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Quantum circuits form a foundational framework in quantum science, enabling the description, analysis, and implementation of quantum computations. However, designing efficient circuits, typically constructed from single- and two-qubit…
In quantum metrology, information about unknown parameters $\mathbf{\theta} = (\theta_1,\ldots,\theta_M)$ is accessed by measuring probe states $\hat{\rho}_{\mathbf{\theta}}$. In experimental settings where copies of…
The computation of \(\operatorname{tr}(AB)\) is essential in quantum science and artificial intelligence, yet classical methods for \( d \)-dimensional matrices \( A \) and \( B \) require \( O(d^2) \) complexity, which becomes infeasible…
Full quantum tomography of high-dimensional quantum systems is experimentally infeasible due to the exponential scaling of the number of required measurements on the number of qubits in the system. However, several ideas were proposed…
Many quantum algorithms rely on the measurement of complex quantum amplitudes. Standard approaches to obtain the phase information, such as the Hadamard test, give rise to large overheads due to the need for global controlled-unitary…
Quantum supremacy poses that a realistic quantum computer can perform a calculation that classical computers cannot in any reasonable amount of time. It has become a topic of significant research interest since the birth of the field, and…
Accurate estimation of observables in quantum systems is a central challenge in quantum information science, yet practical implementations are fundamentally constrained by the limited number of measurement shots. In this work we explore a…
We introduce a method that allows one to infer many properties of a quantum state -- including nonlinear functions such as R\'enyi entropies -- using only global control over the constituent degrees of freedom. In this protocol, the state…
We revisit the problem of Pauli shadow tomography: given copies of an unknown $n$-qubit quantum state $\rho$, estimate $\text{tr}(P\rho)$ for some set of Pauli operators $P$ to within additive error $\epsilon$. This has been a popular…
Classical shadow tomography provides a randomized scheme for approximating the quantum state and its properties at reduced computational cost with applications in quantum computing. In this Letter we present an algorithm for realizing fewer…
We introduce a variational scheme inspired by classical shadow tomography to compute ground state correlations of quantum spin Hamiltonians. Shadow tomography allows for efficient reconstruction of expectation values of arbitrary…
Measurement in quantum simulations provides a means for extracting meaningful information from a complex quantum state, and for quantum computing reducing the complexity of measurement will be vital for near-term applications. For most…
Classical shadows provide a versatile framework for estimating many properties of quantum states from repeated, randomly chosen measurements without requiring full quantum state tomography. When prior information is available, such as…
Solving differential equations is one of the most promising applications of quantum computing. Recently we proposed an efficient quantum algorithm for solving one-dimensional Poisson equation avoiding the need to perform quantum arithmetic…
Quantum computers solve ever more complex tasks using steadily growing system sizes. Characterizing these quantum systems is vital, yet becoming increasingly challenging. The gold-standard is quantum state tomography (QST), capable of fully…
To improve the efficiency of the state tomography strategy via weak value, we have searched the optimal coupling strength between the system and measuring device. For an arbitrary d-dimensional quantum system, the optimal strengths being…
High-dimensional quantum information processing has become a mature field of research with several different approaches being adopted for the encoding of $D$-dimensional quantum systems. Such progress has fueled the search of reliable…
Efficiently estimating large numbers of non-commuting observables is an important subroutine of many quantum science tasks. We present the derandomized shallow shadows (DSS) algorithm for efficiently learning a large set of non-commuting…
Quantum tomography is the main method used to assess the quality of quantum information processing devices, but its complexity presents a major obstacle for the characterization of even moderately large systems. The number of experimental…
We generalize the classical shadow tomography scheme to a broad class of finite-depth or finite-time local unitary ensembles, known as locally scrambled quantum dynamics, where the unitary ensemble is invariant under local basis…