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Quantum query complexity plays an important role in studying quantum algorithms, which captures the most known quantum algorithms, such as search and period finding. A query algorithm applies $U_tO_x\cdots U_1O_xU_0$ to some input state,…
Accurate calculations of the spectral density in a strongly correlated quantum many-body system are of fundamental importance to study its dynamics in the linear response regime. Typical examples are the calculation of inclusive and…
This paper develops a methodological framework for addressing a novel and application-oriented inverse nodal problem in Sturm-Liouville operators, having significant applications in seismic wave analysis and submarine underwater radar…
We consider quantum algorithms for the unique sink orientation problem on cubes. This problem is widely considered to be of intermediate computational complexity. This is because there no known polynomial algorithm (classical or quantum)…
Quantum computation requires qubits that satisfy often-conflicting criteria, including scalable control and long-lasting coherence. One approach to creating a suitable qubit is to operate in an encoded subspace of several physical qubits.…
Reflections are omnipresent tools in quantum algorithms. We consider the task of reflecting through the eigenspace of an implementable unitary. Such reflections are generally designed using phase estimation or linear combination of…
Highly uniform quantum systems are essential for the practical implementation of scalable quantum processors. While quantum dot spin qubits based on semiconductor technology are a promising platform for large-scale quantum computing, their…
Combinatorial optimization is considered a promising class of problems in which quantum computers can show significant advantages. However, problems of practical relevance typically have more variables than current or foreseeable quantum…
We present a quantum algorithm for European option pricing in finance, where the key idea is to work in the unary representation of the asset value. The algorithm needs novel circuitry and is divided in three parts: first, the amplitude…
Resource-efficient and high-precision approximate synthesis of quantum circuits expressed in the Clifford+T gate set is vital for Fault-Tolerant quantum computing. Efficient optimal methods are known for single-qubit RZ unitaries, otherwise…
Exploiting permutation invariance to reduce the exponential scaling of semidefinite programs in quantum information has emerged as a powerful computational technique. In this work, we develop a systematic framework for using this reduction…
Quasi-one-dimensional quantum structures with spectra scaling faster than the square of the eigenmode number (superscaling) can generate intrinsic, off-resonant optical nonlinearities near the fundamental physical limits, independent of the…
Adaptive quantum design identifies the best broken-symmetry configurations of atoms and molecules that enable a desired target function response. In this work, numerical optimization is used to design atomic clusters with specified…
We present a novel, computationally efficient approach to accelerate quantum optimal control calculations of large multi-qubit systems used in a variety of quantum computing applications. By leveraging the intrinsic symmetry of finite…
Shadow estimation is a powerful approach for estimating the expectation values of many observables. Thrifty shadow estimation is a simple variant that is proposed to reduce the experimental overhead by reusing random circuits repeatedly.…
A scalable Bayesian machine learning framework is introduced for estimating scalar properties of an unknown quantum state from measurement data, which bypasses full density matrix reconstruction. This work is the first to integrate the…
The development of quantum control methods is an essential task for emerging quantum technologies. In general, the process of optimizing quantum controls scales very unfavorably in system size due to the exponential growth of the Hilbert…
The idea that symmetries simplify or reduce the complexity of a system has been remarkably fruitful in physics, and especially in quantum mechanics. On a mathematical level, symmetry groups single out a certain structure in the Hilbert…
Although spin is a core property in fermionic systems, its symmetry can be easily violated in a variational simulation, especially when strong correlation plays a vital role therein. In this study, we will demonstrate that the broken…
Shadow estimation is a method for deducing numerous properties of an unknown quantum state through a limited set of measurements, which suffers from noises in quantum devices. In this paper, we introduce an error-mitigated shadow estimation…