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The logarithm-determinant is an widely-present operation in many areas of physics and computer science. Derivatives of the logarithm-determinant compute physically relevant quantities in statistical physics models, quantum field theories,…
Quantum state tomography (QST) is one of the fundamental problems in quantum information. Among various metrics, sample complexity is widely used to evaluate QST algorithms. While multi-copy measurements are known to achieve optimal sample…
Motivated by the recent advances in the field of quantum computing, quantum systems are modelled and analyzed as networks of decentralized quantum nodes which employ distributed quantum consensus algorithms for coordination. In the…
We transform the problem of solving linear system of equations $A\mathbf{x}=\mathbf{b}$ to a problem of finding the right singular vector with singular value zero of an augmented matrix $C$, and present two quantum algorithms for solving…
Noise and errors are inevitable parts of any practical implementation of a quantum computer. As a result, large-scale quantum computation will require ways to detect and correct errors on quantum information. Here, we present such a quantum…
Finding the minimal relative entropy of two quantum states under semidefinite constraints is a pivotal problem located at the mathematical core of various applications in quantum information theory. An efficient method for providing…
We revisit the extendability-based semi-definite programming hierarchy introduced by Berta et al. [Mathematical Programming, 1 - 49 (2021)], which provides converging outer bounds on the optimal fidelity of approximate quantum error…
Estimating the ground state energy of a multiparticle system with relative error $\e$ using deterministic classical algorithms has cost that grows exponentially with the number of particles. The problem depends on a number of state…
We give an approximation algorithm for Quantum Max-Cut which works by rounding an SDP relaxation to an entangled quantum state. The SDP is used to choose the parameters of a variational quantum circuit. The entangled state is then…
Quantum algorithms for binary optimization problems have been the subject of extensive study. However, the application of quantum algorithms to integer optimization problems remains comparatively unexplored. In this paper, we study the…
The quantum approximate optimization algorithm (QAOA) conceived for solving combinatorial optimization problems has attracted significant interest since it can be run on the existing noisy intermediate-scale quantum (NISQ) devices. A…
Gate model quantum computers with too many qubits to be simulated by available classical computers are about to arrive. We present a strategy for programming these devices without error correction or compilation. This means that the number…
Debugging quantum states transformations is an important task of modern quantum computing. The use of quantum tomography for these purposes significantly expands the range of possibilities. However, the presence of preparation and…
We propose a class of randomized quantum algorithms for the task of sampling from matrix functions, without the use of quantum block encodings or any other coherent oracle access to the matrix elements. As such, our use of qubits is purely…
Understanding open quantum systems using information encoded in its complex eigenvalues has been a subject of growing interest. In this paper, we study higher-order gap ratios of the singular values of generic open quantum systems. We show…
We present a quantum algorithm for adiabatic state preparation on a gate-based quantum computer, with complexity polylogarithmic in the inverse error. Our algorithm digitally simulates the adiabatic evolution between two self-adjoint…
Estimating the trace of quantum state powers, $\text{Tr}(\rho^k)$, for $k$ identical quantum states is a fundamental task with numerous applications in quantum information processing, including nonlinear function estimation of quantum…
Currently available quantum computers, so called Noisy Intermediate-Scale Quantum (NISQ) devices, are characterized by relatively low number of qubits and moderate gate fidelities. In such scenario, the implementation of quantum error…
We consider the task of simulating time evolution under a Hamiltonian $H$ within its low-energy subspace. Assuming access to a block-encoding of $H'=(H-E)/\lambda$ for some $E \in \mathbb R$, the goal is to implement an…
Many problems in linear algebra -- such as those arising from non-Hermitian physics and differential equations -- can be solved on a quantum computer by processing eigenvalues of the non-normal input matrices. However, the existing Quantum…