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As an trade, we’re all collectively dedicated to bringing scaled quantum computing to fruition. Understanding what it is going to take to succeed in this aim is essential not only for measuring trade progress, but additionally for growing a strong technique to construct a quantum machine and a quantum-ready neighborhood. That’s why in June 2023, we provided how quantum computing should graduate via three implementation ranges to attain utility scale: Stage 1 Foundational, Stage 2 Resilient, Stage 3 Scale. All quantum computing applied sciences right now are at Stage 1, and whereas quite a few NISQ machines have been developed, they don’t provide sensible quantum benefit. True utility will solely come from orchestrating resilient quantum computation throughout a sea of logical qubits — one thing that, to one of the best of our information, can solely be achieved via fault tolerance and error correction. And it has not but been demonstrated.
The subsequent step towards sensible quantum benefit, and Stage 3 Scale, is to display resilient quantum computation on a logical qubit. Resilience on this context means the flexibility to point out that quantum error correction helps—quite than hinders—non-trivial quantum computation. Nevertheless, an necessary aspect of this non-triviality is the interplay between logical qubits and the entanglement it generates, which implies resilience of only one logical qubit won’t be sufficient. Subsequently, demonstrating two logical qubits performing an error-corrected computation that outperforms the identical computation on bodily qubits will mark the primary demonstration of a resilient quantum computation in our area’s historical past.
Earlier than our trade can declare victory on reaching Stage 2 Resilient Quantum Computing, by performing such an illustration on a given quantum computing {hardware}, it’s necessary to agree on what this entails, and the trail from there to Stage 3 Scale.
Defining a logical qubit
Essentially the most significant definition of a logical qubit hinges on what one can do with that qubit – demonstrating a qubit that may solely stay idle, that’s, be preserved in reminiscence, will not be as significant as demonstrating a non-trivial operation. Subsequently, we outline a logical qubit such that it initially permits some non-trivial, encoded computation to be carried out on it.
A big problem in formally defining a logical qubit is accounting for distinct {hardware}; for instance, the definition shouldn’t favor one {hardware} over one other. To deal with this, we suggest a set of standards that marks the doorway into the resilient stage of quantum computation. In different phrases, these are the standards for calling one thing a “logical qubit”.
Entrance standards to Stage 2
Graduating to Stage 2 resilient quantum computing is achieved when fewer errors are noticed on the output of a logical, error-corrected quantum circuit than on the analogous bodily circuit with out error correction.[1] We additionally require {that a} resilient stage demonstration embrace some uniquely “quantum” characteristic. In any other case, the demonstration reduces to a merely novel demonstration of probabilistic bits.
Arguably probably the most pure “quantum” characteristic to display on this regard is entanglement. An illustration of the resilient stage of quantum computation ought to then fulfill the next standards:
- demonstrates a convincingly giant separation between the logical error charge and the bodily error charge of a non-trivial logical circuit and its bodily counterpart, respectively
- corrects no less than all particular person circuit faults
- generates entanglement between no less than two logical qubits.
Upon satisfaction of those standards, the time period “logical qubit” can then be used to consult with the encoded qubits concerned.
The excellence between the Resilient and Scale ranges is value emphasizing — a proof of precept demonstration of resiliency should be convincing, but it surely doesn’t require a totally scaled machine. Because of this, a resilient stage demonstration could use sure types of post-selection. Publish-selection right here means the flexibility to just accept solely these runs that fulfill particular standards. Importantly, the chosen post-selection methodology should not substitute error-correction altogether, as error-correction is central to the kind of resiliency that Stage 2 goals to display.
Measuring progress throughout Stage 2
As soon as entrance to the Resilient Stage is achieved, as an trade we want to have the ability to measure continued progress towards Stage 3. Not each kind of quantum computing {hardware} will obtain Stage 3 Scale; the necessities to succeed in sensible quantum benefit at Stage 3 embrace attaining upwards of 1000 logical qubits working at a mega-rQOPS with logical error charges higher than 10-12. And so it’s essential to have the ability to perceive developments inside Stage 2 towards these necessities.
Impressed partly by DiVincenzo’s standards, we suggest to measure progress alongside 4 axes: universality, scalability, constancy, composability. For every axis we provide the next concepts on find out how to measure it, with hopes the neighborhood will construct on them:
- Universality: A common quantum laptop requires each Clifford and non-Clifford operations. Is there a set of high-fidelity Clifford-complete logical operations? Is there a set of high-fidelity common logical operations? A typical technique employed is to design the previous, which may then be used along with a loud non-Clifford state to appreciate a common set of logical operations. In fact, completely different {hardware} and approaches to fault-tolerance could make use of completely different methods.
- Scalability: At its core, useful resource necessities for benefit should be cheap (i.e., a really small fraction of the Earth’s sources or an individual’s lifetime). Extra technically, does the useful resource overhead required scale polynomially with goal logical error charge of any quantum algorithm? Be aware that some {hardware} could obtain very excessive constancy however could have restricted numbers of bodily qubits, in order that enhancing the error correction codes in the obvious approach (growing code distance) could also be tough.
- Constancy: Logical error charges of all operations should enhance with code energy. Extra strictly, is the logical error charge higher than the bodily error charge, i.e., are every of the operation fidelities “sub-pseudothreshold”? Progress on this axis will be measured with Quantum Characterization Verification & Validation (QCVV) carried out on the logical stage, or by partaking in operational duties comparable to Bell inequality violations and self-testing protocols.
- Composability: Are the fault-tolerant devices for all logical operations composable? It isn’t enough to display operations individually, quite it’s essential to display their composition into richer circuits and finally extra highly effective algorithms. Extra crucially, the efficiency of the circuits should be bounded by the efficiency of the elements within the anticipated approach. Metrics alongside this line will allow us to verify what logical circuits will be run, and with what anticipated constancy.
Standards to advance from Stage 2 to Stage 3 Scale
The exit of the resilient stage of logical computation shall be marked by giant depth, excessive constancy computations involving upwards of a whole lot of logical qubits. For instance, a logical, fault-tolerant computation on ~100 logical qubits or extra with a common set of composable logical operations with an error charge of ~10-8 or higher shall be vital. At Stage 3, efficiency of a quantum supercomputer can then be measured by dependable quantum operations per second (rQOPS). Finally, a quantum supercomputer shall be achieved as soon as the machine is ready to display 1000 logical qubits working at a mega-rQOPS with logical error charge of 10-12 or higher.
Conclusion
It’s little doubt an thrilling time to be in quantum computing. Our trade is on the brink of reaching the subsequent implementation stage, Stage 2, which places our trade on path to in the end attaining sensible quantum benefit. Collectively as a neighborhood we have now a possibility to assist measure progress throughout Stage 2, and to introduce benchmarks for the trade. You probably have concepts or suggestions on standards to enter Stage 2, or find out how to measure progress, we’d love to listen to from you.
[1] Our standards construct on and complement standards of each DiVincenzo (DiVincenzo, David P. (2000-04-13). “The Bodily Implementation of Quantum Computation”. Fortschritte der Physik. 48 (9–11): 771–783) and Gottesman (Gottesman, Daniel. (2016-10). “Quantum fault tolerance in small experiments”. https://arxiv.org/abs/1610.03507), who’ve beforehand outlined necessary standards for attaining quantum computing and its fault tolerance.
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