Related papers: Brick Wall Quantum Circuits with Global Fermionic …
We give quantum circuits that simulate an arbitrary two-qubit unitary operator up to global phase. For several quantum gate libraries we prove that gate counts are optimal in worst and average cases. Our lower and upper bounds compare…
We consider a generic elementary gate sequence which is needed to implement a general quantum gate acting on n qubits -- a unitary transformation with 4^n degrees of freedom. For synthesizing the gate sequence, a method based on the…
We consider a hybrid digital-analog quantum computing approach, which allows implementing any quantum algorithm without standard two-qubit gates. This approach is based on the always-on interaction between qubits, which can provide an…
We analyze a scheme for quantum computation where quantum gates can be continuously changed from standard dynamic gates to purely geometric ones. These gates are enacted by controlling a set of parameters that are subject to unwanted…
By investigating the $SU(2)$ Yang-Mills matrix model coupled to fundamental fermions in the adiabatic limit, we demonstrate quantum critical behaviour at special corners of the gauge field configuration space. The quantum scalar potential…
Universal quantum computation (UQC) using Majorana fermions on a 2D topological superconducting (TS) medium remains an outstanding open problem. This is because the quantum gate set that can be generated by braiding of the Majorana fermions…
We study quantum field theories which have quantum groups as global internal symmetries. We show that in such theories operators are generically non-local, and should be thought as living at the ends of topological lines. We describe the…
Geometric phase is a promising element to induce high-fidelity and robust quantum operations due to its built-in noise-resilience feature. Unfortunately, its practical applications are usually circumscribed by requiring complex interactions…
We propose and analyze an approach to realize quantum computation and simulation using fermionic particles under quantum gas microscopes. Our work is inspired by a recent experimental demonstration of large-scale quantum registers, where…
We study scattering of particles which obey an $SU(N)$ global symmetry through the lens of quantum computation and quantum algorithms. We show that for scattering between particles which transform in the fundamental or anti-fundamental…
Implementation of high-dimensional (HD) quantum gates shows very promising perspectives for HD quantum computation. A bipartite quantum system with arbitrary dimensions $n$ and $m$ is termed a quNit-quMit. Here we propose a synthesis scheme…
We propose a practical implementation of a universal quantum computer that uses local fermionic modes (LFM) rather than qubits. The device layout consists of quantum dots tunnel coupled by a hybrid superconducting island and a tunable…
Supersymmetric models are grounded in the intriguing concept of a hypothetical symmetry that relates bosonic and fermionic particles. This symmetry has profound implications, offering valuable extensions to the Standard Model of particle…
In this work, we study distributions of unitaries generated by random quantum circuits containing only symmetry-respecting gates. We develop a unified approach applicable to all symmetry groups and obtain an equation that determines the…
We consider the ground state of a one-dimensional critical quantum system carrying a global symmetry in the bulk, which is explicitly broken by its boundary conditions. We probe the system via a string-order parameter, showing how it…
Spins associated to solid-state colour centers are a promising platform for investigating quantum computation and quantum networks. Recent experiments have demonstrated multi-qubit quantum processors, optical interconnects, and basic…
We prove that the boundaries of all non-trivial 1+1 dimensional intrinsically fermionic symmetry-protected-topological phases, protected by finite on-site symmetries (unitary or anti-unitary), are supersymmetric quantum mechanical systems.…
We investigate the combinatorial structures of a holonomic controlled quantum gate based on toric varieties. In particular, we in detail discuss the combinatorial structures of a two-qubit holonomic controlled quantum gate on a two-qubit, a…
Boundary conditions in quantum graph vertices are generally given in terms of a unitary matrix $U$. Observing that if $U$ has at most two eigenvalues, then the scattering matrix $\mathcal{S}(k)$ of the vertex is a linear combination of the…
Quantum computing represents a central challenge in modern science. Neutral atoms in optical lattices have emerged as a leading computing platform, with collisional gates offering a stable mechanism for quantum logic. However, previous…