Related papers: Qudit Designs and Where to Find Them
Shadow estimation is a sample-efficient protocol for learning the properties of a quantum system using randomized measurements, but the current understanding of qudit shadow estimation is quite limited compared with the qubit setting. Here…
We investigate the emergence of quantum complexity and chaos in doped Clifford circuits acting on qudits of odd prime dimension $d$. Using doped Clifford Weingarten calculus and a replica tensor network formalism, we derive exact results…
The rapid development of quantum technology demands efficient characterization of complex quantum many-body states. However, full quantum state tomography requires an exponential number of measurements in system size, preventing its…
One of the most promising routes towards fault-tolerant quantum computation utilizes topological quantum error correcting codes, such as the $\mathbb{Z}_2$ surface code. Logical qubits can be encoded in a variety of ways in the surface…
This paper presents a deep reinforcement learning approach for synthesizing unitaries into quantum circuits. Unitary synthesis aims to identify a quantum circuit that represents a given unitary while minimizing circuit depth, total gate…
Distributed inner product estimation (DIPE) is a fundamental task in quantum information, aiming to estimate the inner product between two unknown quantum states prepared on distributed quantum platforms. Existing rigorous sample complexity…
Characterising quantum processes is a key task in and constitutes a challenge for the development of quantum technologies, especially at the noisy intermediate scale of today's devices. One method for characterising processes is randomised…
Quantum computers have the potential to solve important problems which are fundamentally intractable on a classical computer. The underlying physics of quantum computing platforms supports using multi-valued logic, which promises a boost in…
We generalize the notion of quantum state designs to infinite-dimensional spaces. We first prove that, under the definition of continuous-variable (CV) state $t$-designs from Comm. Math. Phys. 326, 755 (2014), no state designs exist for…
Epsilon-nets and approximate unitary $t$-designs are natural notions that capture properties of unitary operations relevant for numerous applications in quantum information and quantum computing. The former constitute subsets of unitary…
We introduce group surface codes, which are a natural generalization of the $\mathbb{Z}_2$ surface code, and equivalent to quantum double models of finite groups with specific boundary conditions. We show that group surface codes can be…
The Clifford group is a finite subgroup of the unitary group generated by the Hadamard, the CNOT, and the Phase gates. This group plays a prominent role in quantum error correction, randomized benchmarking protocols, and the study of…
We describe criteria for implementation of quantum computation in qudits. A qudit is a d-dimensional system whose Hilbert space is spanned by states |0>, |1>,... |d-1>. An important earlier work of Mathukrishnan and Stroud [1] describes how…
Quantum logic gates are the key elements in quantum computing. Here we investigate the possibility of achieving a scalable and compact quantum computing based on stationary electron-spin qubits, by using the giant optical circular…
Galois qudits are $q$-dimensional quantum systems whose choice of Pauli group encodes the arithmetic of some finite field $\mathbb{F}_q$. They differ from the more familiar modular qudit, which are the same quantum system but whose choice…
The Clifford+T gate set is a topological generating set for PU(2), which has been well-studied from the perspective of quantum computation on a single qubit. The discovery that it generates a full S-arithmetic subgroup of PU(2) has led to a…
This note presents a simple and unified formulation of the most fundamental structures used in quantum information with qubits, arbitrary dimension qudits, and quantum continuous variables. This \emph{general quantum variables} construction…
The n-qubit Pauli group and its normalizer the n-qubit Clifford group have applications in quantum error correction and device characterization. Recent applications have made use of the representation theory of the Clifford group. We apply…
One of the key challenges in quantum information is coherently manipulating the quantum state. However, it is an outstanding question whether control can be realized with low error. Only gates from the Clifford group -- containing $\pi$,…
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…