146,758 research outputs found
Quantum Annealing and Analog Quantum Computation
We review here the recent success in quantum annealing, i.e., optimization of
the cost or energy functions of complex systems utilizing quantum fluctuations.
The concept is introduced in successive steps through the studies of mapping of
such computationally hard problems to the classical spin glass problems. The
quantum spin glass problems arise with the introduction of quantum
fluctuations, and the annealing behavior of the systems as these fluctuations
are reduced slowly to zero. This provides a general framework for realizing
analog quantum computation.Comment: 22 pages, 7 figs (color online); new References Added. Reviews of
Modern Physics (in press
Progress of analog-hybrid computation
Review of fast analog/hybrid computer systems, integrated operational amplifiers, electronic mode-control switches, digital attenuators, and packaging technique
The Phillips Machine, The Analogue Computing Traditoin in Economics and Computability
In this paper I try to argue for the desirability of analog computation in economics from a variety of perspectives, using the example of the Phillips Machine. Ultimately, a case is made for the underpinning of both analog and digital computing theory in constructive mathematics. Some conceptual confusion in the meaning of analog computing and its non-reliance on the theory of numerical analysis is also discussed. Digital computing has its mathematical foundations in (classical) recursion theory and constructive mathematics. The implicit, working, assumption of those who practice the noble art of analog computing may well be that the mathematical foundations of their subject is as sound as the foundations of the real analysis. That, in turn, implies a reliance on the soundness of set theory plus the axiom of choice. This is, surely, seriously disturbing from a computation point of view. Therefore, in this paper, I seek to locate a foundation for analog computing in exhibiting some tentative dualities with results that are analogous to those that are standard in computability theory. The main question, from the point of view of economics, is whether the Phillips Machine, as an analog computer, has universal computing properties. The conjectured answer is in the negative.Phillips Machine, Analogue Computation, Digital Computation, Computability, General Purpose Analogue Computer
High-threshold fault-tolerant quantum computation with analog quantum error correction
To implement fault-tolerant quantum computation with continuous variables,
the Gottesman-Kitaev-Preskill (GKP) qubit has been recognized as an important
technological element. However,it is still challenging to experimentally
generate the GKP qubit with the required squeezing level, 14.8 dB, of the
existing fault-tolerant quantum computation. To reduce this requirement, we
propose a high-threshold fault-tolerant quantum computation with GKP qubits
using topologically protected measurement-based quantum computation with the
surface code. By harnessing analog information contained in the GKP qubits, we
apply analog quantum error correction to the surface code.Furthermore, we
develop a method to prevent the squeezing level from decreasing during the
construction of the large scale cluster states for the topologically protected
measurement based quantum computation. We numerically show that the required
squeezing level can be relaxed to less than 10 dB, which is within the reach of
the current experimental technology. Hence, this work can considerably
alleviate this experimental requirement and take a step closer to the
realization of large scale quantum computation.Comment: 14 pages, 7 figure
Introduction to the Phillips Machine and the Analogue Computing Tradition in Economics
In this paper I try to argue for the desirability of analog computation in economics from a variety of perspectives, using the example of the Phillips Machine. Ultimately, a case is made for the underpinning of both analog and digital computing theory in constructive mathematics. Some conceptual confusion in the meaning of analog computing and its non-reliance on the theory of numerical analysis is also discussed.
The Cost of Emulating a Small Quantum Annealing Problem in the Circuit-Model
Demonstrations of quantum advantage for certain sampling problems has
generated considerable excitement for quantum computing and has further spurred
the development of circuit-model quantum computers, which represent quantum
programs as a sequence of quantum gates acting on a finite number of qubits.
Amongst this excitement, analog quantum computation has become less prominent,
with the expectation that circuit-model quantum computers will eventually be
sufficient for emulating analog quantum computation and thus rendering analog
quantum computation obsolete. In this work we explore the basic requirements
for emulating a specific analog quantum computation in the circuit model: the
preparation of a biased superposition of degenerate ground states of an Ising
Hamiltonian using an adiabatic evolution. We show that the overhead of
emulation is substantial even for this simple problem. This supports using
analog quantum computation for solving time-dependent Hamiltonian dynamics in
the short and mid-term, assuming analog errors can be made low enough and
coherence times long enough to solve problems of practical interest
Digital-Analog Quantum Computation
Digital quantum computing paradigm offers highly-desirable features such as
universality, scalability, and quantum error correction. However, physical
resource requirements to implement useful error-corrected quantum algorithms
are prohibitive in the current era of NISQ devices. As an alternative path to
performing universal quantum computation, within the NISQ era limitations, we
propose to merge digital single-qubit operations with analog multi-qubit
entangling blocks in an approach we call digital-analog quantum computing
(DAQC). Along these lines, although the techniques may be extended to any
resource, we propose to use unitaries generated by the ubiquitous Ising
Hamiltonian for the analog entangling block and we prove its universal
character. We construct explicit DAQC protocols for efficient simulations of
arbitrary inhomogeneous Ising, two-body, and -body spin Hamiltonian dynamics
by means of single-qubit gates and a fixed homogeneous Ising Hamiltonian.
Additionally, we compare a sequential approach where the interactions are
switched on and off (stepwise~DAQC) with an always-on multi-qubit interaction
interspersed by fast single-qubit pulses (banged DAQC). Finally, we perform
numerical tests comparing purely digital schemes with DAQC protocols, showing a
remarkably better performance of the latter. The proposed DAQC approach
combines the robustness of analog quantum computing with the flexibility of
digital methods
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