Related papers: Simulations of Shor's Algorithm using Matrix Produ…
Data representation in quantum state space offers an alternative function space for machine learning tasks. However, benchmarking these algorithms at a practical scale has been limited by ineffective simulation methods. We develop a quantum…
We give a test that can distinguish efficiently between product states of n quantum systems and states which are far from product. If applied to a state psi whose maximum overlap with a product state is 1-epsilon, the test passes with…
In the Max $r$-SAT problem, the input is a CNF formula with $n$ variables where each clause is a disjunction of at most $r$ literals. The objective is to compute an assignment which satisfies as many of the clauses as possible. While there…
We give algorithms to factorize large integers in the duality computer. We provide three duality algorithms for factorization based on a naive factorization method, the Shor algorithm in quantum computing, and the Fermat's method in…
Matrix Product State (MPS) wavefunctions have many applications in quantum information and condensed matter physics. One application is to represent states in the thermodynamic limit directly, using a small set of position independent…
This is an investigation of the limits of quantum circuit simulation with Schrodinger's formulation and low precision arithmetic. The goal is to estimate how much memory can be saved in simulations that involve random, maximally entangled…
We show how to approximately represent a quantum state using the square root of the usual amount of classical memory. The classical representation of an $n$-qubit state $\psi$ consists of its inner products with $O(\sqrt{2^n})$ stabilizer…
An extremely scalable linear-algebraic algorithm was developed for quantum material simulation (electronic state calculation) with 10$^8$ atoms or 100-nm-scale materials. The mathematical foundation is generalized shifted linear equations…
We present TFORM, the version of the symbolic manipulation system FORM that can make simultaneous use of several processors in a shared memory architecture. The implementation uses Posix threads, also called pthreads, and is therefore…
State preparation and measurement (SPAM) errors limit the performance of near-term quantum computers and their potential for practical application. SPAM errors are partly correctable after a calibration step that requires, for a complete…
A prerequisite to the successful development of quantum computers and simulators is precise understanding of physical processes occurring therein, which can be achieved by measuring the quantum states they produce. However, the resources…
In this paper, an exact algorithm in polynomial time is developed to solve unrestricted binary quadratic programs. The computational complexity is $O\left( n^{\frac{15}{2}}\right) $, although very conservative, it is sufficient to prove…
Quantum computing technology may soon deliver revolutionary improvements in algorithmic performance, but these are only useful if computed answers are correct. While hardware-level decoherence errors have garnered significant attention, a…
The NP-hard problem of task scheduling with communication delays (P|prec,c_{ij}|C_{\mathrm{max}}) is often tackled using approximate methods, but guarantees on the quality of these heuristic solutions are hard to come by. Optimal schedules…
We report on the current state of factoring integers on both digital and analog quantum computers. For digital quantum computers, we study the effect of errors for which one can formally prove that Shor's factoring algorithm fails. For…
The reconstruction of quantum states from experimental measurements, often achieved using quantum state tomography (QST), is crucial for the verification and benchmarking of quantum devices. However, performing QST for a generic…
This paper introduces a structured memory which can be easily integrated into a neural network. The memory is very large by design and significantly increases the capacity of the architecture, by up to a billion parameters with a negligible…
Grover's algorithm is a cornerstone of quantum search algorithm, offering quadratic speedup for unstructured problems. However, limited qubit counts and noise in today's noisy intermediate-scale quantum (NISQ) devices hinder large-scale…
The advent of quantum computers promises exponential speed ups in the execution of various computational tasks. While their capabilities are hindered by quantum decoherence, they can be exactly simulated on classical hardware at the cost of…
Pollard's Rho is a method for solving the integer factorization problem. The strategy searches for a suitable pair of elements belonging to a sequence of natural numbers that given suitable conditions yields a nontrivial factor. In…