Related papers: Learning quantum states prepared by shallow circui…
Equilibrium statistical ensembles impose stringent constraints on phases of quantum matter. For example, the Mermin-Wagner theorem prohibits long-range order in low-dimensional systems beyond the ground state. Here, we show that quantum…
The problem of quantum state classification asks how accurately one can identify an unknown quantum state that is promised to be drawn from a known set of pure states. In this work, we introduce the notion of $k$-learnability, which…
We introduce a new approach for quantum linear algebra based on quantum subspace states and present three new quantum machine learning algorithms. The first is a quantum determinant sampling algorithm that samples from the distribution…
We show how techniques from machine learning and optimization can be used to find circuits of photonic quantum computers that perform a desired transformation between input and output states. In the simplest case of a single input state,…
We provide a polynomial-time classical algorithm for noisy quantum circuits. The algorithm computes the expectation value of any observable for any circuit, with a small average error over input states drawn from an ensemble (e.g. the…
We study efficient quantum certification algorithms for quantum state set and unitary quantum channel. We present an algorithm that uses $O(\varepsilon^{-4}\ln |\mathcal{P}|)$ copies of an unknown state to distinguish whether the unknown…
The simulation of the dynamics of a system coupled to a low-temperature environment is a promising application of quantum computers to determine ground-state properties of physical systems. However, this approach requires not only the…
The preparation of $n$-qubit quantum states is a cross-cutting subroutine for many quantum algorithms, and the effort to reduce its circuit complexity is a significant challenge. In the literature, the quantum state preparation algorithm by…
We prove that recognizing the phase of matter of an unknown quantum state is quantum computationally hard. More specifically, we show that the quantum computational time of any phase recognition algorithm must grow exponentially in the…
We describe a quantum algorithm to prepare an arbitrary pure state of a register of a quantum computer with fidelity arbitrarily close to 1. Our algorithm is based on Grover's quantum search algorithm. For sequences of states with suitably…
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…
Accurate control of quantum states is crucial for quantum computing and other quantum technologies. In the basic scenario, the task is to steer a quantum system towards a target state through a sequence of control operations. Determining…
The ability to efficiently state-prepare Gaussian distributions is critical to the success of numerous quantum algorithms. The most popular algorithm for this subroutine (Kitaev-Webb) has favorable polynomial resource scaling, however it…
Shallow quantum circuits feature not only computational advantages over their classical counterparts but also cutting-edge applications. Storing quantum information generated by shallow circuits is a fundamental question of both theoretical…
Efficient state preparation is a challenging and important problem in quantum computing. In this work, we present a recursive state preparation algorithm that combines logarithmic-depth Dicke state circuits with Hamming weight encoders for…
Efficient characterization of highly entangled multi-particle systems is an outstanding challenge in quantum science. Recent developments have shown that a modest number of randomized measurements suffices to learn many properties of a…
Quantum state preparation is a fundamental component of quantum algorithms, particularly in quantum machine learning and data processing, where classical data must be encoded efficiently into quantum states. Existing amplitude encoding…
The Quantum State Preparation problem aims to prepare an $n$-qubit quantum state $|\psi_v\rangle =\sum_{k=0}^{2^n-1}v_k|k\rangle$ from the initial state $|0\rangle^{\otimes n}$, for a given unit vector $v=(v_0,v_1,v_2,\ldots,v_{2^n-1})^T\in…
In this paper we give a polynomial-time quantum algorithm for computing orders of solvable groups. Several other problems, such as testing membership in solvable groups, testing equality of subgroups in a given solvable group, and testing…
The vast complexity is a daunting property of generic quantum states that poses a significant challenge for theoretical treatment, especially in non-equilibrium setups. Therefore, it is vital to recognize states which are locally less…