Emerging directions in fault-tolerant quantum computing – Call for proposals

This call for proposals is now closed. The deadline to apply was August 29, 2025. Contact us at NRC.QuantumComputing-Informatiquequantique.CNRC@nrc-cnrc.gc.ca if you have any questions.

1. Overview
2. Objectives
3. Eligibility
4. Project costing overview
5. Funding and support
6. Application timelines and process
7. Projects and funding agreements
8. Contact information
Annex A. Selection criteria for expressions of interest (EOI)

1. Overview

The National Research Council of Canada (NRC)'s Applied Quantum Computing Challenge program is launching a call for proposals to support research in quantum algorithms and error correction. The call aims to enable collaboration between the NRC and researchers from Canadian universities and small to medium-sized enterprises to produce research results that will build the foundation for a sustainable and profitable quantum computing sector in Canada.

The Applied Quantum Computing Challenge program focuses on quantum algorithms that enable scientific discovery across a range of domains, benefiting Canadians in health, climate change, economic prosperity and more. The program has a secondary focus on technologies to enable quantum computing, such as error correction, quantum compiling and resource estimation.

The NRC is Canada's federal research and development organization. Our mission is to have an impact by advancing knowledge and applying leading-edge technologies. We work with other innovators to find creative, relevant and sustainable solutions to Canada's current and future economic, social and environmental challenges.

The Applied Quantum Computing Challenge program is enabled by the Collaborative Science, Technology and Innovation Program (CSTIP) with the goal of delivering breakthroughs across the innovation continuum that matter to Canadians. The Applied Quantum Computing Challenge program leverages the expertise of NRC science professionals. As a result, this call is based on collaboration between NRC researchers and external applicants.

2. Objectives

This call is targeting collaborative projects that have the potential to develop methods for quantum computers to solve specific computing problems where there is the potential for an exponential advantage over classical techniques, and to advance the state-of-the-art in quantum error correction (QEC) and fault tolerance to enable quantum computers to reach practical scale sooner.

Projects must demonstrate that their research outcomes align with the mandate of the Applied Quantum Computing Challenge program.

Priority areas

The program is seeking collaborative projects in the following technology areas:

Quantum algorithms for differential equations
QEC and fault tolerance
NP approximation, combinatorics and quantum computing

Quantum algorithms for differential equations

Background

Differential equations are used in many scientific and engineering disciplines to model a wide range of events, such as the evolution of galaxies or the dynamics of financial markets. However, solving these equations is often a major computational challenge, especially in high dimensions or for complex systems. Quantum computing offers a promising avenue for tackling these challenges with its potential to harness the principles of quantum mechanics for computational advantage. Recently, remarkable progress has been made in developing quantum algorithms for differential equations, leading to intense research efforts aimed at unlocking the full potential of quantum computers to revolutionize our ability to simulate complex systems governed by differential equations.

A notable approach for simulating linear differential equations is based on quantum linear system algorithms. In these algorithms, standard classical discretization techniques are used to obtain a system of linear equations encoding the discretized evolution. Quantum linear system algorithms such as HHL are then used on the resulting linear system to obtain a quantum state encoding the solution in its amplitudes. Another line of research on simulating linear differential equations is focused on the evolution-based approach in which the problem of simulating a general ordinary differential equation (ODE) is reduced to the more familiar problem of Hamiltonian simulation.

The Linear Combination of Hamiltonian Simulation framework is a recently introduced technique that combines Hamiltonian simulation with the Linear Combination of Unitaries framework to simulate general ODEs. A closely related line of work, based on the Schrödingerization framework, transforms a non-unitary linear differential equation into a higher-dimensional Schrödinger equation, which can be solved using quantum simulation algorithms. Another method, the quantum time-marching algorithm, mimics the classical explicit time-marching methods by propagating the solution through sequential implementation of the evolution in short time steps.

When considering nonlinear differential equations, the landscape becomes even more complex. The prospect of substantial quantum advantage in simulating nonlinear differential equations requires further investigation. Quantum Carleman linearization is a notable approach applied in solving dissipative and non-dissipative nonlinear differential equations with very strict requirements and limited applicability. In addition, the possibility of chaos in systems with 3 or more dynamical dimensions means that predictions are only reliable for time frames whose scale is logarithmic with the precision of initial conditions and highlights the exponential complexity for long-term accuracy. These inherent complexities raise questions about whether quantum algorithms can offer exponential advantages over classical methods in predicting the evolution of such chaotic systems.

In many applications modelled by dynamical systems, the primary interest is in understanding the long-term behaviour of the system, such as whether it evolves toward a steady state, rather than obtaining the exact solution for given initial conditions.

Such long-term behaviours can be inferred from the system's topological behaviours. For systems governed by time-independent linear ODEs, the topological behaviour is influenced by the eigenvalues of the coefficient matrix.

Possible behaviours include:

stable nodes
unstable nodes
saddles
stable foci
centres

Nonlinear ODEs exhibit more complex behaviours, including stable and unstable limit cycles, as well as chaos and strange attractors. By analyzing fixed points and their stability, and the system's stability under perturbations, potentially using bifurcation theory, we can gain significant insights into the system's long-term behaviour.

Objectives

Develop efficient quantum algorithms to analyze the long-term qualitative behaviours of dynamical systems governed by both linear and nonlinear differential equations, including assessing the evaluation of end-to-end computational complexity
Identify specific scenarios where quantum approaches outperform classical methods, or establish 'no-go' results showing no quantum advantage for these tasks
Investigate the potential of quantum algorithms to assess the stability of dynamical systems under perturbations by developing methods to efficiently detect bifurcations, specifically by determining whether invariant sets within solution space change qualitatively across regions of the parameter space
Investigate the potential of quantum algorithms to achieve provable exponential advantage over classical algorithms for nonlinear differential equations
Understand the limitations and expand the applicability of Carleman linearization, as well as investigate alternative methods for simulating nonlinear differential equations
Explore promising applications of quantum algorithms for differential equations in areas that support scientific discovery with a detailed stability analysis, rigorous error bounds and end-to-end computational complexity estimates of the algorithm, including state preparation and state readout, for the specific use case

Quantum error correction and fault tolerance

Background

Quantum computation holds the promise of outperforming classical computers in tasks such as simulating complex quantum systems and optimizing complex problems. However, the fragile nature of qubits, which are prone to noise and interference, presents a significant challenge to reliable quantum computation. QEC is fundamental to overcoming these challenges, as it seeks to safeguard quantum information from errors by encoding logical information across multiple physical qubits and correcting the errors without disrupting the encoded data. As the field grows, QEC research has become central to unlocking practical, large-scale systems.

Recently, there has been significant progress in this field. One noteworthy advancement is the development of good low-density parity-check codes, which achieve near-optimal efficiency and protection using sparse syndrome checks. Experimentally, there have been significant advancements in early-stage QEC, showing its potential for practical implementation.

Despite its potential, the field of QEC faces substantial challenges. Existing error-correcting codes often struggle with scalability and practical implementation. Integrating these codes seamlessly with quantum algorithms remains an ongoing challenge. Innovative solutions are needed to overcome these hurdles and to expand the theoretical framework that supports them.

The next phase of QEC demands the co-design of hardware, algorithms and error-correcting architectures. Success depends on minimizing overhead while maximizing computational flexibility, a delicate balance that will define quantum computing's transition from lab curiosity to transformative technology.

Objectives

Novel QEC codes: Develop innovative coding architectures that improve error resilience and reduce qubit overhead for practical quantum systems
Efficient fault-tolerant logical operations: Develop and enhance novel protocols for implementing fault-tolerant logical operations within existing or newly designed QEC codes
Decoding algorithm optimization: Design and optimize decoding algorithms to achieve high-efficiency, noise-resistant decoders capable of real-time signal recovery in noisy environments
Fault-tolerant quantum computing architectures: Design integrated frameworks that combine QEC with quantum algorithms to achieve fault-tolerant computation with minimal overhead
Fundamental exploration of QEC: Develop unified theoretical frameworks to classify QEC codes and identify fundamental limitations and theoretical bounds on error correction capabilities
Interdisciplinary innovations: Apply insights from information theory, statistical physics or graph theory to deepen our understanding of QEC and reimagine novel solutions

NP approximation, combinatorics, and quantum computing

Background

Many business stakeholders are showing interest in quantum computing to revolutionize their performance and be in a ready-to-upgrade state when quantum computers become prevalent. With that said, the majority of the interest is coming from industry, which is focused on solving NP-hard optimization problems. Quantum advantage in approximating optimal solutions for NP-hard problems has been seen in the recent work of the Decoded Quantum Interferometry (DQI) algorithm. In the DQI algorithm, the technique for state-preparation is the main challenge and is what gives the algorithm its name, where classical error-correction is used as a workaround in generating the appropriate state.

In combinatorial optimization, many of the problems correspond to ground-state-search problems, which opens up a wide range of interesting questions. In 2006, different versions of Grover's search algorithm were used to improve the query complexity of decision problems like connectivity, single source shortest path and minimum spanning tree. There is an intuition that projecting an algorithm such as DQI (or a similar construction) to a particular combinatorial optimization problem can lead to a proven quantum advantage, ideally for a practically interesting optimization problem or use case.

While DQI is an example of quantum algorithms being used to solve problems that involve combinatorics and graph theory, the reverse also carries potential. Over the past few years, it has been almost a recurrent theme to see graph theoretic tools in action once the quantum problem goes higher in correlation levels.

Particularly, in the topic of QEC codes, there appears to be significant potential for graph theory in characterizing codes. On a parallel line of research, designing and modelling quantum circuits is yet another area with recent interest in graph theory and Tensor networks.

It is clear, however, that techniques from combinatorics and graph theory are still not used to their fullest potential for advancing quantum computing. Even though there has been extensive use of algebraic and spectral graph theory tools, other topics are yet to be involved, such as graph connectivity, graph minors, colouring and infinite graphs.

We are interested in supporting research that can help uncover new connections between combinatorics, combinatorial optimization and quantum computing. We are also interested in studying the capacity of DQI and the similar algorithms.

Objectives

Research avenues that extend DQI or are parallel to it in the bigger picture of approximating NP problems on fault-tolerant quantum computers
Identify quantum computing problems for which there is a potential for the use of graph theory

3. Eligibility

3.1 Eligible applicants

Applicants collaborating with the NRC who are eligible for funding under this call:

Academic institutions
Research institutions
Not-for-profit research organizations
Canadian small and medium-sized enterprises (those with fewer than 500 employees)

Note: International collaborators may be eligible if their participation in the project would result in a benefit for Canada and Canadians. Eligible applicants can also propose to engage third-party collaborators and subcontractors from across the technology ecosystem, which will be subject to approval.

3.2 Requirements

Applicants must review the NRC Statement on Research Security and the information regarding Safeguarding Your Research and understand the need to take extra precautions to protect the security of their research, intellectual property and knowledge development from potential interference, misappropriation or misalignment with the interests of Canada
Project teams must include at least one NRC researcher delivering on the collaborative initiative
Projects must be clearly aligned with the call objectives, the program mandate and the priority areas of the Applied Quantum Computing Challenge program
Projects must be completed within 2 years
Teams must complete an expression of interest (EOI) form

3.3 Commitment to EDI and GBA+

Project teams must clearly demonstrate their commitment to equity, diversity and inclusion (EDI) and gender-based analysis plus (GBA+) in their full proposals, including composition of their project teams, research methods, analysis and knowledge mobilization plans. Undertaking GBA+ and critically considering factors related to EDI adds valuable dimensions in research and improves the quality, social relevance and impact of the research.

EDI and GBA+ considerations should influence all stages of the research or development processes, from establishing priorities and building theory to formulating questions, designing methodologies and interpreting data. Applicants are invited to consult the Government of Canada's guide on best practices in equity, diversity and inclusion in research practice and design.

4. Project costing overview

4.1 Eligible costs

Salaries for highly qualified personnel (HQP) working on the project activities
Research support costs: direct costs incurred in the project implementation phase, for example:
- Consumable materials
- Supplies
- Equipment up to $10,000
Costs for travel and accommodation required specifically for execution of the project
Amounts invoiced to the recipient by a contractor for services rendered relating directly to the project (e.g., fees for professional services)
Indirect costs not directly applicable to carrying out the project but necessary for conducting the recipient's general business, up to a maximum of 10% of total eligible project costs

4.2 Ineligible costs

Purchase of land
Leasehold interest
Property taxes
Any portion of costs subject to refunds, rebates or credits, including HST, GST and PST
Costs incurred or paid by the NRC

5. Funding and support

The Applied Quantum Computing Challenge program is planning to make up to $4.2M available to support this call, with anticipated funding of up to $400k in the form of non-repayable grants and contributions per project over 2 years.

Determination of financial awards will be made on the basis of the final evaluation (including risk assessment) of proposed projects.

Funding provided by the NRC's National Program Office follows the CSTIP terms and conditions. CSTIP is intended to position the NRC as a collaborative platform that uses science excellence to respond to Canada's most pressing challenges.

As such, projects supported under this initiative benefit from NRC assets (special-purpose research facilities, scientific expertise and networks) and financial assistance in the form of non-repayable grants or contributions. For more information on CSTIP funding, consult the grant and contribution funding for collaborators page.

5.1 Government stacking provisions

The stacking provisions for projects are as follows:

The maximum limit of total Canadian government assistance (federal, provincial, territorial and municipal assistance for the same eligible costs) cannot exceed 100% of the total eligible project costs

6. Application timelines and process

The NRC is committed to a consistent, fair and transparent selection process to identify, select and approve the allocation of funding to projects that best fit the objectives of the collaborative call.

EOIs will be used to determine applicant and project eligibility and assess alignment with the goals of the call on the basis of the criteria in annex A.

Eligible applicant projects deemed to have high impact potential on the basis of the EOI will be invited to submit a full project proposal (FPP). Applicants may be asked to provide supplementary information at various points in the review process.

Applicants chosen to submit an FPP will be notified and invited to submit an FPP. They will be provided with the required templates to be completed and the FPP assessment criteria.

Applicants must provide all mandatory information in order to be considered for funding. Note that an invitation to submit an FPP is not a funding commitment from the NRC. All FPPs will undergo due diligence and verification, including a peer review process, to determine which projects will be recommended for funding.

6.1 Key dates and deadlines

June 2, 2025: Call opens
August 29, 2025: Submission deadline for expression of interest
September 2025: Invitations sent out for a FPP
September–October 2025: Submission deadline for FPP
November 2025: Notification of final results
March–April 2026: Anticipated start date for funding and project

6.2 General call process steps

Step 1: Assemble the project team, which will include at least one eligible applicant and an NRC collaborator. If you have a project idea but no NRC contact, send an email to NRC.QuantumComputing-Informatiquequantique.CNRC@nrc-cnrc.gc.ca, and we will try to make a match for projects aligned with the scope of the call.

Step 2: Request the EOI form by sending an email to NRC.QuantumComputing-Informatiquequantique.CNRC@nrc-cnrc.gc.ca and return completed form to same email address.

Step 3: The NRC's National Program Office (NPO) coordinates a review of EOIs received and assesses their eligibility and fit for the call.

Step 4: The NPO sends a notice of outcome to eligible applicants.

Step 5: The NPO sends the FPP templates to selected eligible applicants to learn more about their project idea.

Step 6: Eligible applicants develop the FPP together with their NRC partner.

Step 7: Eligible applicant principal investigators (PIs) submit the FPP on behalf of the project team by email to Razieh.Annabestani@cnrc-nrc.gc.ca, copying the program team at NRC.QuantumComputing-Informatiquequantique.CNRC@nrc-cnrc.gc.ca.

Step 8: NRC collaborator PIs submit internal NRC project documents such as the NRC workplan and NRC project workbook for the Applied Quantum Computing Challenge program.

Step 9: The NPO coordinates the peer review process.

Step 10: The NPO sends a notice of outcome to the eligible applicants.

Step 11: The NPO completes a due diligence review of the FPPs.

Step 11: The NPO develops collaborative research and funding agreements for successful projects with support from the research centres.

Step 12: Projects begins.

6.3 Expression of interest (EOI)

Request the EOI form by sending an email to NRC.QuantumComputing-Informatiquequantique.CNRC@nrc-cnrc.gc.ca. Return your completed form to same email address no later than 11:59 pm ET on August 29, 2025. Use the subject line "Institution, PI Name – Expression of Interest Request – AQC 2025" in your email.

If you wish to withdraw your EOI at any stage of the evaluation, you must do so by sending an email to NRC.QuantumComputing-Informatiquequantique.CNRC@nrc-cnrc.gc.ca. If you wish to be considered for funding for the same project in the future, you will be required to resubmit an EOI.

7. Project and funding agreements

After receiving notice of project approval from the NPO, eligible recipients must enter into a collaborative research and funding agreement with the NRC. If this agreement is not finalized within a reasonable timeframe, funding will be reallocated to other projects.

8. Contact information

For more information on this specific collaboration opportunity with the Applied Quantum Computing Challenge program, send an email to NRC.QuantumComputing-Informatiquequantique.CNRC@nrc-cnrc.gc.ca.

Annex A. Selection criteria for EOI

The 6 criteria below will be used to evaluate EOI applications. While each criterion will be equally weighted in the evaluation process, consideration will also be given to regional diversity and distribution across streams and strategic areas.

1. Methodology

Describe how the project will be carried out, including a high-level description of the tasks and methodology.