A question we often hear at GQI is “When will we start witnessing quantum advantage where users are regularly relying on quantum technology for commercial use?”

The answer to that question relies on two factors. The first is how quickly will the quantum hardware improve? The second is how will quantum algorithms get smarter and more efficient?

When those two meet, we will start seeing end users run quantum computing for production applications.

**A Plethora of QRE Approaches**

The good news is that we are starting to see more detailed roadmaps from the quantum providers that give us an idea of how powerful their machines will be in the next few years.

Over the past few years we have published in these pages roadmaps from Pasqal, Infleqtion, D-Wave, QuEra, Microsoft, Rigetti, IonQ, IBM, Google, PsiQuantum, and others. So, we have a good idea of where quantum hardware is headed.

What is less obvious is what hardware resources are needed to execute a commercially relevant algorithm, and what innovations are taking place that may make those algorithms more efficient and require less powerful hardware to provide significant results.

This is where Quantum Resource Estimators (QRE) can help, and several have been introduced in recent years that might provide answers to this question. Available QRE tools include QREF/BARTIQ from PsiQuantum, QUALTRAN from Google, BenchQ from Zapata, MetriQ by the Unitary Fund and the Azure Quantum Resource Estimator from Microsoft.

Going forward, these resource estimators can provide value in other areas besides providing raw metrics of resource requirements. For quantum software engineers who want to compare two different variants of an algorithm, they can offer some visibility on differences in results. For software engineers working on a new optimization compiler, these tools can help determine which algorithm would work the best. And for hardware engineers, it can help set targets on the number of qubits and qubit quality requirements in their future architecture designs.

**Challenges of QRE**

At the same time, users of these tools need to take great care in providing accurate input parameters. On the hardware side they need to provide the tool with information such as qubits available, qubit quality parameters, error correction code parameters and many others. And on the software side they need to input a reasonable quantum algorithm. As they say, “Garbage In, Garbage Out” and the wrong inputs can result in wildly inaccurate estimates.

Today, GQI is launching a program to investigate use cases and algorithms for quantum computing to track performance across qubit modalities and vendor platforms. Hopefully, this effort will help identify what algorithms and use cases might be some of the earliest to achieve useful quantum advantage in a production environment.

GQI, an independent, unbiased third-party, with long running, deep ties to the quantum computing community, will serve as a trusted resource to help bring transparency to this approach.

How will we do that?

**The GQI QRE Project**

As part of the GQI intelligence, we maintain a database of use cases, which currently contains 174 entries categorized by industry, qubit modality, vendor platform, region and algorithm class. We are continuously expanding this DB and currently have a backlog of close to 100 additional use cases that we are reviewing and categorizing.

Using this database as a foundation, we have partnered with Microsoft to use their Azure Quantum Resource Estimator (AQRE) and assess the performance of algorithms and use cases.

Every couple of weeks, we will try and assess one quantum computing use case or algorithm – independent from Microsoft or any vendor, but with their support and input.

We will thrive to implement real world conditions – no hero gates, no sandbox-style performance optimization – and share the results.

We will work with QC vendors and users to ensure we have their true parameters and conditions in which these might have been executed. And rely on available (via the cloud or otherwise) performance measures.

In working with vendors and users, GQI will assure, as we have done since 2015, the confidentiality of all sensitive data and only publish the QRE performance results but not specific algorithm, use case or qubit platform parameters that are proprietary IP or non-public.

**The GQI QRE Playbook**

The results will be published in a public “GQI Playbook” – a playbook consists of a live data visualization with all results and the ability to analyze it, a description of the framework used (in this case the Microsoft QRE) and a write up and analysis of all results.

We will publish this QRE Playbook, free of charge, on our *Quantum Computing Report by QCI* website thanks to Microsoft’s support. And we hope to have updates available on a regular basis for the foreseeable future.

Our focus for now will be on FTQC applications and we will work our way “down” from there.

**Our First Results**

The estimations for the table below were performed on 11 different use cases as described below:

**Quantum Dynamics (2D Ising)**is a simulation of a 2D transverse-field Ising model with 100 quantum spins, propagate for ten time steps using a fourth-order Trotter algorithm**Quantum Dynamics (Reduced T factories)**is the same use case as above with the number of T factories reduces to show the trade off of qubits needed and runtime**Factoring**calculates the pair of prime factors of a 2048 bit integer**Quantum Chemistry (Ruthenium)**calculates the energy of a ruthenium-based catalyst for carbon fixation**Quantum Chemistry (Nitrogenase)**demonstrates the application of quantum computing to explore reaction mechanisms in complex chemical systems, specifically focusing on biological nitrogen fixation in nitrogenase.**Quantum Phase Estimation (SHO)**utilized to analyze the energy spectrum of unitary oracles, focusing on estimating the phase (energy) of a particle confined in a simple harmonic oscillator trap. This method serves as a fundamental tool for dissecting basic systems in physics.**Bayesian QPE**is an example of a QPE applications in calculating an inner product between two 2-dimensional vectors and estimating the energy of a simple Hamiltonian while integrating Bayesian statistics in the phase estimation process.**Iterative QPE**is another example of a QPE application which represents the most basic application among the discussed cases, potentially explaining why its estimates are an order of magnitude lower.**QFT**demonstrates capabilities in solving problems in number theory and quantum physics, applying QFT to a uniformly prepared state ∣ + ⟩.**Grover’s Search Algorithm**designed to efficiently identify the unique input that leads to a specific output value in a black box function. It achieves this with a significantly higher probability and speed compared to classical search methods**.****Quantum Amplitude Estimation (QAE)**utilizes advance quantum computing’s capacity to resolve complex computational problems by estimating amplitudes of a given quantum state with high precision.

The table was generated using the Microsoft Azure Quantum Resource Estimator tool which provides resource estimates for programs running on fault tolerant machines (the tool does not support NISQ processors). A previous article posted on the *Quantum Computing Repor*t about this tool can be seen here. A complete overview of the Azure Quantum Resource Estimator is available in a technical paper posted on arXiv here. Additional information about this tool is available on Microsoft’s website in blog posts here, here, and here. The open source for this tool is available on GitHub here.

This tool has a large number of parameters that can be used to specify the parameters of the quantum processor being used as well as the ECC code. Details on how to do that are explained in the references listed above. For the results table shown, here are the definitions of the parameters that were used as the inputs and outputs for the tests we ran.

**Q** Number of Logical Qubits**Cmin** Minimum Local Time Steps**C** Logical Time Steps**M** Number of T States**d** Code Distance**f** Number of T State Distillation Factories**Factory **Percentage of Physical Qubits Used**Ratio **T State Distillation Factories**Physical **Number of Physical Qubits to Run the Algorithm with the**Qubits** Specified Machine

The characteristics of the target quantum computer can be specified as well. These include things like gate delays, measurement times, QEC code scheme, error budgets, constraints, etc. The Azure Quantum Resource Estimator includes eight pre-defined sets of qubit parameters which we used in the table above. These are noted as follows:

**(us, 10-3)SC** 100 usec. gate times, 10-3 error rate, surface code.

Possible ion trap processor

**(us, 10-4)SC** 100 usec. gate times, 10-4 error rate, surface code.

Possible ion trap processor

**(ns, 10-3)SC** 100 nsec. gate times, 10-3 error rate, surface code.

Possible superconducting processor

**(ns, 10-4)SC** 100 nsec. gate times, 10-4 error rate, surface code.

Possible superconducting processor

**(ns, 10-4)SC** 100 nsec. gate times, 10-4 error rate, surface code.

Possible Majorana processor

**(ns, 10-6)SC** 100 nsec. gate times, 10-6 error rate, surface code.

Possible Majorana processor

**(ns, 10-4)FC** 100 nsec. gate times, 10-4 error rate, floquet code.

Possible Majorana processor

**(ns, 10-6)FC** 100 nsec. gate times, 10-6 error rate, floquet code.

Possible Majorana processor

This chart below graphically presents a resource estimation for the ten different quantum computing use cases, visually comparing their requirements in terms of physical qubits and runtime. Each use case, including Quantum Dynamics, Factoring, Quantum Chemistry, Grover’s Search Algorithm, and various forms of Quantum Phase Estimation (QPE), is represented with a distinct color-coded area, illustrating the scale and feasibility across a range of computational tasks.

It is interesting to note that the results above show substantial improvements in both qubit numbers and runtime for the four same use cases using the same assumptions published by Microsoft in the arXiv paper in November 2022. We attribute this to subsequent improvements in later versions for both Microsoft’s optimizing compilers and the Quantum Resource Estimator tool that they have made since that time.

As can be seen from the table above, each of these three algorithms require substantially larger, and faster quantum computers than those available today. Also, the run times can start to get quite long with one test showing a run time of 447 years. One of the future uses of this tool would be to compare different architectures or examine tradeoffs between different scenarios, for example increase the number of qubits in order to get a shorter run time. Our hope is that this will become a tool for our ecosystem with a transparent and practical approach towards assessing actual performance. So, stay tuned!

August 5, 2024