Aluminum on sapphire qubits provide proof of concept for surface codes and digitized adiabatic evolution.

An earlier series of articles on quantum computing discussed the differences between the gate logic model and the quantum annealing model. The gate logic model, like transistor logic, uses a limited number of “gates” to construct a general purpose computer, theoretically capable of solving any problem for which a suitable algorithm can be found. In systems designed around the gate logic model, noise from a variety of sources is a significant issue. Complex error correction mechanisms are needed to preserve the system state for the duration of the calculation.

In the quantum annealing model, in contrast, the calculation takes place through adiabatic evolution of the system from the original “problem” state to an optimal “solution” state. A quantum annealer models the problem to be solved as an Ising glass, a system of interacting spins. Adiabatic evolution maintains the system in the ground state, so it is less vulnerable to noise than a gate logic system. Because the initial state can be arbitrary, such a system is also relatively simple to program. However, it is not a general purpose computer, and it is not yet clear how much of an advantage this approach will offer for the problems that it does address.

Since the original series, several major software companies have made substantial investments in quantum computing. Google’s Quantum AI Lab, for example, has partnered with UC Santa Barbara’s quantum computing research group. This team, headed by John Martinis, is pursuing a hybrid approach they call “digitized adiabatic evolution,” which seeks to capture many of the advantages of a quantum annealer in a general purpose, gate-based computing system.

**Digitizing adiabatic evolution**

This approach is described in detail elsewhere, particularly in a lengthy supplementary material section. Briefly, though, they observe that the adiabatic evolution of a Hamiltonian can be approximated by the Lie-Trotter-Suzuki formula, much as a complex waveform can be approximated by a Fourier series. In this way, the essentially analog evolution process can be digitized and represented by manipulation of binary qubits. In theory, such a system can be applied to general problems, independent of the connectivity between nodes and the strict applicability of the Ising glass model. At the same time, it preserves the basic idea of the quantum annealing model as a solver of optimization problems.

However, the strictly binary nature of qubits in the gate logic model introduces fluctuating energy levels and noise back into the system. In particular, one of the most significant sources of noise is quantum leakage. While a logical qubit, like a theoretical transistor, is a binary device, the underlying physical system used to realize it may not be. It may be able to assume energy states other than the designated ON and OFF values of the qubit. (For example, excess heat may excite the device to higher energy states.) These so-called “non-computational” energy states represent a loss of information from the computation and can randomize the values of adjacent qubits. Ultimately, leakage and other noise degrades the quantum superposition of states.

Quantum computing theorists have proposed “surface codes,” discussed in detail in Nature, as a method for protecting calculations from degradation due to noise. Essentially, the surface code stores multiple copies of the data, using parity correction qubits to ensure that no data errors have occurred. If the data and correction qubits are arranged in a checkerboard pattern, a board with (4n+1)² qubits can tolerate up to n+1 errors. The error rate is predictable from the decoherence time of the quantum system being used.

If the first significant advance by the Google/UCSB group was digitization of adiabatic evolution, the second is the realization of this theoretical construct in actual hardware. They constructed a chain of nine superconducting qubits, made of cross-shaped aluminum on a sapphire substrate. While nine qubits — alternating between measure and data — doesn’t seem like very many, the group was able to demonstrate the principles underlying surface codes. Their device is a proof-of-concept for both surface codes and the idea of digitized adiabatic evolution.

Nine qubits isn’t very many. The first Intel microprocessors had more than two thousand transistors. Quantum computing is clearly still in its infancy. But this work is among the first to show the critical elements of a viable quantum computing platform.

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