Quantum Sciences

  • Efficient quantum measurement of Pauli operators in the presence of finite sampling error
    Quantum 5, 385 (2021). https://doi.org/10.22331/q-2021-01-20-385 Estimating the expectation value of an operator corresponding to an observable is a fundamental task in quantum computation. It is often impossible to obtain such estimates directly, as the computer is restricted to measuring in a fixed computational basis. One common solution splits the operator into a weighted sum of…
  • The Multi-round Process Matrix
    Quantum 5, 384 (2021). https://doi.org/10.22331/q-2021-01-20-384 We develop an extension of the process matrix (PM) framework for correlations between quantum operations with no causal order that allows multiple rounds of information exchange for each party compatibly with the assumption of well-defined causal order of events locally. We characterise the higher-order process describing such correlations, which we…
  • How Dynamical Quantum Memories Forget
    Quantum 5, 382 (2021). https://doi.org/10.22331/q-2021-01-17-382 Motivated by recent work showing that a quantum error correcting code can be generated by hybrid dynamics of unitaries and measurements, we study the long time behavior of such systems. We demonstrate that even in the “mixed'' phase, a maximally mixed initial density matrix is purified on a time scale…
  • Autonomous Ticking Clocks from Axiomatic Principles
    Quantum 5, 381 (2021). https://doi.org/10.22331/q-2021-01-17-381 There are many different types of time keeping devices. We use the phrase $textit{ticking clock}$ to describe those which – simply put – “tick'' at approximately regular intervals. Various important results have been derived for ticking clocks, and more are in the pipeline. It is thus important to understand the…
  • Exponentially faster implementations of Select(H) for fermionic Hamiltonians
    Quantum 5, 380 (2021). https://doi.org/10.22331/q-2021-01-12-380 We present a simple but general framework for constructing quantum circuits that implement the multiply-controlled unitary $text{Select}(H) equiv sum_ell |ellranglelangleell|otimes H_ell$, where $H = sum_ell H_ell$ is the Jordan-Wigner transform of an arbitrary second-quantised fermionic Hamiltonian. $text{Select}(H)$ is one of the main subroutines of several quantum algorithms, including state-of-the-art techniques…
  • Experiment-friendly formulation of quantum backflow
    Quantum 5, 379 (2021). https://doi.org/10.22331/q-2021-01-11-379 Quantum backflow is usually understood as a quantum interference phenomenon where probability current of a quantum particle points in the opposite direction to particle's momentum. Here, we quantify the amount of quantum backflow for arbitrary momentum distributions, paving the way towards its experimental verification. We give examples of backflow in…
  • Hello 2021, hello Plan S!
    The year 2021 has begun and Plan S, an initiative aimed at pushing open-access publishing that is backed by an international consortium of funding agencies and research organisations called cOAlition S, is coming into effect. In short, Plan S requires that scientific publications that result from research funded (at least partially) by grants of cOAlition…
  • The three types of normal sequential effect algebras
    Quantum 4, 378 (2020). https://doi.org/10.22331/q-2020-12-24-378 A sequential effect algebra (SEA) is an effect algebra equipped with a $textit{sequential product}$ operation modeled after the Lüders product $(a,b)mapsto sqrt{a}bsqrt{a}$ on C$^*$-algebras. A SEA is called $textit{normal}$ when it has all suprema of directed sets, and the sequential product interacts suitably with these suprema. The effects on a…
  • Multi-spin counter-diabatic driving in many-body quantum Otto refrigerators
    Quantum 4, 377 (2020). https://doi.org/10.22331/q-2020-12-24-377 Quantum refrigerators pump heat from a cold to a hot reservoir. In the few-particle regime, counter-diabatic (CD) driving of, originally adiabatic, work-exchange strokes is a promising candidate to overcome the bottleneck of vanishing cooling power. Here, we present a finite-time many-body quantum refrigerator that yields finite cooling power at high…
  • High-Dimensional Pixel Entanglement: Efficient Generation and Certification
    Quantum 4, 376 (2020). https://doi.org/10.22331/q-2020-12-24-376 Photons offer the potential to carry large amounts of information in their spectral, spatial, and polarisation degrees of freedom. While state-of-the-art classical communication systems routinely aim to maximize this information-carrying capacity via wavelength and spatial-mode division multiplexing, quantum systems based on multi-mode entanglement usually suffer from low state quality, long…
  • Thermodynamics of Minimal Coupling Quantum Heat Engines
    Quantum 4, 375 (2020). https://doi.org/10.22331/q-2020-12-23-375 The minimal-coupling quantum heat engine is a thermal machine consisting of an explicit energy storage system, heat baths, and a working body, which alternatively couples to subsystems through discrete strokes — energy-conserving two-body quantum operations. Within this paradigm, we present a general framework of quantum thermodynamics, where a work extraction…
  • Translating Uncontrolled Systems in Time
    Quantum 4, 374 (2020). https://doi.org/10.22331/q-2020-12-15-374 We show that there exist non-relativistic scattering experiments which, if successful, freeze out, speed up or even reverse the free dynamics of any ensemble of quantum systems present in the scattering region. This “time translation'' effect is universal, i.e., it is independent of the particular interaction between the scattering particles…
  • Quantum computed moments correction to variational estimates
    Quantum 4, 373 (2020). https://doi.org/10.22331/q-2020-12-15-373 The variational principle of quantum mechanics is the backbone of hybrid quantum computing for a range of applications. However, as the problem size grows, quantum logic errors and the effect of barren plateaus overwhelm the quality of the results. There is now a clear focus on strategies that require fewer…
  • Near-optimal ground state preparation
    Quantum 4, 372 (2020). https://doi.org/10.22331/q-2020-12-14-372 Preparing the ground state of a given Hamiltonian and estimating its ground energy are important but computationally hard tasks. However, given some additional information, these problems can be solved efficiently on a quantum computer. We assume that an initial state with non-trivial overlap with the ground state can be efficiently…
  • The Prime state and its quantum relatives
    Quantum 4, 371 (2020). https://doi.org/10.22331/q-2020-12-11-371 The Prime state of $n$ qubits, ${|mathbb{P}_n{rangle}}$, is defined as the uniform superposition of all the computational-basis states corresponding to prime numbers smaller than $2^n$. This state encodes, quantum mechanically, arithmetic properties of the primes. We first show that the Quantum Fourier Transform of the Prime state provides a direct…
  • Un-Weyl-ing the Clifford Hierarchy
    Quantum 4, 370 (2020). https://doi.org/10.22331/q-2020-12-11-370 The teleportation model of quantum computation introduced by Gottesman and Chuang (1999) motivated the development of the Clifford hierarchy. Despite its intrinsic value for quantum computing, the widespread use of magic state distillation, which is closely related to this model, emphasizes the importance of comprehending the hierarchy. There is currently…
  • Synthesis of CNOT-Dihedral circuits with optimal number of two qubit gates
    Quantum 4, 369 (2020). https://doi.org/10.22331/q-2020-12-07-369 In this note we present explicit canonical forms for all the elements in the two-qubit CNOT-Dihedral group, with minimal numbers of controlled-$S$ ($CS$) and controlled-$X$ ($CX$) gates, using the generating set of quantum gates $[X, T, CX, CS]$. We provide an algorithm to successively construct the $n$-qubit CNOT-Dihedral group, asserting…
  • A review of Quantum Cellular Automata
    Quantum 4, 368 (2020). https://doi.org/10.22331/q-2020-11-30-368 Discretizing spacetime is often a natural step towards modelling physical systems. For quantum systems, if we also demand a strict bound on the speed of information propagation, we get quantum cellular automata (QCAs). These originally arose as an alternative paradigm for quantum computation, though more recently they have found application…
  • Quantum reference frames for general symmetry groups
    Quantum 4, 367 (2020). https://doi.org/10.22331/q-2020-11-30-367 A fully relational quantum theory necessarily requires an account of changes of quantum reference frames, where quantum reference frames are quantum systems relative to which other systems are described. By introducing a relational formalism which identifies coordinate systems with elements of a symmetry group $G$, we define a general operator…
  • Fast optimization of parametrized quantum optical circuits
    Quantum 4, 366 (2020). https://doi.org/10.22331/q-2020-11-30-366 Parametrized quantum optical circuits are a class of quantum circuits in which the carriers of quantum information are photons and the gates are optical transformations. Classically optimizing these circuits is challenging due to the infinite dimensionality of the photon number vector space that is associated to each optical mode. Truncating…
  • Experimental Comparison of Bohm-like Theories with Different Primary Ontologies
    Quantum 4, 365 (2020). https://doi.org/10.22331/q-2020-11-26-365 The de Broglie-Bohm theory is a hidden-variable interpretation of quantum mechanics which involves particles moving through space along deterministic trajectories. This theory singles out position as the primary ontological variable. Mathematically, it is possible to construct a similar theory where particles are moving through momentum-space, and momentum is singled out…
  • Operational, gauge-free quantum tomography
    Quantum 4, 364 (2020). https://doi.org/10.22331/q-2020-11-17-364 As increasingly impressive quantum information processors are realized in laboratories around the world, robust and reliable characterization of these devices is now more urgent than ever. These diagnostics can take many forms, but one of the most popular categories is $textit{tomography}$, where an underlying parameterized model is proposed for a…
  • Information and disturbance in operational probabilistic theories
    Quantum 4, 363 (2020). https://doi.org/10.22331/q-2020-11-16-363 Any measurement is intended to provide $information$ on a system, namely knowledge about its state. However, we learn from quantum theory that it is generally impossible to extract information without disturbing the state of the system or its correlations with other systems. In this paper we address the issue of…
  • A volumetric framework for quantum computer benchmarks
    Quantum 4, 362 (2020). https://doi.org/10.22331/q-2020-11-15-362 We propose a very large family of benchmarks for probing the performance of quantum computers. We call them $textit{volumetric benchmarks}$ (VBs) because they generalize IBM's benchmark for measuring quantum volume [1]. The quantum volume benchmark defines a family of $textit{square}$ circuits whose depth $d$ and width $w$ are the same.…
  • Optimal polynomial based quantum eigenstate filtering with application to solving quantum linear systems
    Quantum 4, 361 (2020). https://doi.org/10.22331/q-2020-11-11-361 We present a quantum eigenstate filtering algorithm based on quantum signal processing (QSP) and minimax polynomials. The algorithm allows us to efficiently prepare a target eigenstate of a given Hamiltonian, if we have access to an initial state with non-trivial overlap with the target eigenstate and have a reasonable lower…