Related papers: On the Complexity of Random Quantum Computations a…
The one clean qubit model (or the DQC1 model) is a restricted model of quantum computing where only a single input qubit is pure and all other input qubits are maximally mixed. In spite of the severe restriction, the model can solve several…
The repertoire of problems theoretically solvable by a quantum computer recently expanded to include the approximate evaluation of knot invariants, specifically the Jones polynomial. The experimental implementation of this evaluation,…
We study the complexity of approximately evaluating the Ising and Tutte partition functions with complex parameters. Our results are partly motivated by the study of the quantum complexity classes BQP and IQP. Recent results show how to…
We reveal a natural algebraic problem whose complexity appears to interpolate between the well-known complexity classes BQP and NP: (*) Decide whether a univariate polynomial with exactly m monomial terms has a p-adic rational root. In…
Query complexity measures the amount of information an algorithm needs about a problem to compute a solution. On a quantum computer there are different realizations of a query and we will show that these are not always equivalent. Our…
Motivated by the recent experimental demonstrations of quantum supremacy, proving the hardness of the output of random quantum circuits is an imperative near term goal. We prove under the complexity theoretical assumption of the…
We consider the hypothesis that quantum mechanics is an approximation to another, cosmological theory, accurate only for the description of subsystems of the universe. Quantum theory is then to be derived from the cosmological theory by…
Recent research has demonstrated that quantum computers can solve certain types of problems substantially faster than the known classical algorithms. These problems include factoring integers and certain physics simulations. Practical…
Quantum computational complexity estimates the difficulty of constructing quantum states from elementary operations, a problem of prime importance for quantum computation. Surprisingly, this quantity can also serve to study a completely…
This thesis studies three topics in quantum computation and information: The approximability of quantum problems, quantum proof systems, and non-classical correlations in quantum systems. In the first area, we demonstrate a polynomial-time…
Instantaneous quantum polynomial-time (IQP) computation is a class of quantum computation consisting only of commuting two-qubit gates and is not universal in the sense of standard quantum computation. Nevertheless, it has been shown that…
We provide evidence that it is computationally difficult to approximate the partition function of the ferromagnetic q-state Potts model when q>2. Specifically we show that the partition function is hard for the complexity class #RHPi_1…
In this work we initiate the question of whether quantum devices can provide us with an almost perfect source of classical randomness, and more generally, suffice for classical cryptographic tasks, such as encryption. Indeed, it is well…
In this paper, we give a description of a recent quantum algorithm created by Aharonov, Jones, and Landau for approximating the values of the Jones polynomial at roots of unity of the form exp(2$\pi$i/k). This description is given with two…
We develop a theory of the algorithmic information in bits contained in an individual pure quantum state. This extends classical Kolmogorov complexity to the quantum domain retaining classical descriptions. Quantum Kolmogorov complexity…
Randomness is both a useful way to model natural systems and a useful tool for engineered systems, e.g. in computation, communication and control. Fully random transformations require exponential time for either classical or quantum…
A fundamental problem in numerical analysis and approximation theory is approximating smooth functions by polynomials. A much harder version under recent consideration is to enforce bounds constraints on the approximating polynomial. In…
We consider the hardness of computing additive approximations to output probabilities of random quantum circuits. We consider three random circuit families, namely, Haar random, $p=1$ QAOA, and random IQP circuits. Our results are as…
Quantum computing involving physical systems with continuous degrees of freedom, such as the quantum states of light, has recently attracted significant interest. However, a well-defined quantum complexity theory for these bosonic…
Clifford gates are a winsome class of quantum operations combining mathematical elegance with physical significance. The Gottesman-Knill theorem asserts that Clifford computations can be classically efficiently simulated but this is true…