Deterministic Quantum Computation Research Articles

Deterministic quantum computation with one photonic qubit

We show that deterministic quantum computing with one qubit (DQC1) can be experimentally implemented with a spatial light modulator, using the polarization and the transverse spatial degrees of freedom of light. The scheme allows the computation of the trace of a high dimension matrix, being limited by the resolution of the modulator panel, and the technical imperfections. In order to illustrate the method, we compute the normalized trace of unitary matrices, and implement the Deutsch-Jozsa algorithm. The largest matrix that can be manipulated with our set-up is 1080$\times$1920, which is able to represent a system with approximately 21 qubits.

Quantum dissonance and deterministic quantum computation with a single qubit

Mixed state quantum computation can perform certain tasks which are believed to be efficiently intractable on a classical computer. For a specific model of mixed state quantum computation, namely, deterministic quantum computation with a single qubit (DQC1), recent investigations suggest that quantum correlations other than entanglement might be responsible for the power of DQC1 model. However, strictly speaking, the role of entanglement in this model of computation was not entirely clear. We provide conclusive evidence that there are instances where quantum entanglement is not present in any part of this model, nevertheless we have advantage over classical computation. This establishes the fact that quantum dissonance (a kind of quantum correlations) present in fully separable (FS) states provide power to DQC1 model.

Catching Time-Reversed Microwave Coherent State Photons with 99.4% Absorption Efficiency

We demonstrate a high efficiency deterministic quantum receiver to convert flying qubits to logic qubits. We employ a superconducting resonator, which is driven with a shaped pulse through an adjustable coupler. For the ideal "time reversed" shape, we measure absorption and receiver fidelities at the single microwave photon level of, respectively, 99.41% and 97.4%. These fidelities are comparable with gates and measurement and exceed the deterministic quantum communication and computation fault tolerant thresholds.

A cold-atoms based processor for deterministic quantum computation with one qubit in intractably large Hilbert spaces

We propose the use of Rydberg interactions and ensembles of cold atoms in mixed state for the implementation of a protocol for deterministic quantum computation with one quantum bit that can be readily operated in high dimensional Hilbert spaces. We propose an experimental test for the scalability of the protocol and to study the physics of discord. Furthermore, we explore the possibility of extending to non-trivial unitaries, such as those associated to many-body physics. Finally develop a scheme to add control to cold atom unitaries in order to facilitate their implementation in our proposal.

Hardness of classically simulating the one-clean-qubit model.

Deterministic quantum computation with one quantum bit (DQC1) [E. Knill and R. Laflamme, Phys. Rev. Lett. 81, 5672 (1998)] is a model of quantum computing where the input is restricted to containing a single qubit in a pure state and has all other qubits in a completely mixed state. Only the single pure qubit is measured at the end of the computation. While it is known that DQC1 can efficiently solve several problems for which no known classical efficient algorithms exist, the question of whether DQC1 is really more powerful than classical computation remains open. In this Letter, we introduce a slightly modified version of DQC1, which we call DQC1(k), where k output qubits are measured, and show that DQC1(k) cannot be classically efficiently simulated for any k≥3 unless the polynomial hierarchy collapses at the third level.

Scheme for measurement-based quantum computation on projected entangled-pair states

Recently it has been shown that projected entangled-pair states can be considered as a (physically motivated) resource state for measurement-based quantum computation. Here we elaborate on how to construct a deterministic measurement-based quantum computation model on projected entangled-pair states. In particular, we use this scheme to build a 4-level many-body model for universal quantum computation on qubits. We also derive a 3-local parent Hamiltonian for this model, whose ground state is non-degenerate.

Compact quantum gates on electron-spin qubits assisted by diamond nitrogen-vacancy centers inside cavities

Constructing compact quantum circuits for universal quantum gates on solid-state systems is crucial for quantum computing. We present some compact quantum circuits for a deterministic solid-state quantum computing, including the cnot, Toffoli, and Fredkin gates on the diamond NV centers confined inside cavities, achieved by some input-output processes of a single photon. Our quantum circuits for these universal quantum gates are simple and economic. Moreover, additional electron qubits are not employed, but only a single-photon medium. These gates have a long coherent time. We discuss the feasibility of these universal solid-state quantum gates, concluding that they are feasible with current technology.

Entangling power in deterministic quantum computation with one qubit

The deterministic quantum computing with one qubit (DQC1) is a mixed-state quantum computation algorithm that evaluates the normalized trace of a unitary matrix and is more powerful than the classical counterpart. We find that the normalized trace of the unitary matrix can be directly described by the entangling power of the quantum circuit of the DQC1, so the nontrivial DQC1 is always accompanied with the non-vanishing entangling power. In addition, it is shown that the entangling power also determines the intrinsic complexity of this quantum computation algorithm, i.e., the larger entangling power corresponds to higher complexity. Besides, it is also shown that the non-vanishing entangling power does always exist in other similar tasks of DQC1.

Quantum dissonance is rejected in an overlap measurement scheme

The overlap measurement scheme accomplishes to evaluate the overlap of two input quantum states by only measuring an introduced auxiliary qubit, irrespective of the complexity of the two input states. We find a counterintuitive phenomenon that no quantum dissonance can be found, even though the auxiliary qubit might be entangled, classically correlated or even uncorrelated with the two input states based on different types of input states. In principle, this provides an opposite but supplementary example to the remarkable algorithm of the deterministic quantum computation with one qubit in which no entanglement is present. Finally, we consider a simple overlap measurement model to demonstrate the continuous change (including potential sudden death of quantum discord) with the input states from entangled to product states by only adjusting some simple initial parameters.

Observable Measure of Bipartite Quantum Correlations

We introduce a measure Q of bipartite quantum correlations for arbitrary two-qubit states, expressed as a state-independent function of the density matrix elements. The amount of quantum correlations can be quantified experimentally by measuring the expectation value of a small set of observables on up to four copies of the state, without the need for a full tomography. We extend the measure to 2×d systems, providing its explicit form in terms of observables and applying it to the relevant class of multiqubit states employed in the deterministic quantum computation with one quantum bit model. The number of required measurements to determine Q in our scheme does not increase with d. Our results provide an experimentally friendly framework to estimate quantitatively the degree of general quantum correlations in composite systems.

Quantum computational capability of a 2D valence bond solid phase

Quantum phases of naturally-occurring systems exhibit distinctive collective phenomena as manifestation of their many-body correlations, in contrast to our persistent technological challenge to engineer at will such strong correlations artificially. Here we show theoretically that quantum correlations exhibited in the 2D valence bond solid phase of a quantum antiferromagnet, modeled by Affleck, Kennedy, Lieb, and Tasaki (AKLT) as a precursor of spin liquids and topological orders, are sufficiently complex yet structured enough to simulate universal quantum computation when every single spin can be measured individually. This unveils that an intrinsic complexity of naturally-occurring 2D quantum systems—which has been a long-standing challenge for traditional computers—could be tamed as a computationally valuable resource, even if we are limited not to create newly entanglement during computation. Our constructive protocol leverages a novel way to herald the correlations suitable for deterministic quantum computation through a random sampling, and may be extensible to other ground states of various 2D valence bond phases beyond the AKLT state.

Necessary and Sufficient Condition for Nonzero Quantum Discord

Quantum discord characterizes "nonclassicality" of correlations in quantum mechanics. It has been proposed as the key resource present in certain quantum communication tasks and quantum computational models without containing much entanglement. We obtain a necessary and sufficient condition for the existence of nonzero quantum discord for any dimensional bipartite states. This condition is easily experimentally implementable. Based on this, we propose a geometrical way of quantifying quantum discord. For two qubits this results in a closed form of expression for discord. We apply our results to the model of deterministic quantum computation with one qubit, showing that quantum discord is unlikely to be the reason behind its speedup.

Deterministic photon-photonSWAPgate using aΛsystem

We theoretically present a method to realize a deterministic photon-photon (SWAP)^{1/2} gate using a three-level lambda system interacting with single photons in reflection geometry. The lambda system is used completely passively as a temporary memory for a photonic qubit; the initial state of the lambda system may be arbitrary, and active control by auxiliary fields is unnecessary throughout the gate operations. These distinct merits make this entangling gate suitable for deterministic and scalable quantum computation.

Experimental demonstration of deterministic one-way quantum computation on a NMR quantum computer

One-way quantum computing is an important and novel approach to quantum computation. By exploiting the existing particle-particle interactions, we report an experimental realization of the complete process of deterministic one-way quantum Deutsch-Josza algorithm in NMR, including graph state preparation, single-qubit measurements, and feed-forward corrections. The findings in our experiment may shed light on the future scalable one-way quantum computation.

Experimental Approximation of the Jones Polynomial with One Quantum Bit

We present experimental results approximating the Jones polynomial using 4 qubits in a liquid state nuclear magnetic resonance quantum information processor. This is the first experimental implementation of a complete problem for the deterministic quantum computation with one quantum bit model of quantum computation, which uses a single qubit accompanied by a register of completely random states. The Jones polynomial is a knot invariant that is important not only to knot theory, but also to statistical mechanics and quantum field theory. The implemented algorithm is a modification of the algorithm developed by Shor and Jordan suitable for implementation in NMR. These experimental results show that for the restricted case of knots whose braid representations have four strands and exactly three crossings, identifying distinct knots is possible 91% of the time.

Correlations in local measurements on a quantum state, and complementarity as an explanation of nonclassicality

We consider the classical correlations that two observers can extract by measurements on a bipartite quantum state and we discuss how they are related to the quantum mutual information of the state. We show with several examples how complementarity gives rise to a gap between the quantum and the classical correlations and we relate our quantitative finding to the so-called classical correlation locked in a quantum state. We derive upper bounds for the sum of classical correlation obtained by measurements in different mutually unbiased bases and we show that the complementarity gap is also present in the deterministic quantum computation with one quantum bit.

Experimental Quantum Computing without Entanglement

Deterministic quantum computation with one pure qubit (DQC1) is an efficient model of computation that uses highly mixed states. Unlike pure-state models, its power is not derived from the generation of a large amount of entanglement. Instead it has been proposed that other nonclassical correlations are responsible for the computational speedup, and that these can be captured by the quantum discord. In this Letter we implement DQC1 in an all-optical architecture, and experimentally observe the generated correlations. We find no entanglement, but large amounts of quantum discord-except in three cases where an efficient classical simulation is always possible. Our results show that even fully separable, highly mixed, states can contain intrinsically quantum mechanical correlations and that these could offer a valuable resource for quantum information technologies.

Parameter estimation with mixed-state quantum computation

We present a quantum algorithm to estimate parameters at the quantum metrology limit using deterministic quantum computation with one bit. When the interactions occurring in a quantum system are described by a Hamiltonian $H=\ensuremath{\theta}{H}_{0}$, we estimate $\ensuremath{\theta}$ by zooming in on previous estimations and by implementing an adaptive Bayesian procedure. The final result of the algorithm is an updated estimation of $\ensuremath{\theta}$ whose variance has been decreased in proportion to the time of evolution under $H$. For the problem of estimating several parameters, we implement dynamical-decoupling techniques and use the results of single parameter estimation. The cases of discrete-time evolution and reference frame alignment are also studied within the adaptive approach.

Active One-Way Quantum Computation with Two-Photon Four-Qubit Cluster States

By using 2-photon 4-qubit cluster states we demonstrate deterministic one-way quantum computation in a single qubit rotation algorithm. In this operation feed-forward measurements are automatically implemented by properly choosing the measurement basis of the qubits, while Pauli error corrections are realized by using two fast driven Pockels cells. We realized also a C-NOT gate for equatorial qubits and a C-PHASE gate for a generic target qubit. Our results demonstrate that 2-photon cluster states can be used for rapid and efficient deterministic one-way quantum computing.

Quantum Discord and the Power of One Qubit

We use quantum discord to characterize the correlations present in the model called deterministic quantum computation with one quantum bit (DQC1), introduced by Knill and Laflamme [Phys. Rev. Lett. 81, 5672 (1998)10.1103/PhysRevLett.81.5672]. The model involves a collection of qubits in the completely mixed state coupled to a single control qubit that has nonzero purity. The initial state, operations, and measurements in the model all point to a natural bipartite split between the control qubit and the mixed ones. Although there is no entanglement between these two parts, we show that the quantum discord across this split is nonzero for typical instances of the DQC1 ciruit. Nonzero values of discord indicate the presence of nonclassical correlations. We propose quantum discord as figure of merit for characterizing the resources present in this computational model.