Quantum Sciences

  • Mapping graph state orbits under local complementation
    Quantum 4, 305 (2020). https://doi.org/10.22331/q-2020-08-07-305 Graph states, and the entanglement they posses, are central to modern quantum computing and communications architectures. Local complementation – the graph operation that links all local-Clifford equivalent graph states – allows us to classify all stabiliser states by their entanglement. Here, we study the structure of the orbits generated by … Read MoreRead more
  • On maximum-likelihood decoding with circuit-level errors
    Quantum 4, 304 (2020). https://doi.org/10.22331/q-2020-08-06-304 Error probability distribution associated with a given Clifford measurement circuit is described exactly in terms of the circuit error-equivalence group, or the circuit subsystem code previously introduced by Bacon, Flammia, Harrow, and Shi. This gives a prescription for maximum-likelihood decoding with a given measurement circuit. Marginal distributions for subsets of … Read MoreRead more
  • A robust W-state encoding for linear quantum optics
    Quantum 4, 303 (2020). https://doi.org/10.22331/q-2020-08-03-303 Error-detection and correction are necessary prerequisites for any scalable quantum computing architecture. Given the inevitability of unwanted physical noise in quantum systems and the propensity for errors to spread as computations proceed, computational outcomes can become substantially corrupted. This observation applies regardless of the choice of physical implementation. In the … Read MoreRead more
  • Sum-of-squares decompositions for a family of noncontextuality inequalities and self-testing of quantum devices
    Quantum 4, 302 (2020). https://doi.org/10.22331/q-2020-08-03-302 Violation of a noncontextuality inequality or the phenomenon referred to `quantum contextuality' is a fundamental feature of quantum theory. In this article, we derive a novel family of noncontextuality inequalities along with their sum-of-squares decompositions in the simplest (odd-cycle) sequential-measurement scenario capable to demonstrate Kochen-Specker contextuality. The sum-of-squares decompositions allow … Read MoreRead more
  • Law without law: from observer states to physics via algorithmic information theory
    Quantum 4, 301 (2020). https://doi.org/10.22331/q-2020-07-20-301 According to our current conception of physics, any valid physical theory is supposed to describe the objective evolution of a unique external world. However, this condition is challenged by quantum theory, which suggests that physical systems should not always be understood as having objective properties which are simply revealed by … Read MoreRead more
  • A link between symmetries of critical states and the structure of SLOCC classes in multipartite systems
    Quantum 4, 300 (2020). https://doi.org/10.22331/q-2020-07-20-300 Central in entanglement theory is the characterization of local transformations among pure multipartite states. As a first step towards such a characterization, one needs to identify those states which can be transformed into each other via local operations with a non-vanishing probability. The classes obtained in this way are called … Read MoreRead more
  • Entanglement-breaking superchannels
    Quantum 4, 299 (2020). https://doi.org/10.22331/q-2020-07-16-299 In this paper we initiate the study of entanglement-breaking (EB) superchannels. These are processes that always yield separable maps when acting on one side of a bipartite completely positive (CP) map. EB superchannels are a generalization of the well-known EB channels. We give several equivalent characterizations of EB supermaps and … Read MoreRead more
  • Quasirandom quantum channels
    Quantum 4, 298 (2020). https://doi.org/10.22331/q-2020-07-16-298 Mixing (or quasirandom) properties of the natural transition matrix associated to a graph can be quantified by its distance to the complete graph. Different mixing properties correspond to different norms to measure this distance. For dense graphs, two such properties known as spectral expansion and uniformity were shown to be … Read MoreRead more
  • A Quantum Money Solution to the Blockchain Scalability Problem
    Quantum 4, 297 (2020). https://doi.org/10.22331/q-2020-07-16-297 We put forward the idea that classical blockchains and smart contracts are potentially useful primitives not only for classical cryptography, but for quantum cryptography as well. Abstractly, a smart contract is a functionality that allows parties to deposit funds, and release them upon fulfillment of algorithmically checkable conditions, and can … Read MoreRead more
  • Improved Fault-Tolerant Quantum Simulation of Condensed-Phase Correlated Electrons via Trotterization
    Quantum 4, 296 (2020). https://doi.org/10.22331/q-2020-07-16-296 Recent work has deployed linear combinations of unitaries techniques to reduce the cost of fault-tolerant quantum simulations of correlated electron models. Here, we show that one can sometimes improve upon those results with optimized implementations of Trotter-Suzuki-based product formulas. We show that low-order Trotter methods perform surprisingly well when used … Read MoreRead more
  • Generating Fault-Tolerant Cluster States from Crystal Structures
    Quantum 4, 295 (2020). https://doi.org/10.22331/q-2020-07-13-295 Measurement-based quantum computing (MBQC) is a promising alternative to traditional circuit-based quantum computing predicated on the construction and measurement of cluster states. Recent work has demonstrated that MBQC provides a more general framework for fault-tolerance that extends beyond foliated quantum error-correcting codes. We systematically expand on that paradigm, and use … Read MoreRead more
  • Cellular automata in operational probabilistic theories
    Quantum 4, 294 (2020). https://doi.org/10.22331/q-2020-07-09-294 The theory of cellular automata in operational probabilistic theories is developed. We start introducing the composition of infinitely many elementary systems, and then use this notion to define update rules for such infinite composite systems. The notion of causal influence is introduced, and its relation with the usual property of … Read MoreRead more
  • The Platonic solids and fundamental tests of quantum mechanics
    Quantum 4, 293 (2020). https://doi.org/10.22331/q-2020-07-09-293 The Platonic solids is the name traditionally given to the five regular convex polyhedra, namely the tetrahedron, the octahedron, the cube, the icosahedron and the dodecahedron. Perhaps strongly boosted by the towering historical influence of their namesake, these beautiful solids have, in well over two millennia, transcended traditional boundaries and … Read MoreRead more
  • Squeezing metrology: a unified framework
    Quantum 4, 292 (2020). https://doi.org/10.22331/q-2020-07-09-292 Quantum metrology theory has up to now focused on the resolution gains obtainable thanks to the entanglement among $N$ probes. Typically, a quadratic gain in resolution is achievable, going from the $1/sqrt{N}$ of the central limit theorem to the $1/N$ of the Heisenberg bound. Here we focus instead on quantum … Read MoreRead more
  • Option Pricing using Quantum Computers
    Quantum 4, 291 (2020). https://doi.org/10.22331/q-2020-07-06-291 We present a methodology to price options and portfolios of options on a gate-based quantum computer using amplitude estimation, an algorithm which provides a quadratic speedup compared to classical Monte Carlo methods. The options that we cover include vanilla options, multi-asset options and path-dependent options such as barrier options. We … Read MoreRead more
  • Variational quantum state preparation via quantum data buses
    Quantum 4, 290 (2020). https://doi.org/10.22331/q-2020-07-06-290 We propose a variational quantum algorithm to prepare ground states of 1D lattice quantum Hamiltonians specifically tailored for programmable quantum devices where interactions among qubits are mediated by Quantum Data Buses (QDB). For trapped ions with the axial Center-Of-Mass (COM) vibrational mode as single QDB, our scheme uses resonant sideband … Read MoreRead more
  • Quantum Zeno Dynamics from General Quantum Operations
    Quantum 4, 289 (2020). https://doi.org/10.22331/q-2020-07-06-289 We consider the evolution of an arbitrary quantum dynamical semigroup of a finite-dimensional quantum system under frequent kicks, where each kick is a generic quantum operation. We develop a generalization of the Baker-Campbell-Hausdorff formula allowing to reformulate such pulsed dynamics as a continuous one. This reveals an adiabatic evolution. We … Read MoreRead more
  • Optimal probes and error-correction schemes in multi-parameter quantum metrology
    Quantum 4, 288 (2020). https://doi.org/10.22331/q-2020-07-02-288 We derive a necessary and sufficient condition for the possibility of achieving the Heisenberg scaling in general adaptive multi-parameter estimation schemes in presence of Markovian noise. In situations where the Heisenberg scaling is achievable, we provide a semidefinite program to identify the optimal quantum error correcting (QEC) protocol that yields … Read MoreRead more
  • Efficient Quantum Walk Circuits for Metropolis-Hastings Algorithm
    Quantum 4, 287 (2020). https://doi.org/10.22331/q-2020-06-29-287 We present a detailed circuit implementation of Szegedy's quantization of the Metropolis-Hastings walk. This quantum walk is usually defined with respect to an oracle. We find that a direct implementation of this oracle requires costly arithmetic operations. We thus reformulate the quantum walk, circumventing its implementation altogether by closely following … Read MoreRead more
  • On the Entanglement Cost of One-Shot Compression
    Quantum 4, 286 (2020). https://doi.org/10.22331/q-2020-06-25-286 We revisit the task of visible compression of an ensemble of quantum states with entanglement assistance in the one-shot setting. The protocols achieving the best compression use many more qubits of shared entanglement than the number of qubits in the states in the ensemble. Other compression protocols, with potentially larger … Read MoreRead more
  • Optimal Detection of Rotations about Unknown Axes by Coherent and Anticoherent States
    Quantum 4, 285 (2020). https://doi.org/10.22331/q-2020-06-22-285 Coherent and anticoherent states of spin systems up to spin $j=2$ are known to be optimal in order to detect rotations by a known angle but unknown rotation axis. These optimal quantum rotosensors are characterized by minimal fidelity, given by the overlap of a state before and after a rotation, … Read MoreRead more
  • String Theory in Fiction
    String theory and multiverses in fiction
  • Quantum Codes of Maximal Distance and Highly Entangled Subspaces
    Quantum 4, 284 (2020). https://doi.org/10.22331/q-2020-06-18-284 We present new bounds on the existence of general quantum maximum distance separable codes (QMDS): the length $n$ of all QMDS codes with local dimension $D$ and distance $d geq 3$ is bounded by $n leq D^2 + d – 2$. We obtain their weight distribution and present additional bounds … Read MoreRead more
  • Switching Quantum Reference Frames for Quantum Measurement
    Quantum 4, 283 (2020). https://doi.org/10.22331/q-2020-06-18-283 Physical observation is made relative to a reference frame. A reference frame is essentially a quantum system given the universal validity of quantum mechanics. Thus, a quantum system must be described relative to a quantum reference frame (QRF). Further requirements on QRF include using only relational observables and not assuming … Read MoreRead more
  • A two-player dimension witness based on embezzlement, and an elementary proof of the non-closure of the set of quantum correlations
    Quantum 4, 282 (2020). https://doi.org/10.22331/q-2020-06-18-282 We describe a two-player non-local game, with a fixed small number of questions and answers, such that an $epsilon$-close to optimal strategy requires an entangled state of dimension $2^{Omega(epsilon^{-1/8})}$. Our non-local game is inspired by the three-player non-local game of Ji, Leung and Vidick [17]. It reduces the number of … Read MoreRead more