How Much of One-Way Computation Is Just Thermodynamics (original) (raw)
Related papers
Experimental one-way quantum computing
Nature, 2005
Standard quantum computation is based on sequences of unitary quantum logic gates which process qubits. The one-way quantum computer proposed by Raussendorf and Briegel is entirely different. It has changed our understanding of the requirements for quantum computation and more generally how we think about quantum physics. This new model requires qubits to be initialized in a
Measurement-based quantum computation beyond the one-way model
2007
We introduce novel schemes for quantum computing based on local measurements on entangled resource states. This work elaborates on the framework established in [Phys. Rev. Lett. 98, 220503 (2007), quant-ph/0609149]. Our method makes use of tools from many-body physics -matrix product states, finitely correlated states or projected entangled pairs states -to show how measurements on entangled states can be viewed as processing quantum information. This work hence constitutes an instance where a quantum information problem -how to realize quantum computation -was approached using tools from many-body theory and not vice versa. We give a more detailed description of the setting, and present a large number of new examples. We find novel computational schemes, which differ from the original one-way computer for example in the way the randomness of measurement outcomes is handled. Also, schemes are presented where the logical qubits are no longer strictly localized on the resource state. Notably, we find a great flexibility in the properties of the universal resource states: They may for example exhibit non-vanishing long-range correlation functions or be locally arbitrarily close to a pure state. We discuss variants of Kitaev's toric code states as universal resources, and contrast this with situations where they can be efficiently classically simulated. This framework opens up a way of thinking of tailoring resource states to specific physical systems, such as cold atoms in optical lattices or linear optical systems.
Noisy one-way quantum computations: The role of correlations
Physical Review A, 2011
We show that neither entanglement nor quantum discord can be regarded as fundamental resources for noisy quantum computation. A scheme to evaluate computation fidelities within the one-way model is developed, and promptly applied to unveil that the Deutsch-Jozsa algorithm requires no entanglement.
Fundamentals of universality in one-way quantum computation
New Journal of Physics, 2007
In this article, we build a framework allowing for a systematic investigation of the fundamental issue: "Which quantum states serve as universal resources for measurement-based (one-way) quantum computation?" We start our study by reexamining what is exactly meant by "universality" in quantum computation, and what the implications are for universal one-way quantum computation. Given the framework of a measurement-based quantum computer, where quantum information is processed by local operations only, we find that the most general universal one-way quantum computer is one which is capable of accepting arbitrary classical inputs and producing arbitrary quantum outputs-we refer to this property as CQ-universality. We then show that a systematic study of CQ-universality in one-way quantum computation is possible by identifying entanglement features that are required to be present in every universal resource. In particular, we find that a large class of entanglement measures must reach its supremum on every universal resource. These insights are used to identify several families of states as being not universal, such as 1D cluster states, GHZ states, W states, and ground states of non-critical 1D spin systems. Our criteria are strengthened by considering the efficiency of a quantum computation, and we find that entanglement measures must obey a certain scaling law with the system size for all efficient universal resources. This again leads to examples of non-universal resources, such as, e.g., ground states of critical 1D spin systems. On the other hand, we provide several examples of efficient universal resources, namely graph states corresponding to hexagonal, triangular and Kagome lattices. Finally, we consider the more general notion of encoded CQ-universality, where quantum outputs are allowed to be produced in an encoded form. Again we provide entanglement-based criteria for encoded universality. Moreover, we present a general procedure to construct encoded universal resources.
An economical route to one-way quantum computation
We assess the effects of an intrinsic model for imperfections in cluster states by introducing noisy cluster states and characterizing their role in the one-way model for quantum computation. The action of individual dephasing channels on cluster qubits is also studied. We show that the effect of non-idealities is limited by using small clusters, which requires compact schemes for computation. In light of this, we address an experimentally realizable four-qubit linear cluster which simulates a controlled-NOT (CNOT).
Experimental characterization of universal one-way quantum computing
We report the characterization of a universal set of logic gates for one-way quantum computing using a four-photon 'star' cluster state generated by fusing photons from two independent photonic crystal fibre sources. We obtain a fidelity for the cluster state of 0.66 ± 0.01 with respect to the ideal case. We perform quantum process tomography to completely characterize a controlled-NOT, Hadamard and T gate all on the same compact entangled resource. Together, these operations make up a universal set of gates such that arbitrary quantum logic can be efficiently constructed from combinations of them. We find process fidelities with respect to the ideal cases of 0.64 ± 0.01 for the CNOT, 0.67 ± 0.03 for the Hadamard and 0.76 ± 0.04 for the T gate. 2 and algorithms. As a basic example, we simulate a Swap gate consisting of three concatenated CNOT gates. Our work provides some pragmatic insights into the prospects for building up to a fully scalable and fault-tolerant one-way quantum computer with photons in realistic conditions.
Quantum Foundations of Classical Reversible Computing
2021
The reversible computation paradigm aims to provide a new foundation for general classical digital computing that is capable of circumventing the thermodynamic limits to the energy efficiency of the conventional, non-reversible paradigm. However, to date, the essential rationale for and analysis of classical reversible computing (RC) has not yet been expressed in terms that leverage the modern formal methods of non-equilibrium quantum thermodynamics (NEQT). In this paper, we begin developing an NEQT-based foundation for the physics of reversible computing. We use the framework of Gorini-Kossakowski-Sudarshan-Lindblad dynamics (a.k.a. Lindbladians) with multiple asymptotic states, incorporating recent results from resource theory, full counting statistics, and stochastic thermodynamics. Important conclusions include that, as expected: (1) Landauer's Principle indeed sets a strict lower bound on entropy generation in traditional non-reversible architectures for deterministic compu...
Computational model underlying the one-way quantum computer
Quantum Information and Computation, 2002
In this paper we present the computational model underlying the one-way quantum computer which we introduced recently [Phys. Rev. Lett. {\bf{86}}, 5188 (2001)]. The one-way quantum computer has the property that any quantum logic network can be simulated on it. Conversely, not all ways of quantum information processing that are possible with the one-way quantum computer can be understood properly in network model terms. We show that the logical depth is, for certain algorithms, lower than has so far been known for networks. For example, every quantum circuit in the Clifford group can be performed on the one-way quantum computer in a single step.
Adiabatic quantum computation and quantum phase transitions
Physical Review A, 2004
We analyze the ground state entanglement in a quantum adiabatic evolution algorithm designed to solve the NP-complete Exact Cover problem. The entropy of entanglement seems to obey linear and universal scaling at the point where the energy gap becomes small, suggesting that the system passes near a quantum phase transition. Such a large scaling of entanglement suggests that the effective connectivity of the system diverges as the number of qubits goes to infinity and that this algorithm cannot be efficiently simulated by classical means. On the other hand, entanglement in Grover's algorithm is bounded by a constant. PACS numbers: 03.67.-a, 03.65.Ud, 03.67.Hk
2000
Standard quantum computation is based on sequences of unitary quantum logic gates that process qubits. The one-way quantum computer proposed by Raussendorf and Briegel is entirely different. It has changed our understanding of the requirements for quantumcomputationandmoregenerallyhowwethinkaboutquantumphysics.This newmodelrequires qubitstobeinitializedin a highly entangled cluster state. From this point, the quantum computation proceeds by a sequence of single-qubit measurements with classical feedforward