相关论文: Efficient unitary designs with nearly time-indepen…
The realization of unitary designs is of fundamental interest in quantum science and typically requires the ability to implement structured quantum circuits. Recent developments have explored the possibility of generating unitary designs…
Unitary $2$-designs are random unitaries simulating up to the second order statistical moments of the uniformly distributed random unitaries, often referred to as Haar random unitaries. They are used in a wide variety of theoretical and…
We study efficient generations of random diagonal-unitary matrices, an ensemble of unitary matrices diagonal in a given basis with randomly distributed phases for their eigenvalues. Despite the simple algebraic structure, they cannot be…
Unitary $T$-designs play an important role in quantum information, with diverse applications in quantum algorithms, benchmarking, tomography, and communication. Until now, the most efficient construction of unitary $T$-designs for $n$-qudit…
We investigate protocols for generating a state $t$-design by using a fixed separable initial state and a diagonal-unitary $t$-design in the computational basis, which is a $t$-design of an ensemble of diagonal unitary matrices with random…
Quantum pseudorandomness, also known as unitary designs, comprise a powerful resource for quantum computation and quantum engineering. While it is known in theory that pseudorandom unitary operators can be constructed efficiently, realizing…
Implementing quantum operations in the form of natural Hamiltonian dynamics is desirable, since they almost require no external control or feedback. In this work, we propose a NISQ-friendly quantum-classical hybrid approach to designing a…
In this paper, we show that the ability to switch globally between two 2-local Hamiltonians on n qubits is sufficient for achieving universal unitary dynamics on those n qubits. Of the two Hamiltonians used in the construction, one is…
We present a single-quench protocol that generates unitary $k$-designs with minimal control. A system first evolves under a random Hamiltonian $H_1$; at a switch time $t_s \geq t_{\mathrm{Th}}$ (the Thouless time), it is quenched to an…
The nature of randomness and complexity growth in systems governed by unitary dynamics is a fundamental question in quantum many-body physics. This problem has motivated the study of models such as local random circuits and their…
Unitary $k$-designs are central to quantum information and quantum many-body physics as efficient proxies for Haar-random dynamics. We study how chaotic Hamiltonian evolution can generate unitary $k$-designs. Standard approaches typically…
Unitary designs are widely used in quantum computation, but in many practical settings it suffices to construct a diagonal state design generated with unitary gates diagonal in the computational basis. In this work, we introduce a simple…
At its core a $t$-design is a method for sampling from a set of unitaries in a way which mimics sampling randomly from the Haar measure on the unitary group, with applications across quantum information processing and physics. We construct…
We present a unitary control pulse design method for a scalable quantum computer architecture based on electron spins in lateral quantum dots. We employ simultaneous control of spin interactions and derive the functional forms of spin…
The capacity to randomly pick a unitary across the whole unitary group is a powerful tool across physics and quantum information. A unitary $t$-design is designed to tackle this challenge in an efficient way, yet constructions to date rely…
Many quantum information protocols require the implementation of random unitaries. Because it takes exponential resources to produce Haar-random unitaries drawn from the full $n$-qubit group, one often resorts to $t$-designs. Unitary…
We develop a formalism for the robust dynamical decoupling and Hamiltonian engineering of strongly interacting qudit systems. Specifically, we present a geometric formalism that significantly simplifies qudit pulse sequence design, while…
Random unitaries are a central object of study in quantum information, with applications to quantum computation, quantum many-body physics, and quantum cryptography. Recent work has constructed unitary designs and pseudorandom unitaries…
We present a low-space overhead simulation algorithm based on the truncated Dyson series for time-dependent quantum dynamics. This algorithm is applied to simulating time-independent Hamiltonians by transitioning to the interaction picture,…
Simulating Hamiltonian dynamics is one of the most fundamental and significant tasks for characterising quantum materials. Recently, a series of quantum algorithms employing block-encoding of Hamiltonians have succeeded in providing…