Related papers: Identity check problem for shallow quantum circuit…
Suppose two quantum circuit chips are located at different places, for which we do not have any prior knowledge, and cannot see the internal structures either. If we want to find out whether they have the same functions or not with…
We consider process tomography for unitary quantum channels. Given access to an unknown unitary channel acting on a $\textsf{d}$-dimensional qudit, we aim to output a classical description of a unitary that is $\varepsilon$-close to the…
Quantum computers are on the brink of surpassing the capabilities of even the most powerful classical computers. This naturally raises the question of how one can trust the results of a quantum computer when they cannot be compared to…
Suppose one has access to oracles generating samples from two unknown probability distributions P and Q on some N-element set. How many samples does one need to test whether the two distributions are close or far from each other in the…
Random quantum circuits are commonly viewed as hard to simulate classically. In some regimes this has been formally conjectured, and there had been no evidence against the more general possibility that for circuits with uniformly random…
We present a classical algorithm that, for any $D$-dimensional geometrically-local, quantum circuit $C$ of polylogarithmic-depth, and any bit string $x \in {0,1}^n$, can compute the quantity $|<x|C|0^{\otimes n}>|^2$ to within any…
We present two protocols for classical verification of quantum depth. Our protocols allow a purely classical verifier to distinguish devices with different quantum circuit depths even in the presence of classical computation. We show that a…
Quantum programs exhibit inherent non-deterministic behavior, which poses more significant challenges for error discovery compared to classical programs. While several testing methods have been proposed for quantum programs, they often…
We present a quantum circuit implementation of the quantum hashing algorithm (quantum fingerprinting) for a quantum device with restrictions on the application of two-qubit gates by a qubit connectivity graph. We present an optimization…
We define a problem "exact non-identity check": Given a classical description of a quantum circuit with an ancilla system, determine whether it is strictly equivalent to the identity or not. We show that this problem is NQP-complete. In a…
In the paper, we consider quantum circuits for Quantum fingerprinting (quantum hashing) and quantum Fourier transform (QFT) algorithms. Quantum fingerprinting (quantum hashing) is a well-known technique for comparing large objects using…
We perform formal verification of quantum circuits by integrating several techniques specialized to particular classes of circuits. Our verification methodology is based on the new notion of a reversible miter that allows one to leverage…
Quantum computers and quantum algorithms have made great strides in the last few years and promise improvements over classical computing for specific tasks. Although the current hardware is not yet ready to make real impacts at the time of…
What advantage do \emph{sequential} procedures provide over batch algorithms for testing properties of unknown distributions? Focusing on the problem of testing whether two distributions $\mathcal{D}_1$ and $\mathcal{D}_2$ on $\{1,\dots,…
We construct a classical algorithm that designs quantum circuits for algorithmic quantum simulation of arbitrary qudit channels on fault-tolerant quantum computers within a pre-specified error tolerance with respect to diamond-norm…
Quantum computing will change the way we tackle certain problems. It promises to dramatically speed-up many chemical, financial, and machine-learning applications. However, to capitalize on those promises, complex design flows composed of…
The distance of a classical or quantum code is a key figure of merit which reflects its capacity to detect errors. Quantum LDPC code families have considerable promise in reducing the overhead required for fault-tolerant quantum…
Designing quantum processors is a complex task that demands advanced verification methods to ensure their correct functionality. However, traditional methods of comprehensively verifying quantum devices, such as quantum process tomography,…
We consider the problem of $\textit{subgroup testing}$ for a quantum circuit $C$: given access to $C$, determine whether it implements a unitary that is $a$-close or $b$-far from a subgroup $\mathcal{G}$ of the unitary group. It encompasses…
The diamond norm measures the distance between two quantum channels. From an operational vewpoint, this norm measures how well we can distinguish between two channels by applying them to input states of arbitrarily large dimensions. In this…