Today’s quantum computers are noisy and highly prone to errors. As we scale up, we will start to better understand and fix these errors until, eventually, we reach fault tolerance. At this point, the real promise of quantum computing and world-changing applications will be unlocked.
Scaling to fault tolerance is an incremental process and one where successive generations of quantum computers will help us understand (and fix) the errors that these machines are prone to. Early use cases will be unlocked as we continue to scale, and quantum chemistry is expected to be one such application area, requiring the development of application-specific quantum algorithms.
In a new paper, Statistical Phase Estimation and Error Mitigation on a Superconducting Quantum Processor, published in PRX Quantum, our team tested a promising quantum algorithm on a real quantum processor.
The method that we tested (statistical phase estimation) is specifically targeted at near-term and early fault-tolerant quantum computers – and this algorithm indeed looks like an ideal candidate to run on early fault-tolerant devices.
Our work tests this algorithm with error mitigation on Rigetti's quantum processors. The molecules investigated include examples motivated by pharmaceutical applications, in collaboration with Astex Pharmaceuticals, using chemical embedding techniques to make this task tractable on current quantum devices.
Error correction versus mitigation
Quantum error correction and quantum error mitigation are two different schemes to deal with noise in devices, which can cause errors in computation.
Quantum error correction methods use multiple physical qubits to represent a single logical qubit. Data is preserved by distributing the information across multiple qubits. Quantum decoders can then detect and correct any errors that occur during computation.
By contrast, quantum error mitigation methods are employed to infer less noisy outcomes of quantum computations, rather than correcting them. This is often done by repeatedly running slightly different circuits and classically post-processing the results.
Quantum error mitigation methods provide a reduction in noise that can be useful in the NISQ (noisy intermediate-scale quantum) era, as restraints in quantum hardware can make full quantum error correction less feasible.
For useful computation involving many qubits and deep circuits, full quantum error correction will be necessary. However, quantum error mitigation provides us with a way to improve the performance of our algorithms as we start to leave NISQ and enter the quantum error correction era.
QPE and statistical phase estimation
Quantum Phase Estimation (QPE) is one of the leading algorithms to study quantum chemistry and materials science problems on quantum computers. It is a promising algorithm and is already widely studied because of its potential to perform chemical and solid-state calculations on future, fault-tolerant quantum computers.
However, while the algorithm has many benefits, the circuits involved are extremely deep, and so cannot be accurately performed on current quantum computers. Several researchers have proposed statistical alternatives to QPE in recent years to overcome these issues. These modifications provide benefits, including shorter circuits and better suitability for error mitigation. But research into practical implementations on real quantum processors is still lacking.
Our paper presents a practical implementation, testing a quantum algorithm called “statistical phase estimation” as a potentially better quantum algorithm for real-world chemistry problems than QPE, particularly on near-term quantum computers.
Our work shows statistical phase estimation has a natural resilience to noise and can achieve far higher accuracy than previous research suggested. The work was carried out on one of Rigetti’s quantum processors, which was used to compute the ground state of certain molecules using up to seven qubits.
Essentially, we have developed a chemistry compiler that uses error mitigation techniques. As we mentioned, error mitigation is different from error correction. Quantum error correction is when you can spot an error has occurred and then correct it. Error mitigation is when you try to estimate how errors have changed the result and then extrapolate to a result with reduced errors.
The paper also outlines how this implementation could be adapted as quantum computers continue to evolve and push closer to fault tolerance.
This work is an important step as we move towards fault tolerance. Not only has it highlighted the suitability of statistical phase estimation for future fault tolerant devices, but it also combines error mitigation and chemical embedding methods in a novel way, allowing us to reduce circuit depth and unlock exciting, new applications, sooner.
You can read the full Statistical Phase Estimation and Error Mitigation on a Superconducting Quantum Processorpaper here.