In Research Theme I, the QSC will develop ground breaking software to use quantum computers to perform the first useful tasks that could not be solved by any classical machine within our lifetime.

**Aim**

To develop software applications for small-scale quantum computers, and to develop methods that will enable the construction of large-scale quantum machines.

**Theme leader**

Prof.dr. Harry Buhrman (QuSoft, CWI)

**Overview and Motivation**

Quantum algorithms offer significant speedups over classical algorithms. A familiar example is Shor’s factorization algorithm, which can break the security of most cryptographic systems used today. Large-scale engineering efforts are currently on track around the world and in the Netherlands to build quantum computing hardware. It is estimated that already within the next five years we could see small quantum computers of 50 physical qubits.

We know that 50 or more logical qubits could in principle outperform a classical supercomputer. Yet, almost no quantum algorithms are known for the small devices that we hope to have available within the next ten years. Most work in quantum algorithms so far has focused on large-scale quantum computers, and it has been estimated that we would need thousands of logical qubits to factor a number that is large enough to be useful for encryption.

**Challenges**

Challenge I.1: How can the power of few-qubit quantum computers be harnessed? Our goal is that after the ten years spanned by this proposal, we will see a small-scale quantum computer – assisted by a classical supercomputer – perform a useful computation and simulation that would otherwise not be possible on any classical computer within our lifetime.

Challenge I.2: For which computational tasks are quantum computers more powerful than classical machines? The prime example of the power of quantum software run on a quantum computer is Shor’s algorithm for efficiently factoring large numbers into their prime factors. However, the power of quantum computers is still poorly understood and the urge for a better understanding in the form of more applications becomes urgent due to the steady progress in building quantum hardware. Some progress has been made towards finding more problems that can be sped up significantly by a quantum computer, such as searching, matrix multiplication, and solving linear systems of equations.

**Methods**

In order to solve meaningful tasks with a few-qubit quantum computer, we need to work at several levels of abstraction. On the one hand, we will use our expertise in quantum information, machine learning, and theoretical physics to develop new algorithms and simulations. On the other hand, we need software to correct errors, as well as to map and control the implementation of higher-level algorithms to the underlying hardware provided by the demonstrator.

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