Related papers: Non-Hermitian Computers Need No Complex Numbers
We show that in quantum computation almost every gate that operates on two or more bits is a universal gate. We discuss various physical considerations bearing on the proper definition of universality for computational components such as…
An enduring challenge in computer science is reducing the runtime required to solve computational problems. Quantum computing has attracted significant attention due to its potential to deliver asymptotically faster solutions to certain…
Quantum computation has revolutionary potential for speeding algorithms and for simulating quantum systems such as molecules. We report here a quantum computer design that performs universal quantum computation within a single…
Experimental realization of a universal set of quantum logic gates is the central requirement for implementation of a quantum computer. An all-geometric approach to quantum computation offered a paradigm for implementation where all the…
The quantum computer is supposed to process information by applying unitary transformations to the complex amplitudes defining the state of N qubits. A useful machine needing N=1000 or more, the number of continuous parameters describing…
Using transversal gates is a straightforward and efficient technique for fault-tolerant quantum computing. Since transversal gates alone cannot be computationally universal, they must be combined with other approaches such as magic state…
Quantum computing is poised to dramatically change the computational landscape, worldwide. Quantum computers can solve complex problems that are, at least in some cases, beyond the ability of even advanced future classical-style computers.…
While closed timelike curves (CTCs) are not known to exist, studying their consequences has led to nontrivial insights in general relativity, quantum information, and other areas. In this paper we show that if CTCs existed, then quantum…
In the global framework of quantum theory the individual quantum systems seem clearly separated into two families with the respective manifestly Hermitian and hiddenly Hermitian operators of their Hamiltonian. In the light of certain…
High-fidelity and robust quantum manipulation is the key for scalable quantum computation. Therefore, due to the intrinsic operational robustness, quantum manipulation induced by geometric phases is one of the promising candidates. However,…
Most quantum computer realizations require the ability to apply local fields and tune the couplings between qubits, in order to realize single bit and two bit gates which are necessary for universal quantum computation. We present a scheme…
Modeling non-Hermitian Hamiltonians is increasingly important in classical and quantum domains, especially when studying open systems, $PT$ symmetry, and resonances. However, the quantum simulation of these models has been limited by the…
This paper proposes to broaden the canonical formulation of quantum mechanics. Ordinarily, one imposes the condition $H^\dagger=H$ on the Hamiltonian, where $\dagger$ represents the mathematical operation of complex conjugation and matrix…
The nature of quantum computation is discussed. It is argued that, in terms of the amount of information manipulated in a given time, quantum and classical computation are equally efficient. Quantum superposition does not permit quantum…
In a quantum computer, creating superpositions of quantum bits (qubits) in different states can lead to a speed-up over classical computers [1], but quantum mechanics also allows for the superposition of quantum circuits [2]. In fact, it…
Quantum theory promises computational speed-ups over classical approaches. The celebrated Gottesman-Knill Theorem implies that the full power of quantum computation resides in the specific resource of "magic" states -- the secret sauce to…
Among existing approaches to holonomic quantum computing, the adiabatic holonomic quantum gates (HQGs) suffer errors due to decoherence, while the non-adiabatic HQGs either require additional Hilbert spaces or are difficult to scale. Here,…
Simulating the dynamics of electrons and other fermionic particles in quantum chemistry, materials science, and high-energy physics is one of the most promising applications of fault-tolerant quantum computers. However, the overhead in…
An efficient and intuitive framework for universal quantum computation is presented that uses pairs of spin-1/2 particles to form logical qubits and a single physical interaction, Heisenberg exchange, to produce all gate operations. Only…
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,…