&Bullet; *physics* 14, 86

Researchers outline a protocol for performing a popular quantum classical machine learning algorithm using what is known as a measurement-based quantum computer, which could enable more resource-efficient computations.

Much like toddlers turning two years old, researchers working on quantum computers have reached this uncomfortable “intermediate phase”: They begin to understand the full potential of their abilities, but reaching that potential is – temptingly – simply out of reach. Quantum computers have difficulty performing calculations of any length due to hardware limitations, and poorly executed algorithms can easily produce unexpected – and often incorrect – results.

One way researchers are taking to guide quantum computers through this early stage is to run their algorithms on hybrid devices that fuse a quantum child with its more mature sibling – a classic computer. Using machine learning techniques, researchers can couple classical and quantum processors in feedback loops to solve difficult optimization problems. Ryan Ferguson and Luca Dellantonio of the University of Waterloo, Canada, and colleagues are now outlining how a popular quantum machine learning algorithm can be run on a hybrid system in which the quantum processor is “measurement-based”. [1] . Dellantonio says their proposal could enable better use of photonic platforms in hybrid computers.

The type of machine learning algorithm the team is investigating is known as a quantum variation self-solver, or the catchy “VQE” for short. VQE algorithms calculate the ground state energy of a molecule and were specially developed for hybrid computers that delegate tasks between quantum and classical processors. Typically, the quantum processor takes an initial “estimate” of the molecule’s ground-state wave function, codes that guess into its qubits, and then estimates the energy of that wave function by taking measurements on the qubits. The classical processor then adjusts the parameters of the estimated wave function to find options with lower energies.

Researchers have demonstrated VQE algorithms for hybrid systems that use “circuit-based” quantum processors that, like classical processors, perform computations with gates. The protocol that Ferguson, Dellantonio and their colleagues outline uses instead a measurement-based quantum processor that works without gates.

Measurement-based quantum computers – which were first invented 20 years ago – perform calculations by creating an entangled quantum state on which a series of measurements are performed on individual qubits in the state. Hybrid computers that use measurement-based quantum processors are attractive because they potentially allow the quantum part to do more complex calculations with far fewer qubits than circuit-based versions, says Dellantonio. He and his colleagues show that for a computation that could require hundreds of thousands of qubits on a current circuit-based system, their measurement-based approach only requires around 20 qubits.

In the team’s protocol, the quantum calculations are carried out with a so-called graph state, a multi-qubit state, which is typically represented by a network diagram with corners and edges. The vertices represent individual qubits and the edges connect qubits that interact. First, an “approach” graph state is created, which represents the first assumption for the basic state of the system of interest. The initial graph state is expanded by adding qubits and then measuring. The results of these measurements are fed into the classic computer. Then a new batch graph state is generated and the process is repeated.

The measurements from the repeated cycles effectively result in a series of snapshots of the state energy for various input parameters. These snapshots are then used by the classic computer to map the landscape of the energy and to determine the minimum. The process is similar to that of circuit-based quantum processors, says Dellantonio, but the measurement-based method allows more freedom in configuring the qubits that simulate the ground state.

At the moment the new protocol is purely theoretical. Dellantonio says the group is exploring the possibility of testing their method – with some modifications – on a circuit-based quantum computer that is available in the industry. He also notes that there are photonic systems that could be used to generate graph states and perform the measurement-based protocol.

The new work marks a new approach to VQE, says Dan Browne, a quantum physicist at University College London. The team’s measurement-based model potentially offers a better way to implement VQE, he says. “I assume that the research groups and companies developing platforms for photonic quantum computers will be happy to test this idea on their devices.”

–Katherine Wright

Katherine Wright is assistant editor of *physics*.

## References

- RR Ferguson
*et al.*, “Measurement-based variation quantum eigen solver”, Phys. Rev. Lett.**126**, 220501 (2021).