Quantum computing continues to advance at a rapid pace, but one challenge that holds the field back is mitigating the noise that plagues quantum machines. This leads to much higher error rates compared to classical computers.

This noise is often caused by imperfect control signals, interference from the environment, and unwanted interactions between qubits, which are the building blocks of a quantum computer. Performing computations on a quantum computer involves a “quantum circuit,” which is a series of operations called quantum gates. These quantum gates, which are mapped to the individual qubits, change the quantum states of certain qubits, which then perform the calculations to solve a problem.

But quantum gates introduce noise, which can hamper a quantum machine’s performance.

Researchers at

Researchers have developed a technique for making quantum computing more resilient to noise, which boosts performance. Credit: Christine Daniloff, MIT

Their framework, called QuantumNAS (noise adaptive search), is much less computationally intensive than other search methods and can identify quantum circuits that improve the neural networks, including more parameters often increases the model’s accuracy. But in variational quantum computing, more parameters require more quantum gates, which introduce more noise.

With QuantumNAS, the researchers seek to reduce the overall search and training cost while identifying the quantum circuit that contains the ideal number of parameters and appropriate architecture to maximize accuracy and minimize noise.

Building a “SuperCircuit”

To do that, they first design a “SuperCircuit,” which contains all the possible parameterized quantum gates in the design space. That SuperCircuit will be used to generate smaller quantum circuits that can be tested.

They train the SuperCircuit once, and then because all other candidate circuits in the design space are subsets of the SuperCircuit, they inherit corresponding parameters that have already been trained. This reduces the computational overhead of the process.

Once the SuperCircuit has been trained, they use it to search for circuit architectures that meet a targeted objective, in this case high robustness to noise. The process involves searching for quantum circuits and qubit mappings at the same time using what is known as an evolutionary search algorithm.

This algorithm generates some quantum circuit and qubit mapping candidates, then evaluates their accuracy with a noise model or on a real machine. The results are fed back to the algorithm, which selects the best performing parts and uses them to start the process again until it finds the ideal candidates.

“We know that different qubits have different properties and gate error rates. Since we’re only using a subset of the qubits, why don’t we use the most reliable ones? We can do this through co-search of the architecture and qubit mapping,” Wang explains.

Once the researchers have arrived at the best quantum circuit, they train its parameters and perform quantum gate pruning by removing any quantum gates that have values close to zero, since they don’t contribute much to the overall performance. Removing theses gates reduces sources of noise and further improves the performance on real quantum machines. Then they fine-tune the remaining parameters to recover any accuracy that was lost.

After that step is complete, they can deploy the quantum circuit to a real machine.

When the researchers tested their circuits on real quantum devices, they outperformed all the baselines, including circuits hand-designed by humans and others made using other computational methods. In one experiment, they used QuantumNAS to produce a noise-robust quantum circuit that was used to estimate the ground state energy for a particular molecule, which is an important step in quantum chemistry and drug discovery. Their method made a more accurate estimation than any of the baselines.

Now that they have shown the effectiveness of QuantumNAS, they want to use these principles to make the parameters in a quantum circuit robust to noise. The researchers also want to improve the scalability of a quantum neural network by training a quantum circuit on a real quantum machine, rather than a classical computer.

“This is an interesting work that searches for noise-robust ansatz and qubit mapping of parametric quantum circuits,” says Yiyu Shi, a professor of computer science and engineering at the University of Notre Dame, who was not involved with this research. “Different from the naive search method that trains and evaluates a large number of candidates individually, this work trains a SuperCircuit and uses it to evaluate many candidates, which is much more efficient.”

“In this work, Hanrui and collaborators alleviate the challenge of searching for an efficient parametrized quantum circuit by training one SuperCircuit and using it to evaluate many candidates which becomes very efficient as it requires one training procedure. Once the SuperCircuit is trained, it can be used to search for the circuit ansatz and qubit mapping. After training the SuperCircuit, we can use it to search for the circuit ansatz and qubit mapping. The evaluation process is done using noise models or running on the real quantum machine,” says Sona Najafi, a research scientist at IBM Quantum who was not involved with this work. “The protocol has been tested using IBMQ quantum machines on VQE and QNN tasks demonstrating more accurate ground state energy and higher classification accuracy.”

To encourage more work in this area, the researchers created an open-source library, called TorchQuantum, that contains information about their projects, tutorials, and tools that can be used by other research groups.

Reference: “QuantumNAS: Noise-Adaptive Search for Robust Quantum Circuits” by Hanrui Wang, Yongshan Ding, Jiaqi Gu, Zirui Li, Yujun Lin, David Z. Pan, Frederic T. Chong and Song Han, 7 January 2022, Quantum Physics. arXiv:2107.10845

This work was supported by the National Science Foundation, the MIT-IBM Watson AI Lab, the Qualcomm Innovation Fellowship, and the U.S. Department of Energy.