Related papers: Some Coxeter Groups in Reversible and Quantum Comp…
We present two methods for the construction of quantum circuits for quantum error-correcting codes (QECC). The underlying quantum systems are tensor products of subsystems (qudits) of equal dimension which is a prime power. For a QECC…
Implementing a quantum circuit on specific hardware with a reduced available gate set is often associated with a substantial increase in the length of the equivalent circuit. This process is also known as transpilation and due to…
Understanding the boundary between classical simulatability and the power of quantum computation is a fascinating topic. Direct simulation of noisy quantum computation requires solving an open quantum many-body system, which is very costly.…
In an ordinary quantum algorithm the gates are applied in a fixed order on the systems. The introduction of indefinite causal structures allows to relax this constraint and control the order of the gates with an additional quantum state. It…
Almost all of the most successful quantum algorithms discovered to date exploit the ability of the Fourier transform to recover subgroup structure of functions, especially periodicity. The fact that Fourier transforms can also be used to…
When quantum programs are executed on noisy intermediate-scale quantum (NISQ) computers, they experience hardware noise; consequently, the program outputs are often erroneous. To mitigate the adverse effects of hardware noise, it is…
Quantum hashing is a useful technique that allows us to construct memory-efficient algorithms and secure quantum protocols. First, we present a circuit that implements the phase form of quantum hashing using $2^{n-1}$ CNOT gates, where n is…
Quantum computing has been pursued with various hardware platforms, and an optical system is one of the most reasonable choices for large-scale computation. In the optical continuous-variable computation scheme, the incorporation of…
Discrete translational symmetry plays a fundamental role in condensed matter physics and lattice gauge theories, enabling the analysis of systems that would otherwise be intractable. Despite this, many open problems remain. Quantum…
Quantum-circuit optimization is essential for any practical realization of quantum computation, in order to beat decoherence. We present a scheme for implementing the final stage in the compilation of quantum circuits, i.e., for finding the…
Quantum computing has garnered attention for its potential to solve complex computational problems with considerable speedup. Despite notable advancements in the field, achieving meaningful scalability and noise control in quantum hardware…
Quantum circuits consist of gates applied to qubits. Current quantum hardware platforms impose connectivity restrictions on binary CX gates. Hence, Layout Synthesis is an important step to transpile quantum circuits before they can be…
In this note we present explicit canonical forms for all the elements in the two-qubit CNOT-Dihedral group, with minimal numbers of controlled-S (CS) and controlled-X (CX) gates, using the generating set of quantum gates [X, T, CX, CS]. We…
We introduce a simple, widely applicable formalism for designing "error-divisible" two qubit gates: a quantum gate set where fractional rotations have proportionally reduced error compared to the full entangling gate. In current noisy…
Fault-tolerant quantum computation enables reliable quantum computation but incurs a significant overhead from both time and resource perspectives. To reduce computation time, Austin G. Fowler proposed time-optimal quantum computation by…
In this paper, we study CAT(0) groups and Coxeter groups whose boundaries are scrambled sets. Suppose that a group $G$ acts geometrically (i.e. properly and cocompactly by isometries) on a CAT(0) space $X$. (Such group $G$ is called a {\it…
The construction of robust and scalable quantum gates is a uniquely hard problem in the field of quantum computing. Real-world quantum computers suffer from many forms of noise, characterized by the decoherence and relaxation times of a…
Quantum computers are expected to bring drastic acceleration to several computing tasks against classical computers. Noisy intermediate-scale quantum (NISQ) devices, which have tens to hundreds of noisy physical qubits, are gradually…
The circuit model of quantum computation can be interpreted as a scattering process. In particular, factorised scattering operators result in integrable quantum circuits that provide universal quantum computation and are potentially less…
This is a survey of some aspects of the large-scale geometry of right-angled Coxeter groups. The emphasis is on recent results on their negative curvature properties, boundaries, and their quasi-isometry and commensurability classification.