Related papers: Ideal random quantum circuits pass the LXEB test
We propose a general tensor network method for simulating quantum circuits. The method is massively more efficient in computing a large number of correlated bitstring amplitudes and probabilities than existing methods. As an application, we…
A key requirement for scalable quantum computing is that elementary quantum gates can be implemented with sufficiently low error. One method for determining the error behavior of a gate implementation is to perform process tomography.…
The impressive progress in quantum hardware in the last years has raised the interest of the quantum computing community in harvesting the computational power of such devices. However, in the absence of error correction, these devices can…
We prove that random quantum circuits on any geometry, including a 1D line, can form approximate unitary designs over $n$ qubits in $\log n$ depth. In a similar manner, we construct pseudorandom unitaries (PRUs) in 1D circuits in…
Until very recently, it was generally believed that the (approximate) 2-design property is strictly stronger than anti-concentration of random quantum circuits, mainly because it was shown that the latter anti-concentrate in logarithmic…
Random instances of feedforward Boolean circuits are studied both analytically and numerically. Evaluating these circuits is known to be a P-complete problem and thus, in the worst case, believed to be impossible to perform, even given a…
We prove a Carbery-Wright style anti-concentration inequality for the unitary Haar measure, by showing that the probability of a polynomial in the entries of a random unitary falling into an $\varepsilon$ range is at most a polynomial in…
A significant hurdle towards realization of practical and scalable quantum computing is to protect the quantum states from inherent noises during the computation. In physical implementation of quantum circuits, a long-distance interaction…
Quantum Supremacy is a demonstration of a computation by a quantum computer that can not be performed by the best classical computer in a reasonable time. A well-studied approach to demonstrating this on near-term quantum computers is to…
We present a classically solvable model that leads to optimized low-depth quantum circuits leveraging separable pair approximations. The obtained circuits are well suited as a baseline circuit for emerging quantum hardware and can, in the…
High-fidelity mid-circuit measurements, which read out the state of specific qubits in a multiqubit processor without destroying them or disrupting their neighbors, are a critical component for useful quantum computing. They enable…
The treewidth of a graph is a useful combinatorial measure of how close the graph is to a tree. We prove that a quantum circuit with $T$ gates whose underlying graph has treewidth $d$ can be simulated deterministically in…
In a circuit-based quantum computer, the computing is performed via the discrete-time evolution driven by quantum gates. Accurate simulation of continuoustime evolution requires a large number of quantum gates and therefore suffers from…
An $n$-qubit quantum circuit is said to be peaked if it has an output probability that is at least inverse-polynomially large as a function of $n$. We describe a classical algorithm with quasipolynomial runtime $n^{O(\log{n})}$ that…
This paper concerns the problem of checking if two shallow (i.e., constant-depth) quantum circuits perform equivalent computations. Equivalence checking is a fundamental correctness question -- needed, e.g., for ensuring that…
Unitarity randomized benchmarking (URB) is an experimental procedure for estimating the coherence of implemented quantum gates independently of state preparation and measurement errors. These estimates of the coherence are measured by the…
We consider quantum circuits consisting of randomly chosen two-local gates and study the number of gates needed for the distribution over measurement outcomes for typical circuit instances to be anti-concentrated, roughly meaning that the…
We construct a gate and time-independent noise model that results in the output of a logical randomized benchmarking protocol oscillating rather than decaying exponentially. To illustrate our idea, we first construct an example in standard…
We show that several quantum circuit families can be simulated efficiently classically if it is promised that their output distribution is approximately sparse i.e. the distribution is close to one where only a polynomially small, a priori…
In this work, drawing inspiration from the type of noise present in real hardware, we study the output distribution of random quantum circuits under practical non-unital noise sources with constant noise rates. We show that even in the…