Related papers: The Parameterized Complexity of Quantum Verificati…
Parametrised quantum circuits contain phase gates whose phase is determined by a classical algorithm prior to running the circuit on a quantum device. Such circuits are used in variational algorithms like QAOA and VQE. In order for these…
Parameterized complexity theory was developed in the 1990s to enrich the complexity-theoretic analysis of problems that depend on a range of parameters. In this paper we establish a quantum equivalent of classical parameterized complexity…
We introduce a framework for the formal specification and verification of quantum circuits based on the Feynman path integral. Our formalism, built around exponential sums of polynomial functions, provides a structured and natural way of…
We investigate Clifford+$T$ quantum circuits with a small number of $T$-gates. Using the sparsification lemma, we identify time complexity lower bounds in terms of $T$-gate count below which a strong simulator would improve on the…
A quantum circuit must be preprocessed before implementing on NISQ devices due to the connectivity constraint. Quantum circuit mapping (QCM) transforms the circuit into an equivalent one that is compliant with the NISQ device's architecture…
Randomized benchmarking is a widely used experimental technique to characterize the average error of quantum operations. Benchmarking procedures that scale to enable characterization of $n$-qubit circuits rely on efficient procedures for…
Many promising quantum algorithms in economics, medical science, and material science rely on circuits that are parameterized by a large number of angles. To ensure that these algorithms are efficient, these parameterized circuits must be…
With the development of controllable quantum systems, fast and practical characterization for multi-qubit gates is essential for building high-fidelity quantum computing devices. The usual way to fulfill this requirement via randomized…
We present the first fully automatic framework for verifying relational properties of parameterized quantum programs, i.e., a program that, given an input size, generates a corresponding quantum circuit. We focus on verifying input-output…
Parameterized quantum circuits play a key role for the development of quantum variational algorithms in the realm of the NISQ era. Knowing their actual capability of performing different kinds of tasks is then of the utmost importance. By…
In order for quantum computations to be done as efficiently as possible it is important to optimise the number of gates used in the underlying quantum circuits. In this paper we find that many gate optimisation problems for approximately…
Parameterized complexity enables the practical solution of generally intractable NP-hard problems when certain parameters are small, making it particularly useful in real-world applications. The study of string problems in this framework…
We aim to establish a scalable scheme for characterising diagonal non-Clifford gates for single- and multi-qudit systems; \(d\) is a prime-power integer. By employing cyclic operators and a qudit T gate, we generalise the dihedral…
Efficient verification of the functioning of quantum devices is a key to the development of quantum technologies, but is a daunting task as the system size increases. Here we propose a simple and general framework for verifying unitary…
As quantum devices scale up, many-body quantum gates and algorithms begin to surpass what is possible to simulate classically. Validation methods which rely on such classical simulation, such as process tomography and randomized…
The Gottesman-Knill theorem asserts that a quantum circuit composed of Clifford gates can be efficiently simulated on a classical computer. Here we revisit this theorem and extend it to quantum circuits composed of Clifford and T gates,…
It has been known for almost three decades that many $\mathrm{NP}$-hard optimization problems can be solved in polynomial time when restricted to structures of constant treewidth. In this work we provide the first extension of such results…
Quantum computing is seeking to realize hardware-optimized algorithms for application-related computational tasks. NP (nondeterministic-polynomial-time) is a complexity class containing many important but intractable problems like the…
Executing quantum algorithms on a quantum computer requires compilation to representations that conform to all restrictions imposed by the device. Due to devices' limited coherence times and gate fidelities, the compilation process has to…
The classical simulation of quantum circuits is of central importance for benchmarking near-term quantum devices. The fact that gates belonging to the Clifford group can be simulated efficiently on classical computers has motivated a range…