We show that the usefulness of the thermal state of a specific spin-lattice model for measurement-based quantum computing exhibits a transition between two distinct "phases" - one in which every state is a universal resource for quantum computation, and another in which any local measurement sequence can be simulated efficiently on a classical computer. Remarkably, this transition in computational power does not coincide with any phase transition, classical or quantum, in the underlying spin-lattice model.
Non-degenerate wavelength computational ghost imaging with thermal light source is studied theoretically and experimentally. The acquired computational ghost images are of high quality when the wavelength of computed light is different from the light detected by bucket detector. Compared to the necessary light of short wavelength in previous ghost imaging, the use of longer wavelength light is demonstrated to bring about ghost images with higher spatial resolution, in strong atmospheric turbulence.
When a quantum field is in contact with a thermal bath, the vacuum state of the field may be generalized to a thermal vacuum state, which takes into account the thermal noise. In thermo field dynamics, this is realized by doubling the dimensionality of the Fock space of the system. Interestingly, the representation of thermal noise by means of an augmented space is also found in a distinctly different approach based on the Wigner transform of both the field operators and density matrix, which we pursue here. Specifically, the thermal noise is introduced by augmenting the classical-like Wigner …
Measurement-based quantum computation utilizes an initial entangled resource state and proceeds with subsequent single-qubit measurements. It is implicitly assumed that the interactions between qubits can be switched off so that the dynamics of the measured qubits do not affect the computation. By proposing a model spin Hamiltonian, we demonstrate that measurement-based quantum computation can be achieved on a thermal state with always-on interactions. Moreover, computational errors induced by thermal fluctuations can be corrected and thus the computation can be executed fault-tolerantly if th…
'Tis said, to know others is to be learned, to know oneself, wise - I demonstrate that it could be more fundamental than knowing the rest of nature, by applying classical computational principles and engineering hindsight to derive and explain quantum entanglement, state space formalism and the statistical nature of quantum mechanics. I show that an entangled photon pair is literally no more than a 1-bit hologram, that the quantum state formalism is completely derivable from general considerations of representation of physical information, and that both the probabilistic aspects of quantum the…
The success of adiabatic quantum computation (AQC) depends crucially on the ability to maintain the quantum computer in the ground state of the evolution Hamiltonian. The computation process has to be sufficiently slow as restricted by the minimal energy gap. However, at finite temperatures, it might need to be fast enough to avoid thermal excitations. The question is, how fast does it need to be? The structure of evolution Hamiltonians for AQC is generally too complicated for answering this question. Here we model an adiabatic quantum computer as a (parametrically driven) harmonic oscillator.…
We propose an implementation of quantum logic gates via virtual vibrational excitations in an ion trap quantum computer. Transition paths involving unpopulated, vibrational states interfere destructively to eliminate the dependence of rates and revolution frequencies on vibrational quantum numbers. As a consequence quantum computation becomes feasible with ions whos vibrations are strongly coupled to a thermal reservoir.
We show an equivalence relation between fault-tolerant circuits for a stabilizer code and fault-tolerant adiabatic processes for holonomic quantum computation (HQC), in the case where quantum information is encoded in the degenerated ground space of the system Hamiltonian. By this equivalence, we can systematically construct a fault-tolerant HQC scheme, which can geometrically implement a universal set of encoded quantum gates by adiabatically deforming the system Hamiltonian. During this process, quantum information is protected from low weight thermal excitations by an energy gap that does n…
We show that free-space diffraction of photons distributes highly useful entanglement: the receivers of the propagated modes can do a distributed quantum computation using only linear optics and photon counting. The distributed computation requires classical communication between receivers, however, similar to standard measurement-based computation, that communication is of purely random outcomes and so can be indistinguishable from noise. The speculation in the title arises from the further observation that the natural way for a circumspect civilization to hide their photonic entanglement dis…
With bichromatic fields it is possible to deterministically produce entangled states of trapped ions. In this paper we present a unified analysis of this process for both weak and strong fields, for slow and fast gates. Simple expressions for the fidelity of creating maximally entangled states of two or an arbitrary number of ions under non-ideal conditions are derived and discussed.
We present a method of using a nuclear magnetic resonance computer to solve the Deutsch-Jozsa problem in which: (1) the number of molecules in the NMR sample is irrelevant to the number of qubits available to an NMR quantum computer, and (2) the initial state is chosen to be the state of thermal equilibrium, thereby avoiding the preparation of pseudopure states and the resulting exponential loss of signal as the number of qubits increases. The algorithm is described along with its experimental implementation using four active qubits. As expected, measured spectra demonstrate a clear distinctio…
Autonomous Quantum Processing Unit: An Autonomous Thermal Computing Machine & its Physical Limitations
Atominstitut, TU Wien（维也纳工业大学原子研究所）；Vienna Center for Quantum Science and Technology, TU Wien（维也纳量子科学与技术中心）；Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences（奥地利科学院量子光学与量子信息研究所）
Model-independent semantic requirements for user specification and interpretation of data before and after quantum computations are characterized. Classical computational costs of assigning classical data values to quantum registers and to run-time parameters passed across a classical-to-quantum application programming interface are derived. It is shown that the classical computational costs of data definition equal or exceed the classical computational cost of solving the problem of interest for all applications of quantum computing except computations defined over the integers and the simula…
We investigate relations between computational power and correlation in resource states for quantum computational tensor network, which is a general framework for measurement-based quantum computation. We find that if the size of resource states is finite, not all resource states allow correct projective measurements in the correlation space, which is related to non-vanishing two-point correlations in the resource states. On the other hand, for infinite-size resource states, we can always implement correct projective measurements if the resource state can simulate arbitrary single-qubit rotati…
In this white paper, we describe characteristics of tools for classical simulations of quantum computational devices appropriate for High Energy Physics applications.
Unlike the standard Quantum Computational Logic (QCL), where the carrier of information (target) is conventionally assumed to be only the last qubit over a sequence of many qubits, here we propose an extended version of the QCL (we call Multi Target Quantum Computational Logic, briefly MTQCL) where the number and the position of the target qubits are arbitrary.
We study the effect of a thermal environment on adiabatic quantum computation using the Bloch-Redfield formalism. We show that in certain cases the environment can enhance the performance in two different ways: (i) by introducing a time scale for thermal mixing near the anticrossing that is smaller than the adiabatic time scale, and (ii) by relaxation after the anticrossing. The former can enhance the scaling of computation when the environment is superohmic, while the latter can only provide a prefactor enhancement. We apply our method to the case of adiabatic Grover search and show that perf…
We consider measurement-based quantum computation (MBQC) on thermal states of the interacting cluster Hamiltonian containing interactions between the cluster stabilizers that undergoes thermal phase transitions. We show that the long-range order of the symmetry breaking thermal states below a critical temperature drastically enhance the robustness of MBQC against thermal excitations. Specifically, we show the enhancement in two-dimensional cases and prove that MBQC is topologically protected below the critical temperature in three-dimensional cases. The interacting cluster Hamiltonian allows u…
We review the physical foundations of Landauer's Principle, which relates the loss of information from a computational process to an increase in thermodynamic entropy. Despite the long history of the Principle, its fundamental rationale and proper interpretation remain frequently misunderstood. Contrary to some misinterpretations of the Principle, the mere transfer of entropy between computational and non-computational subsystems can occur in a thermodynamically reversible way without increasing total entropy. However, Landauer's Principle is not about general entropy transfers; rather, it mor…
Recently, Li {\it et al.} [Phys. Rev. Lett. {\bf 107}, 060501 (2011)] have demonstrated that topologically protected measurement-based quantum computation can be implemented on the thermal state of a nearest-neighbor two-body Hamiltonian with spin-2 and spin-3/2 particles provided that the temperature is smaller than a critical value, namely, threshold temperature. Here we show that the thermal state of a nearest-neighbor two-body Hamiltonian, which consists of only spin-3/2 particles, allows us to perform topologically protected measurement-based quantum computation. The threshold temperature…
We illustrate the application of Quantum Computing techniques to the investigation of the thermodynamical properties of a simple system, made up of three quantum spins with frustrated pair interactions and affected by a hard sign problem when treated within classical computational schemes. We show how quantum algorithms completely solve the problem, and discuss how this can apply to more complex systems of physical interest, with emphasis on the possible systematics and on their control.
A new quantum algorithm for a search problem and its computational complexity are discussed. It is shown in the search problem containing 2^n objects that our algorithm runs in polynomial time.
Freie Universität Berlin（柏林自由大学）；Helmholtz-Zentrum Berlin für Materialien und Energie（亥姆霍兹柏林材料与能源中心）；Fraunhofer Heinrich Hertz Institute（弗劳恩霍夫海因里希赫兹研究所）
