Maximizing performance improvement

IBM and other vendors have continuously delivered major improvements in the scale and performance of their quantum hardware, bringing us to the era of quantum utility. Hardware developments have been ongoing at a rapid pace. But even with these advances, noise and error often cause quantum algorithms to underperform compared to ideal expectations. Q-CTRL performance management bridges this performance gap by automating deterministic error-suppression with zero user configuration and zero QPU overhead. Running quantum circuits with Q-CTRL's performance management strategy should always provide an advantage over running without. The degree of advantage differs depending on factors outlined in this topic, such as the characteristics of the circuit and the type of algorithm being run.

Expected improvement

While device sizes have increased substantially, up to and over 127 qubits on IBM Quantum services, device coherence limits (T1/T2 times) and gate fidelities improve at a slower rate. Thus, performance management strategies are essential to improving circuit execution and enabling devices to perform up to their potential. Q-CTRL's error suppression prevents errors from occurring during execution, which allows you to run circuits with more qubits and more gates, while still achieving higher performance. Benchmarking shows that Q-CTRL can enable 10× deeper circuits to perform well on IBM hardware, meaning that if an algorithm would typically lose signal around 30 CNOT gates, Q-CTRL can maintain execution quality up to approximately 300 CNOT gates. In fact, the benefit that you get from Q-CTRL's performance management will be much more significant on a larger circuit, since there is more room for improvement. Smaller circuits, with fewer qubits or gates, will yield more comparable results with or without Q-CTRL since the quality of execution will not be as affected by noise.

Circuit width

It's also typical for accuracy to wane at higher qubit counts. As the number of qubits increases, there are more opportunities for error to creep in and corrupt a calculation, due to interactions between qubits and a greater number of hops required to connect qubits that are farther apart. With Q-CTRL performance management, it's possible to get high-quality results while using more qubits in your algorithms. The number of qubits that can be used depends on the complexity of the algorithm. For a compact circuit such as GHZ generation, Q-CTRL's performance management can enable the device to use up to 100 qubits on a 127-qubit device. With a relatively simple benchmarking circuit, such as Bernstein–Vazirani, you can use Q-CTRL to run circuits within the 45-50 qubit range and still get the right answer. When dealing with a more complicated circuit, like quantum Fourier transform, Q-CTRL performance management will allow you to successfully use around 15 qubits. These numbers far surpass what would be possible without using Q-CTRL's error suppression methods.

The following image shows the benchmarking results of running Bernstein–Vazirani circuits up to 27-qubits on IBM Algiers with Q-CTRL performance management enabled. Error suppression extends the hardware's coherence time so that circuits with more qubits can be executed successfully.

At a certain point, even though a device has more qubits available and the best error suppression tools available, there is a limit to the width of a circuit that will still provide meaningful results. This limit will continue to increase as both hardware and software improve rapidly, but for now, it's best to test out those limits on your use case and then work within them.

Circuit depth

Circuit depth is an important property that serves as a measure of complexity. The depth of a quantum circuit signifies how many "layers" of quantum gates, executed sequentially, are required to complete the defined computation. Because quantum gates take time to implement, the depth of a circuit roughly corresponds to the amount of time it takes the quantum computer to execute the circuit. To determine if a quantum circuit can be computed on a given hardware device, circuit depth is a major factor taken into consideration with information about the hardware's tolerance to noise.

Environmental noise causes decoherence to a point where qubits can no longer carry out computation as their states have been too vastly altered by the noise. T1 time is a typical timescale measure used to characterize the amount of error a quantum computer can tolerate before becoming unusable. While Q-CTRL performance management can eliminate or suppress many types of noise, ultimately T1 time is constrained by the hardware device and poses a fundamental limit to the maximum circuit depth that a hardware device can accommodate.

Given the nature of decoherence and its correlation with system size, Q-CTRL performance management provides higher success probabilities when executing on shallower circuits. On the other hand, the difference between results with and without Q-CTRL performance management is more significant with larger circuits, so long as they don't exceed hardware limitations.

If the circuit depth approaches the T1 limit, Q-CTRL performance management will provide a warning in both the execute and validate functions to indicate that you're approaching hardware limits. The benefit that Q-CTRL performance management can bring to performance is expected to be less noticeable in these conditions.

Types of algorithms

Q-CTRL performance management delivers different advantages depending on the algorithm. The performance improvement factor grows with system size until the hardware coherence limits ultimately prevent further execution from being performed. Q-CTRL performance management's error suppression techniques have been benchmarked across various algorithms and saw significant improvement in each. To learn more about how Q-CTRL performance management improves performance across various algorithms, this technical manuscript describes the individual parts of the pipeline in depth.

The previous image compares three types of algorithms and their performance improvement factor as circuit depth increases. As Grover's search increases in complexity, it also quickly increases in circuit width and depth and becomes limited by the T1 constraints of the hardware. In this type of case, an algorithm will not see as pronounced a performance improvement compared to an algorithm that is naturally more shallow. However, more complex algorithms perform orders of magnitude worse on quantum computers, and Q-CTRL performance management makes it possible to achieve useful results that would be otherwise unattainable.

Below are two images showing Q-CTRL performance management's results applied to Berstein–Vazirani (top) and Grover's search (bottom). While Q-CTRL performance management enabled Berstein–Vazirani to consistently reach near optimal success probabilities, it also provided an 8× improvement to Grover's search and eliminated noise to achieve the correct result.

Expected output distribution

The output of quantum algorithms is a probability distribution of corresponding bitstrings, which can be translated to expected values of possible results. The correct output of the computation of a circuit may be a single one of these bitstrings, multiple bitstrings, or even a uniform distribution of probabilities across the entire range of bitstrings.

As the number of possible results that are expected in the correct outcome increases, it becomes more difficult to extract the correct outputs, and there's a greater likelihood that noise will erase the information used to encode the output. For example, if an algorithm expects a uniform probability over a wide range bitstrings, such as Grover's search, the outcome tends to appear close to a flat distribution. Since noisy computations also produce fairly even distributions, this can make it difficult to perceive the benefits of Q-CTRL performance management. For this reason, it's recommended that your anticipated circuit output is distinct from a uniform distribution.

Ready to test out the performance improvement yourself? Try running a tutorial onquantum phase estimation.