Related papers: Efficient Quantum State Synthesis with One Query
We present an efficient method to prepare states of a many-body system on quantum hardware, first isolating individual quantum numbers and then using time evolution to isolate the energy. Our method in its simplest form requires only one…
Ubiquitous in quantum computing is the step to encode data into a quantum state. This process is called quantum state preparation, and its complexity for non-structured data is exponential on the number of qubits. Several works address this…
We study quantum algorithms that are given access to trusted and untrusted quantum witnesses. We establish strong limitations of such algorithms, via new techniques based on Laurent polynomials (i.e., polynomials with positive and negative…
One of the key steps in quantum algorithms is to prepare an initial quantum superposition state with different kinds of features. These so-called state preparation algorithms are essential to the behavior of quantum algorithms, and…
It is well known that quantum computers can efficiently find a hidden subgroup $H$ of a finite Abelian group $G$. This implies that after only a polynomial (in $\log |G|$) number of calls to the oracle function, the states corresponding to…
We study the problem of finding a (pure) product state with optimal fidelity to an unknown $n$-qubit quantum state $\rho$, given copies of $\rho$. This is a basic instance of a fundamental question in quantum learning: is it possible to…
We describe and analyze algorithms for classically simulating measurement of an $n$-qubit quantum state $\psi$ in the standard basis, that is, sampling a bit string $x$ from the probability distribution $|\langle x|\psi\rangle|^2$. Our…
In this work, a scalable algorithm for the approximate quantum state preparation problem is proposed, facing a challenge of fundamental importance in many topic areas of quantum computing. The algorithm uses a variational quantum circuit…
We demonstrate that a high fidelity approximation to $| \Psi_b \rangle$, the quantum superposition over all bit strings within Hamming distance $b$ of the codewords of a dimension-$k$ linear code over $\mathbb{Z}_2^n$, can be efficiently…
Efficient state preparation is essential for implementing efficient quantum algorithms. Whilst several techniques for low-cost state preparation exist, this work facilitates further classes of states, whose amplitudes are well approximated…
We construct a classical oracle relative to which $\mathsf{P} = \mathsf{NP}$ yet single-copy secure pseudorandom quantum states exist. In the language of Impagliazzo's five worlds, this is a construction of pseudorandom states in…
A basic building block of many quantum algorithms is the Phase Estimation algorithm (PEA). It estimates an eigenphase $\phi$ of a unitary operator $U$ using a copy of the corresponding eigenstate $|\phi\rangle$. Suppose, in place of…
State preparation is a fundamental routine in quantum computation, for which many algorithms have been proposed. Among them, perhaps the simplest one is the Grover-Rudolph algorithm. In this paper, we analyse the performance of this…
We consider the problem of efficiently simulating random quantum states and random unitary operators, in a manner which is convincing to unbounded adversaries with black-box oracle access. This problem has previously only been considered…
Most quantum processors requires pulse sequences for controlling quantum states. Here, we present an alternative algorithm for computing an optimal pulse sequence in order to perform a specific task, being an implementation of a quantum…
The compiling of quantum gates is crucial for the successful quantum algorithm implementations. The environmental noise as well as the bandwidth of control pulses pose a challenge to precise and fast qubit control, especially in a weakly…
Quantum state preparation is an important ingredient for other higher-level quantum algorithms, such as Hamiltonian simulation, or for loading distributions into a quantum device to be used e.g. in the context of optimization tasks such as…
We describe algorithms to obtain an approximate classical description of a $d$-dimensional quantum state when given access to a unitary (and its inverse) that prepares it. For pure states we characterize the query complexity for…
Quantum protocols often require the generation of specific quantum states. We describe a quantum algorithm for generating any prescribed quantum state. For an important subclass of states, including pure symmetric states, this algorithm is…
Quantum state preparation (QSP) for a general $n$-qubit state requires $O(2^n)$ CNOT gates and circuit depth, making exact amplitude encoding (EAE) impractical for near-term quantum hardware. We introduce an ancilla-free hybrid…