Deterministic Quantum Computation Research Articles

A distribution testing oracle separation between QMA and QCMA

It is a long-standing open question in quantum complexity theory whether the definition of non−deterministic quantum computation requires quantum witnesses (QMA) or if classical witnesses suffice (QCMA). We make progress on this question by constructing a randomized classical oracle separating the respective computational complexity classes. Previous separations \cite{ak-oracle}, \cite{fefferman-kimmel} required a quantum unitary oracle. The separating problem is deciding whether a distribution supported on regular un-directed graphs either consists of multiple connected components (yes instances) or consists of one expanding connected component (no instances) where the graph is given in an adjacency-list format by the oracle. Therefore, the oracle is a distribution over n-bit boolean functions.

Deterministic quantum computation with one-clean-qubit model as an open quantum system

Deterministic quantum computation with one-clean-qubit model as an open quantum system

Quantum Nondemolition Measurements with Optical Parametric Amplifiers for Ultrafast Universal Quantum Information Processing

Realization of a room-temperature ultrafast photon-number-resolving quantum nondemolition (QND) measurement would have significant implications for photonic quantum information processing, enabling, for example, deterministic quantum computation in discrete-variable architectures, but the requirement for strong coupling has hampered the development of scalable implementations. In this work, we propose and analyze a nonlinear-optical route to photon-number-resolving QND using quadratic (i.e., χ(2)) nonlinear interactions. We show that the coherent pump field driving a frequency-detuned optical parametric amplifier (OPA) experiences displacements conditioned on the number of signal Bogoliubov excitations. A measurement of the pump displacement thus provides a QND measurement of the signal Bogoliubov excitations, projecting the signal mode to a squeezed photon-number state. We then show how our nonlinear OPA dynamics can be utilized to deterministically generate Gottesman-Kitaev-Preskill states with only additional Gaussian resources, offering an all-optical route for fault-tolerant quantum information processing in continuous-variable systems. Finally, we place these QND schemes into a more traditional context by highlighting analogies between the frequency-detuned optical parametric oscillator and multilevel atom-cavity quantum electrodynamics systems by showing how continuous monitoring of the outcoupled pump quadrature induces conditional localization of the intracavity signal mode onto squeezed photon-number states. Our analysis suggests that our proposal may be viable in near-term χ(2) nonlinear nanophotonics, highlighting the rich potential of the OPA as a universal tool for ultrafast non-Gaussian quantum state engineering and quantum computation.Received 18 October 2022Accepted 8 March 2023DOI:https://doi.org/10.1103/PRXQuantum.4.010333Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasQuantum computationQuantum engineeringQuantum information processingQuantum information processing with continuous variablesQuantum opticsQuantum state engineeringSecond order nonlinear optical processesQuantum InformationAtomic, Molecular & Optical

Uncertainties and coherence in DQC1

Correlations have been identified as a necessary ingredient for the speedup of certain mixed-state quantum computation. In this work, we analyze the model of deterministic quantum computation with one bit (DQC1) and study its information-theoretic aspects involving state-channel interaction. This state-channel interaction provides a new perspective for investigating DQC1. More specifically, by calculating some important information-theoretic quantities related to the state-channel interaction, such as uncertainties, coherence of quantum states as measured with respect to channels, etc., we reveal some basic features of quantum resources for the quantum speedup in this model. Moreover, since the state-channel framework is general enough to encompass all computational models, the studies performed here can be similarly applied to analyze other computational models from the perspective of quantum resources.

Partition-function estimation: Quantum and quantum-inspired algorithms

We present two algorithms, one quantum and one classical, for estimating partition functions of quantum spin Hamiltonians. The former is a DQC1 (Deterministic quantum computation with one clean qubit) algorithm, and the first such for complex temperatures. The latter, for real temperatures, achieves performance comparable to a state-of-the-art DQC1 algorithm [Chowdhury et al. Phys. Rev. A 103, 032422 (2021)]. Both our algorithms take as input the Hamiltonian decomposed as a linear combination Pauli operators. We show this decomposition to be DQC1-hard for a given Hamiltonian, providing new insight into the hardness of estimating partition functions.

Temporal trapping: a route to strong coupling and deterministic optical quantum computation

The realization of deterministic photon–photon gates is a central goal in optical quantum computation and engineering. A longstanding challenge is that optical nonlinearities in scalable, room-temperature material platforms are too weak to achieve the required strong coupling, due to the critical loss-confinement trade-off in existing photonic structures. In this work, we introduce a spatio-temporal confinement method, dispersion-engineered temporal trapping, to circumvent the trade-off, enabling a route to all-optical strong coupling. Temporal confinement is imposed by an auxiliary trap pulse via cross-phase modulation, which, combined with the spatial confinement of a waveguide, creates a “flying cavity” that enhances the nonlinear interaction strength by at least an order of magnitude. Numerical simulations confirm that temporal trapping confines the multimode nonlinear dynamics to a single-mode subspace, enabling high-fidelity deterministic quantum gate operations. With realistic dispersion engineering and loss figures, we show that temporally trapped ultrashort pulses could achieve strong coupling on near-term nonlinear nanophotonic platforms. Our results highlight the potential of ultrafast nonlinear optics to become the first scalable, high-bandwidth, and room-temperature platform that achieves strong coupling, opening a path to quantum computing, simulation, and light sources.

Experimental investigation of quantum discord in DQC1

Quantum discord has been proposed as a resource responsible for the exponential speedup in deterministic quantum computation with one pure qubit (DQC1). Investigation of the quantum discord generated in DQC1 is of significant importance from a fundamental perspective. However, in practical applications of DQC1, qubits generally interact with the environment. Thus, it is also important to investigate the discord when DQC1 is implemented in a noisy environment. We implement DQC1 on an electron spin resonance (ESR) architecture in such an environment and nonzero quantum discord is observed. Furthermore, we find that the values of discord correspond to the values of purity <i>α</i> and quantum Fisher information, which reflect the power of the algorithm. Our results provide further evidence for the role of discord as a resource in DQC1 and are beneficial for understanding the origin of the power of quantum algorithms.

Deterministic photonic quantum computation in a synthetic time dimension

Photonics offers unique advantages as a substrate for quantum information processing, but imposes fundamental scalability challenges. Nondeterministic schemes impose massive resource overheads, while deterministic schemes require prohibitively many identical quantum emitters to realize sizeable quantum circuits. Here we propose a scalable architecture for a photonic quantum computer that needs minimal quantum resources to implement any quantum circuit: a single coherently controlled atom. Optical switches endow a photonic quantum state with a synthetic time dimension by modulating photon–atom couplings. Quantum operations applied to the atomic qubit can be teleported onto photonic qubits via projective measurement, and arbitrary quantum circuits can be compiled into a sequence of these teleported operators. This design negates the need for many identical quantum emitters to be integrated into a photonic circuit and allows effective all-to-all connectivity between photonic qubits. The proposed device has a machine size that is independent of quantum circuit depth, does not require single-photon detectors, operates deterministically, and is robust to experimental imperfections.

Promoting quantum correlations in deterministic quantum computation with a one-qubit model via postselection

The deterministic quantum computation with one qubit (DQC1) model is a restricted model of quantum computing able to calculate efficiently the normalized trace of a unitary matrix. In this work we analyse the quantum correlations named entanglement, Bell's nonlocality, quantum discord, and coherence generated by the DQC1 circuit considering only two qubits (auxiliary and control). For the standard DQC1 model only quantum discord and coherence appear. By introducing a filter in the circuit we purify the auxiliary qubit taking it out from the totally mixed state and consequently promoting other quantum correlations between the qubits, such as entanglement and Bell's nonlocality. Through the optimization of the purification process we conclude that even a small purification is enough to generate entanglement and Bell's nonlocality. We obtain, in average, that applying the purification process repeatedly by twelve times the auxiliary qubit becomes 99% pure. In this situation, almost maximally entangled states are achieved, which by its turn, almost maximally violate the Bell's inequality. This result suggests that with a simple modification the DQC1 model can be promoted to a universal model of quantum computing.

Measurement-Based Quantum Correlations for Quantum Information Processing

Measurement-based quantum correlations (MbQCs) depend on how strongly an observer perturbs the unobserved system. This distinctive property differentiates MbQCs from traditional quantum correlations such as entanglement and discord. We utilize MbQCs to elucidate quantum information processing capabilities in quantum computation and quantum state discrimination. We show that MbQCs exist more generally than entanglement and discord in optimal assisted quantum state discrimination and in a deterministic quantum computation with a single qubit. We also propose an MbQC-based dimension witness and analyze it in different noisy and noiseless scenarios.

Witnessing Quantum Resource Conversion within Deterministic Quantum Computation Using One Pure Superconducting Qubit.

Deterministic quantum computation with one qubit (DQC1) is iconic in highlighting that exponential quantum speedup may be achieved with negligible entanglement. Its discovery catalyzed a heated study of general quantum resources, and various conjectures regarding their role in DQC1's performance advantage. Coherence and discord are prominent candidates, respectively, characterizing nonclassicality within localized and correlated systems. Here we realize DQC1 within a superconducting system, engineered such that the dynamics of coherence and discord can be tracked throughout its execution. We experimentally confirm that DQC1 acts as a resource converter, consuming coherence to generate discord during its operation. Our results highlight superconducting circuits as a promising platform for both realizing DQC1 and related algorithms, and experimentally characterizing resource dynamics within quantum protocols.

Quantum computing with classical bits

A bit-quantum map relates probabilistic information for Ising spins or classical bits to quantum spins or qubits. Quantum systems are subsystems of classical statistical systems. The Ising spins can represent macroscopic two-level observables, and the quantum subsystem employs suitable expectation values and correlations. We discuss static memory materials based on Ising spins for which boundary information can be transported through the bulk in a generalized equilibrium state. They can realize quantum operations as the Hadamard or CNOT-gate for the quantum subsystem. Classical probabilistic systems can account for the entanglement of quantum spins. An arbitrary unitary evolution for an arbitrary number of quantum spins can be described by static memory materials for an infinite number of Ising spins which may, in turn, correspond to continuous variables or fields. We discuss discrete subsets of unitary operations realized by a finite number of Ising spins. They may be useful for new computational structures. We suggest that features of quantum computation or more general probabilistic computation may be realized by neural networks, neuromorphic computing or perhaps even the brain. This does neither require small isolated entities nor very low temperature. In these systems the processing of probabilistic information can be more general than for static memory materials. We propose a general formalism for probabilistic computing for which deterministic computing and quantum computing are special limiting cases.

Impossibility of Classically Simulating One-Clean-Qubit Model with Multiplicative Error.

The one-clean-qubit model (or the deterministic quantum computation with one quantum bit model) is a restricted model of quantum computing where all but a single input qubits are maximally mixed. It is known that the probability distribution of measurement results on three output qubits of the one-clean-qubit model cannot be classically efficiently sampled within a constant multiplicative error unless the polynomial-time hierarchy collapses to the third level [T. Morimae, K. Fujii, and J. F. Fitzsimons, Phys. Rev. Lett. 112, 130502 (2014)PRLTAO0031-900710.1103/PhysRevLett.112.130502]. It was open whether we can keep the no-go result while reducing the number of output qubits from three to one. Here, we solve the open problem affirmatively. We also show that the third-level collapse of the polynomial-time hierarchy can be strengthened to the second-level one. The strengthening of the collapse level from the third to the second also holds for other subuniversal models such as the instantaneous quantum polynomial model [M. Bremner, R. Jozsa, and D. J. Shepherd, Proc. R. Soc. A 467, 459 (2011)PRLAAZ1364-502110.1098/rspa.2010.0301] and the boson sampling model [S. Aaronson and A. Arkhipov, STOC 2011, p.333]. We additionally study the classical simulatability of the one-clean-qubit model with further restrictions on the circuit depth or the gate types.

Noise-tolerant parity learning with one quantum bit

Demonstrating quantum advantage with less powerful but more realistic devices is of great importance in modern quantum information science. Recently, a significant quantum speedup was achieved in the problem of learning a hidden parity function with noise. However, if all data qubits at the query output are completely depolarized, the algorithm fails. In this work, we present a quantum parity learning algorithm that exhibits quantum advantage as long as one qubit is provided with nonzero polarization in each query. In this scenario, the quantum parity learning naturally becomes deterministic quantum computation with one qubit. Then the hidden parity function can be revealed by performing a set of operations that can be interpreted as measuring nonlocal observables on the auxiliary result qubit having nonzero polarization and each data qubit. We also discuss the source of the quantum advantage in our algorithm from the resource-theoretic point of view.

Quantifying quantum information resources: a numerical study

Quantum systems present correlations, which cannot be offered by classical objects. These distinctive correlations are not only considered as fundamental features of quantum mechanics, but more importantly, they are regarded as critical resources for different quantum information tasks. For example, quantum entanglement has been established as the key resource for quantum communication, and quantum discord has been suggested as the resource in deterministic quantum computation with one qubit (DQC1). However, quantification of these resources is very difficult, especially for many-body situations. Here, we introduce a unified numerical method to quantify these resources in general multiqubit states and use it to investigate the robustness of quantum discord in multiqubit permutation-invariant states. Our method paves the way to quantitatively investigate the relation between the potential of quantum technologies and quantum resources, particularly, that between quantum computation and quantum correlations.

Total quantum coherence and its applications

Quantum coherence is the most fundamental feature of quantum mechanics. The usual understanding of it depends on the choice of the basis, that is, the coherence of the same quantum state is different within different reference framework. To reveal all the potential coherence, we present the total quantum coherence measures in terms of two different methods. One is optimizing maximal basis-dependent coherence with all potential bases considered and the other is quantifying the distance between the state and the incoherent state set. Interestingly, the coherence measures based on relative entropy and $l_2$ norm have the same form in the two different methods. In particular, we show that the measures based on the non-contractive $l_2$ norm is also a good measure different from the basis-dependent coherence. In addition, we show that all the measures are analytically calculable and have all the good properties. The experimental schemes for the detection of these coherence measures are also proposed by multiple copies of quantum states instead of reconstructing the full density matrix. By studying one type of quantum probing schemes, we find that both the normalized trace in the scheme of deterministic quantum computation with one qubit (DQC1) and the overlap of two states in quantum overlap measurement schemes (QOM) can be well described by the change of total coherence of the probing qubit. Hence the nontrivial probing always leads to the change of the total coherence.

Converting Coherence to Quantum Correlations.

Recent results in quantum information theory characterize quantum coherence in the context of resource theories. Here, we study the relation between quantum coherence and quantum discord, a kind of quantum correlation which appears even in nonentangled states. We prove that the creation of quantum discord with multipartite incoherent operations is bounded by the amount of quantum coherence consumed in its subsystems during the process. We show how the interplay between quantum coherence consumption and creation of quantum discord works in the preparation of multipartite quantum correlated states and in the model of deterministic quantum computation with one qubit.

Power of one bit of quantum information in quantum metrology

We construct a model of quantum metrology inspired by the computational model known as deterministic quantum computation with one quantum bit (DQC1). Using only one pure qubit together with $l$ fully-mixed qubits we obtain measurement precision at the standard quantum limit, which is typically obtained using the same number of uncorrelated qubits in fully-pure states. The standard quantum limit can be exceeded using an additional qubit, which adds only a small amount of purity. We show that the discord in the final state vanishes only in the limit of attaining infinite precision for the parameter being estimated.

Robust deterministic quantum computation of quantum-dot spins inside microcavities based on parity-check building blocks

Parity-check building blocks are useful in quantum algorithms, quantum communications, and quantum computing, and such devices may be helpful in implementing robust universal quantum gates. We propose a scheme to construct a robust deterministic controlled-not gate on static electron-spin qubits with parity-check building blocks, assisted by double-sided-cavity quantum systems. Our device is robust against the polarization-flip errors, and it can work in both the weak coupling and strong coupling regimes, but high fidelity is achieved only when the ratio of the side leakage to the cavity loss is low. Our gate is heralded by the polarization of the single-photon medium. Finally, we assess the feasibility of this device and show it can be implemented with current technology.

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.