int>}.

Supported observables formats:

• Any one of the ObservablesArrayLike formats, such as Pauli, SparsePauliOp, PauliList, or str
• A Pauli string: "XY"
• A dictionary - Pauli strings with coefficients: {"XY": 0.5, "YZ": 0.3}
• A list of Pauli strings: ["XY", "YZ", "ZX"]
• A list of Pauli strings with coefficients: [("XY", 0.5), ("YZ", 0.3)]
• A nested list of Pauli strings: [["XY", "YZ"], ["ZX", "XX"]]
• A nested list of Pauli strings with coefficients: [[("XY", 0.1), ("YZ", 0.2)], [("ZX", 0.3), ("XX", 0.4)]]

Supported backends: The following list of backends are currently supported. If your device is not listed, reach out to Q-CTRL to add support.

service.backends()

[<IBMBackend('ibm_fez')>,
 <IBMBackend('ibm_brisbane')>,
 <IBMBackend('ibm_pittsburgh')>,
 <IBMBackend('ibm_kingston')>,
 <IBMBackend('ibm_torino')>,
 <IBMBackend('ibm_marrakesh')>]

Options:

Name	Type	Description	Default
session_id	str	An existing Qiskit Runtime session ID	"cw4r3je6f0t010870y3g"
default_shots	int	The number of shots to use for each circuit	2048
default_precision	float	The target precision for expectation values to estimate for each circuit	0.015625
job_tags	list[str]	A list of job tags	[]

Estimator outputs

Name	Type	Description	Example
N/A	PrimitiveResult	The PrimitiveResult corresponding to the list of input PUBs	PubResult(data=DataBin(evs=[0.1234], stds=[0.1]))

Sampler primitive

Sampler example

Use Fire Opal Performance Management's Sampler primitive to run a Bernstein–Vazirani circuit. This algorithm, used to find a hidden string from the outputs of a black box function, is a common benchmarking algorithm because there is a single correct answer. 1. Create the circuit

Define the correct answer to the algorithm, the hidden bitstring, and the Bernstein–Vazirani circuit. You can adjust the width of the circuit by simply changing the circuit_width.

import qiskit

circuit_width = 35
hidden_bitstring = "1" * circuit_width

# Create circuit, reserving one qubit for BV oracle
bv_circuit = qiskit.QuantumCircuit(circuit_width + 1, circuit_width)
bv_circuit.x(circuit_width)
bv_circuit.h(range(circuit_width + 1))
for input_qubit, bit in enumerate(reversed(hidden_bitstring)):
    if bit == "1":
        bv_circuit.cx(input_qubit, circuit_width)
bv_circuit.barrier()
bv_circuit.h(range(circuit_width + 1))
bv_circuit.barrier()
for input_qubit in range(circuit_width):
    bv_circuit.measure(input_qubit, input_qubit)

# Create PUB tuple
sampler_pubs = [(bv_circuit,)]

2. Run the circuit

Run the circuit and optionally define the backend and number of shots.

# Run the circuit using the sampler
qctrl_sampler_job = perf_mgmt.run(
    primitive="sampler",
    pubs=sampler_pubs,
    backend_name=backend_name,
)

Check your Qiskit Function workload's status or return results as follows:

qctrl_sampler_job.status()

'QUEUED'

3. Retrieve the result

# Retrieve the job results
sampler_result = qctrl_sampler_job.result()

# Get results for the first (and only) PUB
pub_result = sampler_result[0]
counts = pub_result.data.c.get_counts()

print(f"Counts for the meas output register: {counts}")

Counts for the meas output register: {'00000000000000000000000000000000110': 1, '00000000000000000000000000000000111': 1, '00000000000000000000000000000001010': 1, '00000000000000000000000000000001111': 1, '00000000000000000000000000000010001': 4, '00000000000000000000000000000011010': 1, '00000000000000000000000000000100011': 1, '00000000000000000000000000000101111': 1, '00000000000000000000000000000111010': 1, '00000000000000000000000000001100111': 1, '00000000000000000000000000010111111': 1, '00000000000000000000000000011011111': 1, '00000000000000000000000000011100010': 1, '00000000000000000000000000011101010': 1, '00000000000000000000000000011111111': 1, '00000000000000000000000000100000100': 2, '00000000000000000000000000100101101': 1, '00000000000000000000000000101101111': 1, '00000000000000000000000000101111110': 1, '00000000000000000000000000110110011': 1, '00000000000000000000000001000000000': 1, '00000000000000000000000001000110111': 1, '00000000000000000000000001010010110': 1, '00000000000000000000000001011111110': 3, '00000000000000000000000001111011110': 1, '00000000000000000000000001111111001': 1, '00000000000000000000000001111111101': 1, '00000000000000000000000001111111110': 1, '00000000000000000000000010011011111': 1, '00000000000000000000000010101111110': 1, '00000000000000000000000010111011000': 1, '00000000000000000000000010111110111': 1, '00000000000000000000000010111111101': 1, '00000000000000000000000010111111111': 1, '00000000000000000000000011001111011': 1, '00000000000000000000000011010111011': 1, '00000000000000000000000011101111111': 1, '00000000000000000000000011110111111': 1, '00000000000000000000000011111111111': 3, '00000000000000000000000100110100110': 1, '00000000000000000000000101001011011': 1, '00000000000000000000000101101110100': 1, '00000000000000000000000101111111111': 1, '00000000000000000000000110111111111': 1, '00000000000000000000000111111101110': 1, '00000000000000000000000111111101111': 1, '00000000000000000000000111111111011': 1, '00000000000000000000000111111111110': 1, '00000000000000000000000111111111111': 3, '00000000000000000000001000001001011': 1, '00000000000000000000001000110111111': 1, '00000000000000000000001001001100101': 1, '00000000000000000000001001011111010': 1, '00000000000000000000001010111111001': 1, '00000000000000000000001011101111101': 1, '00000000000000000000001111011110011': 1, '00000000000000000000001111101111111': 1, '00000000000000000000001111111101111': 1, '00000000000000000000001111111111010': 1, '00000000000000000000001111111111011': 1, '00000000000000000000001111111111101': 1, '00000000000000000000001111111111111': 1, '00000000000000000000010000000000110': 1, '00000000000000000000010000111011001': 1, '00000000000000000000010000111111111': 1, '00000000000000000000010001001111001': 1, '00000000000000000000010001001111111': 1, '00000000000000000000010001010101011': 1, '00000000000000000000010111111110100': 1, '00000000000000000000011000001001111': 1, '00000000000000000000011111101111111': 1, '00000000000000000000011111111111101': 1, '00000000000000000000011111111111110': 1, '00000000000000000000100000001101111': 1, '00000000000000000000100000010001011': 1, '00000000000000000000100000011111100': 1, '00000000000000000000100000100101110': 1, '00000000000000000000100001001111111': 1, '00000000000000000000100001101111001': 1, '00000000000000000000100011101111011': 1, '00000000000000000000100100000001011': 1, '00000000000000000000100100111111101': 1, '00000000000000000000100101011111011': 1, '00000000000000000000100101101111111': 1, '00000000000000000000100111101101011': 1, '00000000000000000000100111111101011': 1, '00000000000000000000100111111111011': 1, '00000000000000000000101011001111111': 1, '00000000000000000000101011111111101': 1, '00000000000000000000101101111011011': 1, '00000000000000000000101101111111101': 1, '00000000000000000000101110111101011': 1, 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'11111111111111111101111101111111101': 1, '11111111111111111101111101111111110': 1, '11111111111111111101111110111110110': 1, '11111111111111111101111110111111011': 1, '11111111111111111101111111001110011': 1, '11111111111111111101111111011101011': 1, '11111111111111111101111111101111010': 1, '11111111111111111101111111110010110': 1, '11111111111111111101111111110111011': 1, '11111111111111111101111111111100111': 1, '11111111111111111101111111111110000': 1, '11111111111111111101111111111110111': 2, '11111111111111111101111111111111001': 1, '11111111111111111101111111111111110': 4, '11111111111111111101111111111111111': 4, '11111111111111111110000011111111111': 1, '11111111111111111110000111101110111': 1, '11111111111111111110001000001111110': 1, '11111111111111111110001011111101111': 1, '11111111111111111110001111011111101': 1, '11111111111111111110010000000011111': 1, '11111111111111111110010111010111111': 1, '11111111111111111110010111101111111': 1, '11111111111111111110011001000001000': 1, '11111111111111111110011101111111011': 1, '11111111111111111110011101111111101': 1, '11111111111111111110011110111101111': 1, '11111111111111111110011110111111010': 1, '11111111111111111110011110111111110': 1, '11111111111111111110011111011111101': 1, '11111111111111111110011111100111010': 1, '11111111111111111110011111101111111': 3, '11111111111111111110011111111110101': 1, '11111111111111111110011111111110110': 1, '11111111111111111110100011101011111': 1, '11111111111111111110100011111010101': 1, '11111111111111111110100111111110111': 1, '11111111111111111110101101111011101': 1, '11111111111111111110101111111101111': 1, '11111111111111111110101111111111101': 1, '11111111111111111110101111111111110': 2, '11111111111111111110110101110111011': 1, '11111111111111111110110110111110111': 1, '11111111111111111110110111011111011': 1, '11111111111111111110110111101110110': 1, '11111111111111111110111011111101011': 1, '11111111111111111110111011111111011': 1, '11111111111111111110111011111111111': 2, '11111111111111111110111101111100010': 1, '11111111111111111110111101111111110': 2, '11111111111111111110111101111111111': 2, '11111111111111111110111110100100000': 1, '11111111111111111110111110110111001': 1, '11111111111111111110111110110111101': 1, '11111111111111111110111110111110011': 1, '11111111111111111110111111101111100': 1, '11111111111111111110111111110111111': 1, '11111111111111111110111111111001010': 1, '11111111111111111110111111111011010': 1, '11111111111111111110111111111011011': 1, '11111111111111111110111111111011101': 1, '11111111111111111110111111111101011': 6, '11111111111111111110111111111101101': 1, '11111111111111111110111111111111011': 3, '11111111111111111110111111111111100': 5, '11111111111111111110111111111111110': 2, '11111111111111111110111111111111111': 9, '11111111111111111111000101111101111': 1, '11111111111111111111001001111111111': 1, '11111111111111111111001011011111111': 1, '11111111111111111111001101101101111': 1, '11111111111111111111001101111111110': 1, '11111111111111111111001110100111010': 1, '11111111111111111111001110111011101': 1, '11111111111111111111001110111111001': 1, '11111111111111111111001111101011011': 1, '11111111111111111111001111101111011': 1, '11111111111111111111001111111011100': 1, '11111111111111111111001111111100010': 1, '11111111111111111111001111111101110': 1, '11111111111111111111001111111111010': 1, '11111111111111111111010011111111111': 1, '11111111111111111111010101111101111': 1, '11111111111111111111010111101111011': 1, '11111111111111111111010111111111101': 1, '11111111111111111111011000111111110': 1, '11111111111111111111011001111111011': 1, '11111111111111111111011010101110011': 1, '11111111111111111111011011011011001': 1, '11111111111111111111011011101001111': 1, '11111111111111111111011011101111111': 1, '11111111111111111111011011111111010': 1, '11111111111111111111011100111101011': 1, '11111111111111111111011101011111011': 1, '11111111111111111111011101111101011': 1, '11111111111111111111011101111110110': 1, '11111111111111111111011101111111100': 1, '11111111111111111111011101111111111': 2, '11111111111111111111011110011111111': 1, '11111111111111111111011110101111011': 1, '11111111111111111111011110111101010': 1, '11111111111111111111011110111101111': 1, '11111111111111111111011110111111101': 1, '11111111111111111111011110111111111': 2, '11111111111111111111011111010111011': 1, '11111111111111111111011111011111101': 1, '11111111111111111111011111100111011': 1, '11111111111111111111011111101101101': 1, '11111111111111111111011111101111101': 1, '11111111111111111111011111110011101': 1, '11111111111111111111011111110101110': 1, '11111111111111111111011111110110111': 1, '11111111111111111111011111110111001': 1, '11111111111111111111011111110111110': 1, '11111111111111111111011111110111111': 2, '11111111111111111111011111111011110': 1, '11111111111111111111011111111101101': 1, '11111111111111111111011111111110011': 3, '11111111111111111111011111111111011': 3, '11111111111111111111011111111111111': 6, '11111111111111111111100010111111011': 1, '11111111111111111111100111110111111': 2, '11111111111111111111101011111011111': 1, '11111111111111111111101011111101110': 1, '11111111111111111111101100000110011': 1, '11111111111111111111101100010111111': 1, '11111111111111111111101100111111111': 1, '11111111111111111111101101011011011': 1, '11111111111111111111101101101111110': 1, '11111111111111111111101101110111010': 1, '11111111111111111111101101111101011': 1, '11111111111111111111101110111101000': 1, '11111111111111111111101111010101111': 1, '11111111111111111111101111101011111': 1, '11111111111111111111101111101100011': 1, '11111111111111111111101111101110101': 1, '11111111111111111111101111101111011': 1, '11111111111111111111101111111001011': 1, '11111111111111111111101111111010011': 1, '11111111111111111111101111111101001': 1, '11111111111111111111101111111101110': 2, '11111111111111111111101111111110011': 6, '11111111111111111111101111111110101': 1, '11111111111111111111101111111111011': 3, '11111111111111111111101111111111110': 2, '11111111111111111111101111111111111': 3, '11111111111111111111110000100001001': 1, '11111111111111111111110000111101101': 1, '11111111111111111111110010101101101': 1, '11111111111111111111110010110111011': 1, '11111111111111111111110010111111101': 1, '11111111111111111111110011011111101': 1, '11111111111111111111110011111101011': 1, '11111111111111111111110011111101110': 1, '11111111111111111111110011111111111': 1, '11111111111111111111110100111110111': 1, '11111111111111111111110101011111111': 1, '11111111111111111111110101111101111': 1, '11111111111111111111110101111111001': 1, '11111111111111111111110101111111011': 1, '11111111111111111111110110100101011': 1, '11111111111111111111110110101111111': 1, '11111111111111111111110110111101010': 1, '11111111111111111111110111011111011': 1, '11111111111111111111110111101011010': 1, '11111111111111111111110111101111111': 1, '11111111111111111111110111110011001': 1, '11111111111111111111110111110111011': 1, '11111111111111111111110111111010011': 1, '11111111111111111111110111111011111': 1, '11111111111111111111110111111101011': 1, '11111111111111111111110111111101111': 2, '11111111111111111111110111111110011': 1, '11111111111111111111110111111110110': 1, '11111111111111111111110111111111000': 1, '11111111111111111111110111111111010': 1, '11111111111111111111110111111111111': 5, '11111111111111111111111000000100100': 1, '11111111111111111111111001011111011': 1, '11111111111111111111111001111110111': 1, '11111111111111111111111010110111111': 1, '11111111111111111111111010111110111': 1, '11111111111111111111111011001100011': 1, '11111111111111111111111011001101011': 1, '11111111111111111111111011001111010': 1, '11111111111111111111111011011111011': 1, '11111111111111111111111011101011111': 1, '11111111111111111111111011101111010': 1, '11111111111111111111111011110111100': 1, '11111111111111111111111011111000011': 1, '11111111111111111111111011111001011': 1, '11111111111111111111111011111011111': 1, '11111111111111111111111011111101110': 2, '11111111111111111111111011111111011': 2, '11111111111111111111111011111111110': 1, '11111111111111111111111011111111111': 2, '11111111111111111111111100001101110': 1, '11111111111111111111111100100101111': 1, '11111111111111111111111100110101000': 1, '11111111111111111111111100111100100': 1, '11111111111111111111111100111101111': 1, '11111111111111111111111100111110011': 1, '11111111111111111111111100111110111': 1, '11111111111111111111111100111111100': 1, '11111111111111111111111100111111110': 1, '11111111111111111111111101001111101': 1, '11111111111111111111111101011011111': 1, '11111111111111111111111101011101011': 1, '11111111111111111111111101100111111': 1, '11111111111111111111111101110110010': 1, '11111111111111111111111101111011011': 1, '11111111111111111111111101111101101': 1, '11111111111111111111111101111110011': 1, '11111111111111111111111101111110101': 1, '11111111111111111111111101111110111': 2, '11111111111111111111111101111111001': 1, '11111111111111111111111101111111011': 2, '11111111111111111111111101111111101': 2, '11111111111111111111111101111111110': 2, '11111111111111111111111101111111111': 3, '11111111111111111111111110011110011': 1, '11111111111111111111111110100011111': 1, '11111111111111111111111110101101011': 1, '11111111111111111111111110101101111': 1, '11111111111111111111111110111001101': 1, '11111111111111111111111110111011110': 1, '11111111111111111111111110111101010': 1, '11111111111111111111111110111101110': 1, '11111111111111111111111110111111010': 2, '11111111111111111111111110111111011': 6, '11111111111111111111111110111111100': 1, '11111111111111111111111110111111101': 2, '11111111111111111111111110111111111': 9, '11111111111111111111111111000111111': 1, '11111111111111111111111111001001101': 1, '11111111111111111111111111001101011': 1, '11111111111111111111111111001110111': 1, '11111111111111111111111111001111110': 5, '11111111111111111111111111010101000': 1, '11111111111111111111111111010101010': 1, '11111111111111111111111111010101011': 1, '11111111111111111111111111010101101': 1, '11111111111111111111111111010111001': 1, '11111111111111111111111111010111011': 2, '11111111111111111111111111011101010': 1, '11111111111111111111111111011110101': 1, '11111111111111111111111111011111001': 1, '11111111111111111111111111011111011': 3, '11111111111111111111111111011111100': 1, '11111111111111111111111111011111101': 2, '11111111111111111111111111011111110': 4, '11111111111111111111111111011111111': 17, '11111111111111111111111111100001111': 1, '11111111111111111111111111100101010': 1, '11111111111111111111111111100111110': 1, '11111111111111111111111111100111111': 1, '11111111111111111111111111101010110': 1, '11111111111111111111111111101011101': 3, '11111111111111111111111111101101001': 1, '11111111111111111111111111101101011': 2, '11111111111111111111111111101110111': 1, '11111111111111111111111111101111001': 1, '11111111111111111111111111101111011': 6, '11111111111111111111111111101111111': 2, '11111111111111111111111111110011011': 3, '11111111111111111111111111110011111': 1, '11111111111111111111111111110101111': 4, '11111111111111111111111111110110011': 1, '11111111111111111111111111110111011': 2, '11111111111111111111111111110111111': 1, '11111111111111111111111111111000010': 1, '11111111111111111111111111111001001': 1, '11111111111111111111111111111001110': 1, '11111111111111111111111111111010101': 1, '11111111111111111111111111111010111': 1, '11111111111111111111111111111011000': 1, '11111111111111111111111111111011011': 4, '11111111111111111111111111111100001': 1, '11111111111111111111111111111100011': 1, '11111111111111111111111111111100101': 1, '11111111111111111111111111111101111': 7, '11111111111111111111111111111110010': 3, '11111111111111111111111111111110101': 2, '11111111111111111111111111111110111': 11, '11111111111111111111111111111111000': 2, '11111111111111111111111111111111001': 4, '11111111111111111111111111111111010': 5, '11111111111111111111111111111111011': 29, '11111111111111111111111111111111101': 9, '11111111111111111111111111111111110': 6, '11111111111111111111111111111111111': 33}

3. Plot the top bitstrings

Plot the bitstring with the highest counts to see if the hidden bitstring was the mode.

import matplotlib.pyplot as plt

def plot_top_bitstrings(counts_dict, hidden_bitstring=None):
    # Sort and take the top 100 bitstrings
    top_100 = sorted(counts_dict.items(), key=lambda x: x[1], reverse=True)[
        :100
    ]
    if not top_100:
        print("No bitstrings found in the input dictionary.")
        return

    # Unzip the bitstrings and their counts
    bitstrings, counts = zip(*top_100)

    # Assign colors: purple if the bitstring matches hidden_bitstring, otherwise gray
    colors = [
        "#680CE9" if bit == hidden_bitstring else "gray" for bit in bitstrings
    ]

    # Create the bar plot
    plt.figure(figsize=(15, 8))
    plt.bar(
        range(len(bitstrings)), counts, tick_label=bitstrings, color=colors
    )

    # Rotate the bitstrings for better readability
    plt.xticks(rotation=90, fontsize=8)
    plt.xlabel("Bitstrings")
    plt.ylabel("Counts")
    plt.title("Top 100 Bitstrings by Counts")

    # Show the plot
    plt.tight_layout()
    plt.show()

The hidden bitstring is highlighted in purple, and it should be the bitstring with the highest number of counts.

plot_top_bitstrings(counts, hidden_bitstring)

Sampler inputs

vorsicht

Fire Opal Performance Management accepts abstract circuits, in contrast to the native Qiskit Runtime primitives, which only accept circuits that are written in the target backend’s Instruction Set Architecture (ISA). For best results, do not transpile circuits before submitting via the Performance Management function.

Name	Type	Description	Required	Default	Example
pubs	QctrlSamplerPubLike or list[QctrlSamplerPubLike]	One or more tuples containing the inputs listed under SamplerPubLike components	Yes	N/A	(circuit, parameter_values)
backend_name	str	The name of the backend	No	The least busy backend that your instance has access to	"ibm_fez"
options	dict	Input options; see Options section for more details	No	See the Options section for details	{"default_shots": 2048}

QctrlSamplerPubLike components (derived from the Qiskit Runtime PUB definition):

• A single circuit defined as a QuantumCircuit or in OpenQASM 2.0 or 3.0 string format.
• (Optional) A collection of parameter values to bind the circuit against.
• (Optional) An integer representing the shot count, or a dictionary of runtime options containing the shot count. For example: (circ, None, 123) or (circ, None, {"shots": 123}).

Supported backends: Run the following code to see the list of backends that are currently supported. If your device is not listed, reach out to Q-CTRL to add support.

service.backends()

[<IBMBackend('ibm_fez')>,
 <IBMBackend('ibm_brisbane')>,
 <IBMBackend('ibm_pittsburgh')>,
 <IBMBackend('ibm_kingston')>,
 <IBMBackend('ibm_torino')>,
 <IBMBackend('ibm_marrakesh')>]

Options:

Name	Type	Description	Default
session_id	str	An existing Qiskit Runtime session ID	"cw4r3je6f0t010870y3g"
default_shots	int	The number of shots to use for each circuit	2048
job_tags	list[str]	The list of desired job tags	[]

Sampler outputs

Name	Type	Description	Example
N/A	PrimitiveResult	The PrimitiveResult corresponding to the list of input PUBs	PrimitiveResult([PubResult(data=DataBin(c=BitArray(<shape=(), num_shots=2048, num_bits=35>)), metadata={'shots': 2048})], metadata={})

Get support

For any questions or issues, contact Q-CTRL.

Next steps

Recommendations

• Request access to Q-CTRL Performance Management
• Try the Transverse-Field Ising Model with Q-CTRL's Performance Management tutorial.
• Try the Quantum Phase Estimation with Q-CTRL's Qiskit Functions tutorial
• Review Mundada P. S., et al. (2023). Experimental Benchmarking of an Automated Deterministic Error-Suppression Workflow for Quantum Algorithms. Physical Review Applied, 20, 2.
• Review Kanno, S., et al. (2025). Tensor-based quantum phase difference estimation for large-scale demonstration. arXiv preprint arXiv:2408.04946.
• Review SoftBank Corp, Demonstration Experiment of a Communication Service Fault Diagnosis System Using Quantum Machine Learning (blog), 30 August, 2024.
• Review Yamauchi, H., et al. (2024). Parametrized Energy-Efficient Quantum Kernels for Network Service Fault Diagnosis. arXiv preprint arXiv:2405.09724v1.
• Review Yamauchi, H., et al. (2025). Quantum spectroscopy of topological dynamics via a supersymmetric Hamiltonian. arXiv preprint arXiv:2511.23169v1.
• Review Wang, Y., et al. (2025). Δ-Motif: Subgraph Isomorphism at Scale via Data-Centric Parallelism. arXiv preprint arXiv:2508.21287.
• Review Paterakis, N. G., et al. (2025). Quantum Computing in the Computational Landscape of Power Electronics: Vision and Reality. arXiv preprint arXiv:2507.02577.
• Review Gharibyan, H., et al. (2023). Hierarchical Learning for Quantum ML: Novel Training Technique for Large-Scale Variational Quantum Circuits. arXiv preprint arXiv:2311.12929.
• Review the Mitsubishi Chemical Corp case study.
• Review the Redacted bank case study.
• Review the BlueQubit case study.