Related papers: How to simulate quantum measurement without comput…
We describe a simple algorithm for sampling $n$-qubit Clifford operators uniformly at random. The algorithm outputs the Clifford operators in the form of quantum circuits with at most $5n + 2n^2$ elementary gates and a maximum depth of…
With a combination of the quantum repeater and the cluster state approaches, we show that efficient quantum computation can be constructed even if all the entangling quantum gates only succeed with an arbitrarily small probability $p$. The…
We consider the problem of estimating quantum observables on a collection of qubits, given as a linear combination of Pauli operators, with shallow quantum circuits consisting of single-qubit rotations. We introduce estimators based on…
We introduce a distributed classical simulation algorithm for general quantum circuits, and present numerical results for calculating the output probabilities of universal random circuits. We find that we can simulate more qubits to greater…
Compared to general quantum states, the sparse states arise more frequently in the field of quantum computation. In this work, we consider the preparation for $n$-qubit sparse quantum states with $s$ non-zero amplitudes and propose two…
Increasingly sophisticated programmable quantum simulators and quantum computers are opening unprecedented opportunities for exploring and exploiting the properties of highly entangled complex quantum systems. The complexity of large…
We consider the problem of testing whether an unknown $n$-qubit quantum state $|\psi\rangle$ is a stabilizer state, with only single-copy access. We give an algorithm solving this problem using $O(n)$ copies, and conversely prove that…
We present an algorithm for measurement of $k$-local operators in a quantum state, which scales logarithmically both in the system size and the output accuracy. The key ingredients of the algorithm are a digital representation of the…
We present quantum algorithms for the estimation of n-time correlation functions, the local and non-local density of states, and dynamical linear response functions. These algorithms are all based on block-encodings - a versatile technique…
We report an alternative scheme for implementing generalized quantum measurements that does not require the usage of auxiliary system. Our method utilizes solely: (a) classical randomness and post-processing, (b) projective measurements on…
The amplitude encoding of an arbitrary $n$-qubit state vector requires $\Omega(2^n)$ gate operations, owing to the exponential dimension of the Hilbert space. We can, however, form dimensionality-reduced representations of quantum states…
High-performance techniques to simulate quantum programs on classical hardware rely on exponentially large vectors to represent quantum states. When simulating quantum algorithms, the quantum states that occur are often sparse due to…
Many quantum algorithms contain an important subroutine, the quantum amplitude estimation. As the name implies, this is essentially the parameter estimation problem and thus can be handled via the established statistical estimation theory.…
We develop classical simulation algorithms for adaptive quantum circuits that produce states with low levels of ``magic'' (i.e., non-stabilizerness). These algorithms are particularly well-suited to circuits with high rates of Pauli…
Recent development in quantum information sciences and technologies, especially building programmable quantum computers, provide us new opportunities to study fundamental aspects of quantum mechanics. We propose qubit models to emulate the…
Effective quantum computation relies upon making good use of the exponential information capacity of a quantum machine. A large barrier to designing quantum algorithms for execution on real quantum machines is that, in general, it is…
In a recent work arXiv:2201.07655v2 we showed that there is a constant $\lambda >0$ such that it is possible to efficiently classically simulate a quantum system in which (i) qudits are placed on the nodes of a graph, (ii) each qudit…
Quantum computers are now on the brink of outperforming their classical counterparts. One way to demonstrate the advantage of quantum computation is through quantum random sampling performed on quantum computing devices. However, existing…
Quantum simulation algorithms often require numerous ancilla qubits and deep circuits, prohibitive for near-term hardware. We introduce a framework for simulating quantum channels using ensembles of low-depth circuits in place of many-qubit…
We describe an algorithm for using a quantum computer to calculate mean values of observables and the partition function of a quantum system. Our algorithm includes two sub-algorithms. The first sub-algorithm is for calculating, with…