Related papers: Property testing of unitary operators
Quantifying the effect of noise on unitary operations is an essential task in quantum information processing. We propose the quantum Wasserstein distance between unitary operations, which shows an explanation for quantum circuit complexity…
We study property testing with incomplete or noisy inputs. The models we consider allow for adversarial manipulation of the input, but differ in whether the manipulation can be done only offline, i.e., before the execution of the algorithm,…
We present a simple null test of a dimension of a quantum system, using a single repeated operation in the method of delays, assuming that each instance is identical and independent. The test is well-suited to current feasible quantum…
A state discrimination problem in an operational probabilistic theory (OPT) is investigated in diagrammatic terms. It is well-known that, in the case of quantum theory, if a state set has a certain symmetry, then there exists a…
Determinantal point processes (DPPs) are popular probabilistic models of diversity. In this paper, we investigate DPPs from a new perspective: property testing of distributions. Given sample access to an unknown distribution $q$ over the…
In the uniformity testing task, an algorithm is provided with samples from an unknown probability distribution over a (known) finite domain, and must decide whether it is the uniform distribution, or, alternatively, if its total variation…
A central challenge in property testing is verifying algebraic structure with minimal access to data. A landmark result addressing this challenge, the linearity test of Blum, Luby, and Rubinfeld (JCSS `93), spurred a rich body of work on…
We analyze the complexity of quantum state verification in the context of solving systems of linear equations of the form $A \vec x = \vec b$. We show that any quantum operation that verifies whether a given quantum state is within a…
In quantum computing, knowing the symmetries a given system or state obeys or disobeys is often useful. For example, Hamiltonian symmetries may limit allowed state transitions or simplify learning parameters in machine learning…
Flag verification techniques are useful in quantum error correction for detecting critical faults. Here we present an application of flag verification techniques to improving post-selected performance of near-term algorithms. We extend the…
We experimentally demonstrate a weak measurement and measurement reversal-based scheme to ameliorate the effects of decoherence due to amplitude damping, on an NMR quantum processor. The weak measurement and measurement reversal processes…
The task of testing whether two uncharacterized quantum devices behave in the same way is crucial for benchmarking near-term quantum computers and quantum simulators, but has so far remained open for continuous-variable quantum systems. In…
The aim of this article is to define and compare several distances (or metrics) between operators acting on different (separable) Hilbert spaces. We consider here three main cases of how to measure the distance between two bounded…
Randomized benchmarking is an experimental procedure intended to demonstrate control of quantum systems. The procedure extracts the average error introduced by a set of control operations. When the target set of operations is intended to be…
The problem of discriminating between many quantum channels with certainty is analyzed under the assumption of prior knowledge of algebraic relations among possible channels. It is shown, by explicit construction of a novel family of…
Understanding the complexity of quantum states and circuits is a central challenge in quantum information science, with broad implications in many-body physics, high-energy physics and quantum learning theory. A common way to model the…
We introduce a scheme for realizing arbitrary controlled-unitary operations in a two qubit system. If the 2 \times 2 unitary matrix is special unitary (has unit determinant), the controlled-unitary gate operation can be realized in a single…
Bargmann invariants, multivariate traces of states, completely characterize any unitary-invariant property of a set of states. Unitary invariants enable the description of quantum resources such as basis-independent coherence and…
We introduce a family of identities that express general linear non-unitary evolution operators as a linear combination of unitary evolution operators, each solving a Hamiltonian simulation problem. This formulation can exponentially…
Comparison of quantum objects is a task to determine whether two unknown quantum objects are the same or different. It is one of the most basic information processing tasks for learning property of quantum objects, and comparison of quantum…