Related papers: An Elementary Proof of the Quantum Adiabatic Theor…
We illustrate the adiabatic quantum computing solution of the knapsack problem with both integer profits and weights. For problems with $n$ objects (or items) and integer capacity $c$, we give specific examples using both an Ising class…
A notion of a quantum automorphism group of a finite quantum group, generalising that of a classical automorphism group of a finite group, is proposed and a corresponding existence result proved.
The Quantum Alternating Operator Ansatz (QAOA) and its predecessor, the Quantum Approximate Optimization Algorithm, are one of the most widely used quantum algorithms for solving combinatorial optimization problems. However, as there is yet…
The aim of this short note is to present an elementary, self-contained, and direct proof for the classical Lebesgue decomposition theorem.
The difficulty in producing precisely timed and controlled quantum gates is a significant source of error in many physical implementations of quantum computers. Here we introduce a simple universal primitive, adiabatic gate teleportation,…
In quantum adiabatic algorithm, as the adiabatic parameter $s(t)$ changes slowly from zero to one with finite rate, a transition to excited states inevitably occurs and this induces an intrinsic computational error. We show that this…
This article provides a simple proof of the quadratic formula, which also produces an efficient and natural method for solving general quadratic equations. The derivation is computationally light and conceptually natural, and has the…
Adiabatic quantum computing enables the preparation of many-body ground states. This is key for applications in chemistry, materials science, and beyond. Realisation poses major experimental challenges: Direct analog implementation requires…
We employ quantum mechanical principles in the computability exploration of the class of classically noncomputable Hilbert's tenth problem which is equivalent to the Turing halting problem in Computer Science. The Quantum Adiabatic Theorem…
A gapped quantum system that is adiabatically perturbed remains approximately in its eigenstate after the evolution. We prove that, for constant gap, general quantum processes that approximately prepare the final eigenstate require a…
We provide rigorous bounds for the error of the adiabatic approximation of quantum mechanics under four sources of experimental error: perturbations in the initial condition, systematic time-dependent perturbations in the Hamiltonian,…
The majorization theory has been applied to analyze the mathematical structure of quantum algorithms. An empirical conclusion by numerical simulations obtained in the previous literature indicates that step-by-step majorization seems to…
Automated theorem proving, or more broadly automated reasoning, aims at using computer programs to automatically prove or disprove mathematical theorems and logical statements. It takes on an essential role across a vast array of…
Many proofs of the Fundamental Theorem of Algebra, including various proofs based on the theory of analytic functions of a complex variable, are known. To the best of our knowledge, this proof is different from the existing ones.
I present a simple, elementary proof of Morley's theorem, highlighting the naturalness of this theorem.
We elucidate the geometry of quantum adiabatic evolution. By minimizing the deviation from adiabaticity we find a Riemannian metric tensor underlying adiabatic evolution. Equipped with this tensor, we identify a unified geometric…
We provide elementary proof of several congruences involving single sum and multisums of binomial coefficients.
An adiabatic quantum algorithm is essentially given by three elements: An initial Hamiltonian with known ground state, a problem Hamiltonian whose ground state corresponds to the solution of the given problem and an evolution schedule such…
A proof of quantumness is a method for provably demonstrating (to a classical verifier) that a quantum device can perform computational tasks that a classical device with comparable resources cannot. Providing a proof of quantumness is the…
Most investigations devoted to the conditions for adiabatic quantum computing are based on the first-order correction ${\bra{\Psi_{\rm ground}(t)}\dot H(t)\ket{\Psi_{\rm excited}(t)} /\Delta E^2(t)\ll1}$. However, it is demonstrated that…