Related papers: Quantum Approximate Counting with Additive Error: …
We explore the space "just above" BQP by defining a complexity class PDQP (Product Dynamical Quantum Polynomial time) which is larger than BQP but does not contain NP relative to an oracle. The class is defined by imagining that quantum…
In 2004, Aaronson introduced the complexity class $\mathsf{PostBQP}$ ($\mathsf{BQP}$ with postselection) and showed that it is equal to $\mathsf{PP}$. Following their line of work, we introduce two new complexity classes. The first,…
The computational problem of distinguishing two quantum channels is central to quantum computing. It is a generalization of the well-known satisfiability problem from classical to quantum computation. This problem is shown to be…
Large-scale quantum computation will only be achieved if experimentally implementable quantum error correction procedures are devised that can tolerate experimentally achievable error rates. We describe a quantum error correction procedure…
Quantum compiling addresses the problem of approximating an arbitrary quantum gate with a string of gates drawn from a particular finite set. It has been shown that this is possible for almost all choices of base sets and furthermore that…
The states accepted by a quantum circuit are known as the witnesses for the quantum circuit's satisfiability. The assumption BQP does not equal QMA implies that no efficient algorithm exists for constructing a witness for a quantum circuit…
Recent theoretical results confirm that quantum theory provides the possibility of new ways of performing efficient calculations. The most striking example is the factoring problem. It has recently been shown that computers that exploit…
We study quasi-exact quantum error correcting codes and quantum computation with them. A quasi-exact code is an approximate code such that it contains a finite number of scaling parameters, the tuning of which can flow it to corresponding…
We use the class of commuting quantum computations known as IQP (Instantaneous Quantum Polynomial time) to strengthen the conjecture that quantum computers are hard to simulate classically. We show that, if either of two plausible…
We unconditionally prove that it is NP-hard to compute a constant multiplicative approximation to the QUANTUM MAX-CUT problem on an unweighted graph of constant bounded degree. The proof works in two stages: first we demonstrate a generic…
Weighted counting problems are a natural generalization of counting problems where a weight is associated with every computational path of polynomial-time non-deterministic Turing machines and the goal is to compute the sum of the weights…
Testing the symmetries of quantum states and channels provides a way to assess their usefulness for different physical, computational, and communication tasks. Here, we establish several complexity-theoretic results that classify the…
Fidelity is a fundamental measure for the closeness of two quantum states, which is important both from a theoretical and a practical point of view. Yet, in general, it is difficult to give good estimates of fidelity, especially when one…
Recently Quantum Computation has generated a lot of interest due to the discovery of a quantum algorithm which can factor large numbers in polynomial time. The usefulness of a quantum com puter is limited by the effect of errors. Simulation…
We introduce a variational algorithm based on the quantum alternating operator ansatz (QAOA) for the approximate solution of computationally hard counting problems. Our algorithm, dubbed VQCount, is based on the equivalence between random…
Quantum computers promise significant speedups in solving problems intractable for conventional computers but, despite recent progress, remain limited in scaling and availability. Therefore, quantum software and hardware development heavily…
I provide an alternative way of seeing quantum computation. First, I describe an idealized classical problem solving machine that, thanks to a many body interaction, reversibly and nondeterministically produces the solution of the problem…
We study the computational complexity of certain integrable quantum theories in 1+1 dimensions. We formalize a model of quantum computation based on these theories. In this model, distinguishable particles start out with known momenta and…
The architecture of circuital quantum computers requires computing layers devoted to compiling high-level quantum algorithms into lower-level circuits of quantum gates. The general problem of quantum compiling is to approximate any unitary…
Significant advances in the development of computing devices based on quantum effects and the demonstration of their use to solve various problems have rekindled interest in the nature of the "quantum computational advantage." Although…