Today, how many people buy a computer based on the number of transistors?

The qubit count race today reminds me of the transistor count races of the mid-80s, when every vendor truly believed their architecture, manufacturing process, and performance advantages were real. They didn’t think or even know they were wrong yet.

History is repeating itself once again, now for quantum computing.

This blog is our attempt to cut through the chaos, provide a realistic roadmap for achieving broad quantum advantage, and address the shortcomings of Quantum Volume by introducing a new benchmark that we call** Algorithmic Qubits**. We also introduce an Algorithmic Qubit Estimator to help you compare systems.

The computational power of a quantum computer can be limited by many factors: qubit lifetime and coherence time (T1 and T2), average 2 qubit gate fidelity, number of qubits, and many other things. IBM introduced Quantum Volume (QV) as a benchmark to take into account some of these aspects of early quantum computers. Unlike classical computer benchmarks which determine speed of the computer, this benchmark tried to determine how big a program (circuit) could be run on a quantum computer. The usefulness of the quantum, per se.

If your quantum computer had lots of qubits, but low gate fidelity (i.e. a high error rate), your quantum volume score would be low. Likewise, if your quantum computer had high gate fidelity, but a small number of qubits, again your quantum volume score would be low. The Goldilocks zone increases qubits as fidelity increases in lockstep.

At some point, when gate fidelity can no longer easily be improved, error correction will be needed. Error correction uses multiple physical qubits to produce a single improved qubit. The number of qubits required, or overhead, is dependent on the amount of error to overcome. Because IonQ computers have the best gate fidelity, they have the smallest overhead. IonQ co-founder Chris Monroe, advisor Kenneth Brown, and their academic collaborators recently demonstrated the first fault tolerant error corrected operation using a trapped ion system, with an overhead of just 13:1. Other technologies, because of their poor gate fidelity and qubit connectivity, might need 1,000, 10,000 or even 1,000,000 qubits to create a single error-corrected qubit.

Unfortunately, with better quantum computers, the QV metric will become unusable because the numbers grow so quickly. We foresee a time in the near future when QV numbers will grow so large they won’t fit on your screen.

Hence, we introduce Algorithmic Qubits (AQ), which is defined as the largest number of effectively perfect qubits you can deploy for a typical quantum program^{1 }. It’s a similar idea to Quantum Volume, but takes error-correction into account and has a clear, direct relationship to qubit count. In the absence of error-correction encoding, $AQ ≈ log<sub>2</sub>(QV)$, or inversely, $QV ≈ 2<sup>AQ</sup>$. AQ represents the number of “useful” encoded qubits in a particular quantum computer and is a simple proxy for the ability to execute real quantum algorithms for a given input size.

AQ is generally smaller than the number of physical qubits. Hence, ignore vendors (and by extension, their roadmaps) that describe their systems purely by the number of physical qubits. A 72 qubit chip and a million qubit chip with 95% fidelity gates both have a QV of 8 and an AQ of 3. With that fidelity, only three qubits can be used for calculation, no matter the number of physical qubits.

IonQ’s roadmap is based on the AQ metric. For the next few years, IonQ will focus on improving the quality of our quantum logic gate operations to continue to increase system AQ (i.e. usable qubits). Then, IonQ will focus on implementing quantum error correction with low overhead and scaling the number of physical qubits to substantially boost system AQ further.

By 2023, IonQ will deploy modular quantum computers small enough to be networked together in a datacenter, and by 2025, we expect to achieve broad quantum advantage.

At IonQ, we're working to build the world’s most powerful quantum computers to solve the world’s hardest problems. Our recently announced 32 qubit system is expected to feature 22 Algorithmic Qubits, and this system is but the first of three new systems already in development. In short, we’ll be reaping the benefits of quantum much sooner than most would think.

**1 **We define a typical quantum program (circuit) as one that has a size (number of fully-connected gate operations) that scales with the square of the number of algorithmic qubits.This page was updated on February 23, 2022 to remove an Algorithmic Qubit estimator that did not accurately reflect our defintion of the metric. You can read more about #AQ and how it's calculated in this blog post.↫