Related papers: Exact and Approximate Unitary 2-Designs: Construct…
We define and construct efficient depth-universal and almost-size-universal quantum circuits. Such circuits can be viewed as general-purpose simulators for central classes of quantum circuits and can be used to capture the computational…
We study the problem of efficiently learning an unknown $n$-qubit unitary channel in diamond distance given query access. We present a general framework showing that if Pauli operators remain low-complexity under conjugation by a unitary,…
Complex projective t-designs, particularly SICs and full sets of MUBs, play an important role in quantum information. We introduce a generalization which we call conical t-designs. They include arbitrary rank symmetric informationally…
A fundamental question in the theory of quantum computation is to understand the ultimate space-time resource costs for performing a universal set of logical quantum gates to arbitrary precision. Here we demonstrate that non-Abelian anyons…
We investigate decoupling, one of the most important primitives in quantum Shannon theory, by replacing the uniformly distributed random unitaries commonly used to achieve the protocol, with repeated applications of random unitaries…
This dissertation explores quantum computation using qudits encoded into large spins, emphasizing the concept of quantum co-design to harness the unique capabilities of physical platforms for enhanced quantum information processing. First,…
Determining the quantum circuit complexity of a unitary operation is an important problem in quantum computation. By using the mathematical techniques of Riemannian geometry, we investigate the efficient quantum circuits in quantum…
We introduce the notion of "non-malleability" of a quantum state encryption scheme (in dimension d): in addition to the requirement that an adversary cannot learn information about the state, here we demand that no controlled modification…
Quantum tomography is an important tool for obtaining information about the quantum state from experimental data. In this study, we conduct a comparative analysis of various quantum tomography protocols, including protocols based on highly…
In this paper we provide an explicit parameterization of arbitrary unitary transformation acting on n qubits, in terms of one and two qubit quantum gates. The construction is based on successive Cartan decompositions of the semi-simple Lie…
Designing quantum processors is a complex task that demands advanced verification methods to ensure their correct functionality. However, traditional methods of comprehensively verifying quantum devices, such as quantum process tomography,…
Unitary t-designs have a wide variety of applications in quantum information theory, such as quantum data encryption and randomised benchmarking. However, experimental realisations of t-designs are subject to noise. Here we investigate the…
Special functions, coding theory and $t$-designs have close connections and interesting interplay. A standard approach to constructing $t$-designs is the use of linear codes with certain regularity. The Assmus-Mattson Theorem and the…
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…
We present an algorithm, along with its implementation that finds T-optimal approximations of single-qubit Z-rotations using quantum circuits consisting of Clifford and T gates. Our algorithm is capable of handling errors in approximation…
Maximally entangled bipartite unitary operators or gates find various applications from quantum information to being building blocks of minimal models of many-body quantum chaos, and have been referred to as "dual unitaries". Dual unitary…
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…
Randomness is a fundamental resource in quantum information, with crucial applications in cryptography, algorithms, and error correction. A central challenge is to construct unitary $k$-designs that closely approximate Haar-random unitaries…
This paper concerns the efficient implementation of quantum circuits for qudits. We show that controlled two-qudit gates can be implemented without ancillas and prove that the gate library containing arbitrary local unitaries and one…
Modelling non-linear activation functions on quantum computers is vital for quantum neurons employed in fully quantum neural networks, however, remains a challenging task. We introduce an amplitude-based implementation for approximating…