Related papers: Efficient quantum pseudorandomness under conservat…
The generation of $k$-designs (pseudorandom distributions that emulate the Haar measure up to $k$ moments) with local quantum circuit ensembles is a problem of fundamental importance in quantum information and physics. Despite the extensive…
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…
Local symmetric quantum circuits provide a simple framework to study the dynamics and phases of complex quantum systems with conserved charges. However, some of their basic properties have not yet been understood. Recently, it has been…
Local random circuits scramble efficiently and accordingly have a range of applications in quantum information and quantum dynamics. With a global $U(1)$ charge however, the scrambling ability is reduced; for example, such random circuits…
Quantum information processing in the presence of continuous symmetry is of wide importance and exhibits many novel physical and mathematical phenomena. SU(d) is a continuous group of particular interest since it represents a fundamental…
We have established the method of characterizing the unitary design generated by a symmetric local random circuit. Concretely, we have shown that the necessary and sufficient condition for the circuit asymptotically forming a t-design is…
Quantum computational pseudorandomness has emerged as a fundamental notion that spans connections to complexity theory, cryptography and fundamental physics. However, all known constructions of efficient quantum-secure pseudorandom objects…
Quantum error correction and symmetries play central roles in quantum information science and physics. It is known that quantum error-correcting codes that obey (are covariant with respect to) continuous symmetries in a certain sense cannot…
Pseudorandom circuits generate quantum states and unitary operators which are approximately distributed according to the unitarily invariant Haar measure. We explore how several design parameters affect the efficiency of pseudo-random…
In this work, we study distributions of unitaries generated by random quantum circuits containing only symmetry-respecting gates. We develop a unified approach applicable to all symmetry groups and obtain an equation that determines the…
This thesis discusses the young fields of quantum pseudo-randomness and quantum learning algorithms. We present techniques for derandomising algorithms to decrease randomness resource requirements and improve efficiency. One key object in…
Quantum error correction and symmetries play central roles in quantum information science and physics. It is known that quantum error-correcting codes covariant with respect to continuous symmetries cannot correct erasure errors perfectly…
In the accompanying paper of arXiv:2408.13472, we have established the method of characterizing the maximal order of asymptotic unitary designs generated by symmetric local random circuits, and have explicitly specified the order in the…
In the age of noisy quantum processors, the exploitation of quantum symmetries can be quite beneficial in the efficient preparation of trial states, an important part of the variational quantum eigensolver algorithm. The benefits include…
Randomness is both a useful way to model natural systems and a useful tool for engineered systems, e.g. in computation, communication and control. Fully random transformations require exponential time for either classical or quantum…
Random quantum circuits are proficient information scramblers and efficient generators of randomness, rapidly approximating moments of the unitary group. We study the convergence of local random quantum circuits to unitary $k$-designs.…
We numerically investigate the statement that local random quantum circuits acting on n qubits composed of polynomially many nearest neighbour two-qubit gates form an approximate unitary poly(n)-design [F.G.S.L. Brandao et al.,…
In this work we give an efficient construction of unitary $k$-designs using $\tilde{O}(k\cdot poly(n))$ quantum gates, as well as an efficient construction of a parallel-secure pseudorandom unitary (PRU). Both results are obtained by giving…
We show how to efficiently generate pseudo-random states suitable for quantum information processing via cluster-state quantum computation. By reformulating pseudo-random algorithms in the cluster-state picture, we identify a strategy for…
This thesis presents an efficient quantum algorithm and explicit circuits for generating eigenstates of arbitrary SU(2) and SU(3) representations. These include a wide variety of highly entangled states. The algorithm uses Schur transform…