# Upgrading a Hybrid Computing Algorithm

&ball; *Physics* 14, 86

The researchers describe a protocol to run a popular classical quantum machine learning algorithm with a measurement-based quantum computer, which could enable more resource-efficient calculations.

Much like two-year-old toddlers, researchers working with quantum computers have reached this awkward ‘middle’ stage: They are beginning to understand the full potential of what they can do, but realizing that potential is, in a way tempting, just out of reach. Quantum computers have problems performing arbitrarily long calculations due to hardware limitations, and poorly executed algorithms can easily provide unexpected and often incorrect results.

One path the researchers are taking to guide quantum computers through this first phase is to run their algorithms on hybrid devices that merge a quantum toddler with its more mature sibling, a classical computer. Using machine learning techniques, researchers can combine classical and quantum processors in feedback loops to solve difficult optimization problems. Now, Ryan Ferguson and Luca Dellantonio from the University of Waterloo, Canada, and their colleagues explain how to run a popular quantum machine learning algorithm on a hybrid system where the quantum processor is “based on measurement.” [1]. Dellantonio says their proposal could allow better use of photonics platforms in hybrid computers.

The type of machine learning algorithm the team is investigating is called a variational quantum eigen solver, or the eye-catching “VQE” for short. VQE algorithms calculate the ground state energy of a molecule and are specifically designed for hybrid computers, delegating tasks between quantum and classical processors. Typically, the quantum processor makes a first “estimate” of the ground state wave function of the molecule, encoding this estimate into its qubits, then estimating the energy of that wave function by taking measurements. on the qubits. The conventional processor then adjusts the parameters of the guessed wave function to find options with lower energies.

The researchers demonstrated VQE algorithms for hybrid systems that use “circuit-based” quantum processors, which, like conventional processors, perform calculations with gates. Instead, the protocol Ferguson, Dellantonio, and their colleagues describe uses a measurement-based quantum processor, which operates without gates.

Measurement-based quantum computers—first imagined 20 years ago, perform calculations by creating an entangled quantum state on which a series of measurements are made on individual qubits in the state. Hybrid computers that use measurement-based quantum processors are attractive because they potentially allow the quantum side to perform more complex calculations with far fewer qubits than circuit-based versions, Dellantonio explains. He and his colleagues show that for a computation that can require hundreds of thousands of qubits on a current circuit-based system, their measurement-based approach may need as little as 20 qubits.

In the team’s protocol, quantum calculations are performed with a so-called graph state, which is a multiqubit state that is typically represented by a lattice diagram with vertices and edges. Vertices represent individual qubits, and edges connect the interacting qubits. First, an “ansatz” state of graph is created, which represents the initial estimate of the ground state of the system of interest. The initial state of the graph is extended by adding qubits and then measuring them. The results of these measurements are fed into the conventional computer. A new ansatz state of graph is then created and the process is repeated.

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

For now, the new protocol is purely theoretical. Dellantonio says the group is considering the possibility of testing their method – with some modifications – on an industry-available quantum circuit computer. He also notes that there are photonic systems that could be used to generate graph states and run the measurement-based protocol.

The new work marks a new approach to VQE, says Dan Browne, quantum physicist at University College London. The team’s metrics-based model potentially provides a better way to implement VQE, he says. “I expect research groups and companies developing photonic quantum computing platforms to be eager to test this idea on their devices.”

– Katherine Wright

Katherine Wright is Associate Editor-in-Chief of *Physics*.

## The references

- RR Ferguson
*et al.*, “Eigenvariational quantum solution based on measurement”, Phys. Rev. Lett.**126**, 220501 (2021).