Related papers: Power of Quantum Computation with Few Clean Qubits
In this paper, we give quantum algorithms for two fundamental computation problems: solving polynomial systems over finite fields and optimization where the arguments of the objective function and constraints take values from a finite field…
As basic elements of the quantum computer - quantum bits (qubits) we offer semiconductor quantum dots containing one electron each and consisting each of two tunnel-connected parts. The numerical solution of a Schroedinger equation with the…
Quantum error mitigation has been proposed as a means to combat unwanted and unavoidable errors in near-term quantum computing without the heavy resource overheads required by fault tolerant schemes. Recently, error mitigation has been…
In this paper we consider what can be computed by a user interacting with a potentially malicious server, when the server performs polynomial-time quantum computation but the user can only perform polynomial-time classical (i.e.,…
Machine learning has recently emerged as a fruitful area for finding potential quantum computational advantage. Many of the quantum enhanced machine learning algorithms critically hinge upon the ability to efficiently produce states…
A test of quantumness is a protocol that allows a classical verifier to certify (only) that a prover is not classical. We show that tests of quantumness that follow a certain template, which captures recent proposals such as (Kalai et al.,…
In this paper, we propose two new methods for solving Set Constraint Problems, as well as a potential polynomial solution for NP-Complete problems using quantum computation. While current methods of solving Set Constraint Problems focus on…
Fault tolerant quantum computing methods which work with efficient quantum error correcting codes are discussed. Several new techniques are introduced to restrict accumulation of errors before or during the recovery. Classes of eligible…
Concatenating quantum error correction codes scales error correction capability by driving logical error rates down double-exponentially across levels. However, the noise structure shifts under concatenation, making it hard to choose an…
Quantum tomography makes it possible to obtain comprehensive information about certain logical elements of a quantum computer. In this regard, it is a promising tool for debugging quantum computers. The practical application of tomography,…
We use quantum discord to characterize the correlations present in the quantum computational model DQC1, introduced by Knill and Laflamme [Phys. Rev. Lett. 81, 5672 (1998)]. The model involves a collection of qubits in the completely mixed…
The possibility to save and process information in fundamentally indistinguishable states is the quantum mechanical resource that is not encountered in classical computing. I demonstrate that, if energy constraints are imposed, this…
Probabilistic error cancellation is a quantum error mitigation technique capable of producing unbiased computation results but requires an accurate error model. Constructing this model involves estimating a set of parameters, which, in the…
Quantum error correcting codes protect quantum information, allowing for large quantum computations provided that physical error rates are sufficiently low. We combine post-selection with surface code error correction through the use of a…
Quantum algorithms are known for providing more efficient solutions to certain computational tasks than any corresponding classical algorithm. Here we show that a single qudit is sufficient to implement an oracle based quantum algorithm,…
Entanglement is widely believed to lie at the heart of the advantages offered by a quantum computer. This belief is supported by the discovery that a noiseless (pure) state quantum computer must generate a large amount of entanglement in…
We present a method for quantum error mitigation on partially error-corrected quantum computers - i.e., computers with some logical qubits and some noisy qubits. Our method is inspired by the error cancellation method and is implemented via…
Errors in quantum computers are of two kinds: sudden perturbations to isolated qubits, and slow random drifts of all the qubits. The latter may be reduced, but not eliminated, by means of symmetrization, namely by using many replicas of the…
Quantum state purification is the functionality that, given multiple copies of an unknown state, outputs a state with increased purity. This will be an essential building block for near- and middle-term quantum ecosystems before the…
Quantum Computing (QC) promises computational speedup over classic computing for solving complex problems. However, noise exists in current and near-term quantum computers. Quantum software testing (for gaining confidence in quantum…