Related papers: Stabilizer bootstrapping: A recipe for efficient a…
We define a quantum learning task called agnostic tomography, where given copies of an arbitrary state $\rho$ and a class of quantum states $\mathcal{C}$, the goal is to output a succinct description of a state that approximates $\rho$ at…
We study the complexity of learning quantum states in various models with respect to the stabilizer formalism and obtain the following results: - We prove that $\Omega(n)$ $T$-gates are necessary for any Clifford+$T$ circuit to prepare…
Stabilizer states are fundamental families of quantum states with crucial applications such as error correction, quantum computation, and simulation of quantum circuits. In this paper, we study the problem of testing how close or far a…
Entanglement lies at the heart of quantum information science, serving as a key resource for quantum communication, computation, and metrology. Consequently, high-precision entangled state preparation and efficient verification are…
Certifying the fidelity of a prepared state to a target stabilizer state is a fundamental task in quantum information processing. Ref. [Phys. Rev. A 99, 042337 (2019)] gave the optimal worst-case lower bound from one fixed stabilizer…
We propose a quantum-state-certification protocol for stabilizer states, motivated by application in in-situ testing of NISQ-era quantum computer systems: The number of qubits is bounded, and in terms of cost of running the protocol,…
We study the complexity of two closely related learning problems, one quantum and one classical. In the quantum setting, we consider agnostic tomography for the natural class of product mixed states. Given $N$ copies of an $n$-qubit state…
We give a pair of algorithms that efficiently learn a quantum state prepared by Clifford gates and $O(\log n)$ non-Clifford gates. Specifically, for an $n$-qubit state $|\psi\rangle$ prepared with at most $t$ non-Clifford gates, our…
Statistical verification of a quantum state aims to certify whether a given unknown state is close to the target state with confidence. So far, sample-optimal verification protocols based on local measurements have been found only for…
In this work, we explore a new approach to designing both algorithms and error detection codes for preparing approximate ground states of molecules. We propose a classical algorithm to find the optimal stabilizer state by using excitations…
Large-scale quantum computation is likely to require massive quantum error correction (QEC). QEC codes and circuits are described via the stabilizer formalism, which represents stabilizer states by keeping track of the operators that…
We consider the task of learning a structured stabilizer decomposition of an arbitrary $n$-qubit quantum state $|\psi\rangle$: for $\epsilon > 0$, output a state $|\phi\rangle$ with stabilizer-rank $\textsf{poly}(1/\epsilon)$ such that…
Quantum fidelity estimation is essential for benchmarking quantum states and processes on noisy quantum devices. While stabilizer operations form the foundation of fault-tolerant quantum computing, non-stabilizer resources further enable…
The exponential scaling of the wave function is a fundamental property of quantum systems with far reaching implications in our ability to process quantum information. A problem where these are particularly relevant is quantum state…
We propose a measurement scheme that validates the preparation of an $n$-qubit stabilizer state. The scheme involves a measurement of $n$ Pauli observables, a priori determined from the stabilizer state and which can be realized using…
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…
Non-stabilizerness is an essential resource for quantum computational advantage, as stabilizer states admit efficient classical simulation. We develop a semi-device-independent framework for certifying non-stabilizer states in…
Consider the task of verifying that a given quantum device, designed to produce a particular entangled state, does indeed produce that state. One natural approach would be to characterise the output state by quantum state tomography; or…
The stabiliser formalism plays a central role in quantum computing, error correction, and fault tolerance. Conversions between and verifications of different specifications of stabiliser states and Clifford gates are important components of…
Large-scale quantum computation is likely to require massive quantum error correction (QEC). QEC codes and circuits are described via the stabilizer formalism, which represents stabilizer states by keeping track of the operators that…