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arXiv:2011.07195 · Physical Review A

Counterfactual universal quantum computation

Zhu Cao

Published Nov 13, 2020• 12 citations
arXivHTMLPDF

Abstract

Universal quantum computation is usually associated with interaction among two-level quantum subsystems, as this interaction is commonly viewed as a necessity to achieve universal quantum computation. In this work we show that, contrary to this intuition, universal quantum computation can be achieved without interaction among initially independent two-level quantum subsystems. We call it counterfactual universal quantum computation. As special cases, we show how to achieve counterfactual communication of quantum states, counterfactual quantum swapping, and counterfactual quantum erasure codes. To ease practical implementation, we analyze counterfactual universal quantum computation with realistic devices, including the effects of finite execution time, photon loss, and atom missing. Besides the theoretical interest of illustrating the mysterious and counterintuitive nature of quantum physics, our work has practical applications to color imaging of ancient arts, upon which light is forbidden to shine.

DOI
10.1103/physreva.102.052413

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Universal quantum computation is usually associated with interaction among two-level quantum subsystems, as this interaction is commonly viewed as a necessity to achieve universal quantum computation. In this work we show that, contrary to this intuition, universal quantum computation can be achieved without interaction among initially independent two-level quantum subsystems. We call it counterfactual universal quantum computation. As special cases, we show how to achieve counterfactual communication of quantum states, counterfactual quantum swapping, and counterfactual quantum erasure codes. To ease practical implementation, we analyze counterfactual universal quantum computation with realistic devices, including the effects of finite execution time, photon loss, and atom missing. Besides the theoretical interest of illustrating the mysterious and counterintuitive nature of quantum physics, our work has practical applications to color imaging of ancient arts, upon which light is forbidden to shine.
Universal quantum computation on decoherence-free subspaces and subsystems (DFSs) is examined with particular emphasis on using only physically relevant interactions. A necessary and sufficient condition for the existence of decoherence-free (noiseless) subsystems in the Markovian regime is derived here for the first time. A stabilizer formalism for DFSs is then developed which allows for the explicit understanding of these in their dual role as quantum error correcting codes. Conditions for the existence of Hamiltonians whose induced evolution always preserves a DFS are derived within this stabilizer formalism. Two possible collective decoherence mechanisms arising from permutation symmetries of the system-bath coupling are examined within this framework. It is shown that in both cases universal quantum computation which always preserves the DFS (natural fault-tolerant computation) can be performed using only two-body interactions. This is in marked contrast to standard error correcting codes, where all known constructions using one- or two-body interactions must leave the code space during the on-time of the fault-tolerant gates. A further consequence of our universality construction is that a single exchange Hamiltonian can be used to perform universal quantum computation on an encoded space whose asymptotic coding efficiency is unity. The exchange Hamiltonian, which is naturally present in many quantum systems, is thus asymptotically universal.
A quantum computer is similar to an ordinary computer, except that instead of bits it uses two-level quantum systems (qubits), and the usual logical operations on bits are replaced with noiseless quantum dynamics in the form of unitary gates or Hamiltonian interactions. Many sets of resources that are universal for quantum computation (that is, capable of implementing any quantum computation) have been found, but general conditions for universality are still only partially understood. Improving our understanding of these conditions contributes to two broad goals. On the one hand, understanding what class of physical systems is suitable for quantum computation allows us choose the systems that are most easily controlled or built in the laboratory. On the other hand, identifying the unifying characteristics of such a class provides insight into the fundamental physics responsible for the much greater computational power of quantum computers.        The original results presented in this thesis are a contribution to our understanding of the physical requirements for universal quantum computation. These results lead to the identification of a new, large class of universal dynamics. More specifically, the main problem that is addressed is the following: consider a physical system that is made up of a finite number of qubits that are subject to a natural, fixed interaction described by a two-body Hamiltonian. Suppose we have the ability to control the system only by applying fast one-qubit operations. Under what conditions is this system capable of universal quantum computation? The first original result of the thesis is to prove that universal quantum computation is possible under these conditions given the single extra constraint that the Hamiltonian must entangle, or connect, all of the qubits. In other words, since a two-body Hamiltonian is expressible as a sum of coupling terms each of which acts nontrivially on a pair of qubits, consider the graph whose vertices correspond to qubits and whose edges connect qubits that are coupled by a term in the Hamiltonian. Then this Hamiltonian, together with fast one-qubit unitaries, is universal for quantum computation precisely when the corresponding graph is connected.       This result suggests many potential generalizations, three of which are explored in this thesis. The first generalization is to show that the same result holds for a two-body Hamiltonian that acts on D-dimensional quantum systems (qudits), given fast one-qudit unitaries. A second extension is to the case of a many-body Hamiltonian, that is, a Hamiltonian that has coupling terms that act on more than two qubits. Again, we find that under mild restrictions, such Hamiltonians are universal provided they are connected and that arbitrary one-qubit unitaries are available. We also discover and explore some surprising structure in many-body Hamiltonians that is associated with the parity of the couplings. A third related problem that is addressed is the question of what two-qubit unitaries are universal for quantum computation. This problem was originally solved by J.-L. and R. Brylinski [BB02], who gave a technical proof of the universality of any two-qudit gate that is not the swap gate or a product of one-qudit unitaries, given one-qudit unitaries as a free resource. We develop an elementary and constructive proof for the case of qubits, and prove that our construction is very close to optimal in the number of uses of the two-qubit gate.       Given a qualitative understanding of what dynamical resources are universal for quantum computation, it is natural to consider developing a quantitative measure of the usefulness of quantum dynamics for quantum information processing. This is done in the final chapter of the thesis, in which the beginnings of a quantitative theory of quantum dynamics are developed.
While theoretical ideas from quantum information science have long provided a foundation for understanding communication protocols and thermalization in many-body systems, the advent of near-term quantum devices offers the prospect of application and experimental study. In this thesis, we explore their interplay. The postulates of quantum mechanics generalize classical probability distributions and thus transmission of information, enabling fundamentally novel protocols for communication and cryptography. These algorithms motivate the deployment of quantum networks, a distributed model of computation where universality and fault-tolerance are often not required. We revisit the application of astronomical interferometry and provide a practical scheme based on distributed source coding, enabling powerful telescopes. Based on constructions from communication complexity, we design a voting scheme with efficient scaling of quantum communication and computation, and prove its security. The spread of quantum correlations, besides underlying the performance of many communication protocols, characterizes the process of objects away from equilibrium attaining a uniform state. Evolution is natural, requiring little control and easing study by quantum simulators. We analyze traversable wormholes, initially motivated by gauge-gravity duality, from this perspective. The effect of a gravitational scrambling mechanism is distinguished from generic mixing. Nonetheless, transfer of information is still found in common many-body systems, such as interacting spins. The two themes above are accompanied by proposals for physical realization in atomic and optical platforms. Communication protocols are carried out by photons transmitting quantum information and cavities mediating processing by atomic qubits. Thermalization is studied in strongly interacting systems of Rydberg atoms controlled by electromagnetic fields. These platforms represent the current generation of quantum computers, and so we probe its capabilities.
Quantum computing tries to exploit entanglement and interference to process information more efficiently than the best known classical solutions. Experiments demonstrating the feasibility of this approach have already been performed. However, finding a really scalable and robust quantum computing architecture remains a challenge for both, experimentalists and theoreticians. In most setups decoherence becomes non-negligible when one tries to perform entangling gate operations using the coherent control of qubit-qubit interactions. However, in this proceedings we show that two-qubit gate operations can be implemented even without qubit-qubit interactions and review a recent quantum computing scheme by Lim et al. [Phys. Rev. Lett. 95, 030505 (2005)] using only single photon sources (e.g. atom-cavity systems, NV colour centres or quantum dots) and photon pair measurements.
Integrating the full-duplex capability with quantum communication potentially equips emerging wireless networks with a quantum layer of security for the stringent communication efficiency and security requirements. This paper proposes two new full-duplex quantum communication protocols to exchange classical or quantum information between two remote parties simultaneously without transferring a physical particle over the quantum channel. The first protocol, called quantum duplex coding, enables the exchange of a classical bit using a preshared maximally entangled pair of qubits by means of counterfactual disentanglement. The second protocol, called quantum telexchanging, enables the exchange of an arbitrary unknown qubit without using preshared entanglement by means of counterfactual entanglement and disentanglement. We demonstrate that quantum duplex coding and quantum telexchanging can be achieved by exploiting counterfactual electron-photon interaction gates. It is shown that these tasks can be viewed as full-duplex transmission of bits and qubits via binary erasure channels and quantum erasure channels, respectively.
Symmetry-protected topological phases have attracted significant interest at the fundamental level and as a potential platform for quantum information processing, owing to their protected edge states and resilience to perturbations. Applying these features for practical and efficient quantum computation is highly desirable, but remains an open challenge. Here, we demonstrate the partitioning into multiple independent Haldane phase subsystems of a single spin-1/2 ladder system and propose this as a scalable architecture for gate-based quantum computation, which takes advantage of the symmetry-protected topological order. We encode qubits in the two topological states of the Sz=0S^{z}=0Sz=0 sector of each subsystem. Finite-size effects, typically viewed as detrimental, instead provide a controllable energy splitting that enables single-qubit rotations using only local magnetic fields. An Ising-type interaction between neighboring subsystem edges generates entangling gates, enabling universal quantum computation driven by two control parameters that are easily accessible experimentally. Our results demonstrate how symmetry-protected topological phases can be directly harnessed for circuit-model quantum computation in realistic systems.