Related papers: Non-Hermitian Computers Need No Complex Numbers
Skyrmions in frustrated magnets have the helicity degree of freedom, where two different configurations of Bloch-type skyrmions are energetically favored by the magnetic dipole-dipole interaction and characterized by opposite helicities. A…
Encoding quantum information to protect it from errors is essential for performing large-scale quantum computations. Performing a universal set of quantum gates on encoded states demands a potentially large resource overhead and minimizing…
All-to-all interactions arise naturally in many areas of theoretical physics and across diverse experimental quantum platforms, motivating a systematic study of their information-processing power. Assuming each pair of qubits interacts with…
Fault-tolerant logic gates will consume a large proportion of the resources of a two-dimensional quantum computing architecture. Here we show how to perform a fault-tolerant non-Clifford gate with the surface code; a quantum…
Superposed orders of quantum channels have already been proved - both theoretically and experimentally - to enable unparalleled opportunities in the quantum communication domain. As a matter of fact, superposition of orders can be exploited…
How to find universal sets quantum gates (gates whose composition can form any othergate within a given range) is an important part of the development of quantum computation science that has been explored in the past with success. However,…
In the recently quickly developing context of quantum mechanics of unitary systems using a time-independent non-Hermitian Hamiltonian $H$ (having real spectrum and defined as acting in an unphysical but user-friendly Hilbert space ${\cal…
Quantum computers use quantum mechanical phenomena to perform conventionally intractable calculations for specific problems. Despite being universal machines, quantum computers are not expected to replace classical computers, but rather, to…
Non-stationary version of unitary quantum mechanics formulated in non-Hermitian (or, more precisely, in hiddenly Hermitian) interaction-picture representation is illustrated via an elementary $N$ by $N$ matrix Hamiltonian $H(t)$ mimicking a…
It is well known that a parallel quantum computer is more powerful than a classical one. So far, there are some important works about the construction of universal quantum logic gates, the key elements in quantum computation. However, they…
Quantum Hamiltonian Computing is a recent approach that uses quantum systems, in particular a single molecule, to perform computational tasks. Within this approach, we present explicit methods to construct logic gates using two different…
Anyons obtained from a finite gauge theory have a computational power that depends on the symmetry group. The relationship between group structure and computational power is discussed in this paper. In particular, it is shown that anyons…
Implementing polynomial functions of Hermitian matrices on quantum hardware is a foundational task in quantum computing, critical for accurate Hamiltonian simulation, quantum linear system solving, high-fidelity state preparation, machine…
Despite using a novel model of computation, quantum computers break down programs into elementary gates. Among such gates, entangling gates are the most expensive. In the context of fermionic simulations, we develop a suite of compilation…
The key for realizing fault-tolerant quantum computation lies in maintaining the coherence of all qubits so that high-fidelity and robust quantum manipulations on them can be achieved. One of the promising approaches is to use geometric…
Atomic-scale logic and the minimization of heating (dissipation) are both very high on the agenda for future computation hardware. An approach to achieve these would be to replace networks of transistors directly by classical reversible…
Realization of quantum computing requires the development of high-fidelity quantum gates that are resilient to decoherence, control errors, and environmental noise. While non-adiabatic holonomic quantum computation (NHQC) offers a promising…
Clifford circuits -- i.e. circuits composed of only CNOT, Hadamard, and $\pi/4$ phase gates -- play a central role in the study of quantum computation. However, their computational power is limited: a well-known result of Gottesman and…
Topological quantum computation by way of braiding of Majorana fermions is not universal quantum computation. There are several attempts to make universal quantum computation by introducing some additional quantum gates or quantum states.…
Let G(A,B) denote the 2-qubit gate which acts as the 1-qubit SU(2) gates A and B in the even and odd parity subspaces respectively, of two qubits. Using a Clifford algebra formalism we show that arbitrary uniform families of circuits of…