We provide a noisy intermediate-scale quantum framework for simulating the dynamics of open quantum systems, generalized time evolution, non-linear differential equations and Gibbs state preparation. Our algorithm does not require any classical-quantum feedback loop, bypass the barren plateau problem and does not necessitate any complicated measurements such as the Hadamard test. We introduce the notion of the hybrid density matrix, which allows us to disentangle the different steps of our algorithm and delegate classically demanding tasks to the quantum computer. Our algorithm proceeds in three disjoint steps. First, we select the ansatz, followed by measuring overlap matrices on a quantum computer. The final step involves classical post-processing data from the second step. Our algorithm has potential applications in solving the Navier-Stokes equation, plasma hydrodynamics, quantum Boltzmann training, quantum signal processing and linear systems. Our entire framework is compatible with current experiments and can be implemented immediately.
Many important chemical and biochemical processes in the condensed phase are notoriously difficult to simulate numerically. Often this difficulty arises from the complexity of simulating dynamics resulting from coupling to structured, mesoscopic baths, for which no separation of time scales exists and statistical treatments fail. A prime example of such a process is vibrationally assisted charge or energy transfer. A quantum simulator, capable of implementing a realistic model of the system of interest, could provide insight into these processes in regimes where numerical treatments fail. We t…
Quantum computers are expected to help us to achieve accurate simulation of the dynamics of many-body quantum systems. However, the limitations of current NISQ devices prevents us from realising this goal today. Recently an algorithm for performing quantum simulations called quantum assisted simulator has been proposed that promises realization on current experimental devices. In this work, we extend the quantum assisted simulator to simulate the dynamics of a class of time-dependent Hamiltonians. We show that the quantum assisted simulator is easier to implement as well as can realize multi-q…
Quantum simulation can help us study poorly understood topics such as high-temperature superconductivity and drug design. However, existing quantum simulation algorithms for current quantum computers often have drawbacks that impede their application. Here, we provide a novel hybrid quantum-classical algorithm for simulating the dynamics of quantum systems. Our approach takes the Ansatz wavefunction as a linear combination of quantum states. The quantum states are fixed, and the combination parameters are variationally adjusted. Unlike existing variational quantum simulation algorithms, our al…
We propose a method for quantum algorithm design assisted by machine learning. The method uses a quantum-classical hybrid simulator, where a "quantum student" is being taught by a "classical teacher." In other words, in our method, the learning system is supposed to evolve into a quantum algorithm for a given problem assisted by classical main-feedback system. Our method is applicable to design quantum oracle-based algorithm. As a case study, we chose an oracle decision problem, called a Deutsch-Jozsa problem. We showed by using Monte-Carlo simulations that our simulator can faithfully learn q…
We introduce a scheme that combines photon-assisted tunneling by a moving optical lattice with strong Hubbard interactions, and allows for the quantum simulation of paradigmatic quantum many-body models. We show that, in a certain regime, this quantum simulator yields an effective Hubbard Hamiltonian with tunable bond-charge interactions, a model studied in the context of strongly-correlated electrons. In a different regime, we show how to exploit a correlated destruction of tunneling to explore Nagaoka ferromagnetism at finite Hubbard repulsion. By changing the photon-assisted tunneling param…
Unified and Generalized Approach to Entanglement-Assisted Quantum Error Correction
Xanadu；Department of Mathematics & Statistics, University of Guelph（圭尔夫大学数学与统计系）；Perimeter Institute for Theoretical Physics（理论物理珀米特研究所）；Institute for Quantum Computing, University of Waterloo（滑铁卢大学量子计算研究所）
Controlled quantum mechanical devices provide a means of simulating more complex quantum systems exponentially faster than classical computers. Such "quantum simulators" rely heavily upon being able to prepare the ground state of Hamiltonians, whose properties can be used to calculate correlation functions or even the solution to certain classical computations. While adiabatic preparation remains the primary means of producing such ground states, here we provide a different avenue of preparation: cooling to the ground state via simulated dissipation. This is in direct analogy to contemporary e…
Simulating the dynamics of many-body quantum systems is believed to be one of the first fields that quantum computers can show a quantum advantage over classical computers. Noisy intermediate-scale quantum (NISQ) algorithms aim at effectively using the currently available quantum hardware. For quantum simulation, various types of NISQ algorithms have been proposed with individual advantages as well as challenges. In this work, we propose a new algorithm, truncated Taylor quantum simulator (TTQS), that shares the advantages of existing algorithms and alleviates some of the shortcomings. Our alg…
We introduce the concept of embedding quantum simulators, a paradigm allowing the efficient quantum computation of a class of bipartite and multipartite entanglement monotones. It consists in the suitable encoding of a simulated quantum dynamics in the enlarged Hilbert space of an embedding quantum simulator. In this manner, entanglement monotones are conveniently mapped onto physical observables, overcoming the necessity of full tomography and reducing drastically the experimental requirements. Furthermore, this method is directly applicable to pure states and, assisted by classical algorithm…
We propose a physical setup that can be used to simulate the quantum dynamics of the Ising model with present-day technology. Our scheme consists of electrons floating on superfluid helium which interact via Coulomb forces. In the limit of low temperatures, the system will stay near the ground state where its Hamiltonian is equivalent to the Ising model and thus shows phenomena such as quantum criticality. Furthermore, the proposed design could be generalized in order to study interacting field theories (e.g., $λϕ^4$) and adiabatic quantum computers.
Programming long-range interactions in analog quantum simulators
Institute of Fundamental Physics IFF-CSIC（基础物理研究所）；Departamento de Física, Facultad de Ciencias Ambientales y Bioquímica, Universidad de Castilla-La Mancha（卡斯蒂利亚-拉曼恰大学环境科学与生物化学学院物理系）
Trapped ions are a versatile platform for the investigation of quantum many-body phenomena, in particular for the study of scenarios where long-range interactions are mediated by phonons. Recent experiments have shown that the trapped ion platform can be augmented by exciting high-lying Rydberg states. This introduces controllable state-dependent interactions that are independent from the phonon structure. However, the many-body physics in this newly accessible regime is largely unexplored. We show that this system grants access to generalized Dicke model physics, where dipolar interactions be…
We study possible realizations of generalized quantum measurements on measurement-assisted programmable quantum processors. We focus our attention on the realization of von Neumann measurements and informationally complete POVMs. It is known that two unitary transformations implementable by the same programmable processor require mutually {\it orthogonal} states. It turns out that the situation with von Neumann measurements is different. Specifically, in order to realize two such measurements one does not have to use orthogonal program states. On the other hand, the number of the implementable…
Quantum discord and quantum uncertainty are two important features of the quantum world. In this work, the relation between entropic uncertainty relation and the shareability of quantum discord is studied. First, by using tripartite quantum-memory-assisted entropic uncertainty relation, an upper bound for the shareability of quantum discord among different partites of a composite system is obtained. It is also shown that, for a specific class of tripartite states, the obtained relation could be expressed as monogamy of quantum discord. Moreover, it is illustrated that the relation could be gen…
We propose a method to probe time dependent correlations of non trivial observables in many-body ultracold lattice gases. The scheme uses a quantum non-demolition matter-light interface, first, to map the observable of interest on the many body system into the light and, then, to store coherently such information into an external system acting as a quantum memory. Correlations of the observable at two (or more) instances of time are retrieved with a single final measurement that includes the readout of the quantum memory. Such method brings at reach the study of dynamics of many-body systems i…
We present a proposal for a versatile cold-atom-based quantum simulator of relativistic fermionic theories and topological insulators in arbitrary dimensions. The setup consists of a spin-independent optical lattice that traps a collection of hyperfine states of the same alkaline atom, to which the different degrees of freedom of the field theory to be simulated are then mapped. We show that the combination of bi-chromatic optical lattices with Raman transitions can allow the engineering of a spin-dependent tunneling of the atoms between neighboring lattice sites. These assisted-hopping proces…
Coherent State Assisted Entanglement Generation Between Quantum Memories
The University of Maryland, College Park（马里兰大学帕克分校）；RTX BBN Technologies（RTX BBN技术公司）；Wyant College of Optical Sciences, The University of Arizona（亚利桑那大学怀安特光学科学学院）
The effect of entanglement and correlated noise in a four-player quantum Minority game is investigated. Different time correlated quantum memory channels are considered to analyze the Nash equilibrium payoff of the 1st player. It is seen that the Nash equilibrium payoff is substantially enhanced due to the presence of correlated noise. The behaviour of damping channels (amplitude damping and phase damping) is approximately similar. However, bit-phase flip channel heavily influences the minority game as compared to other channels in the presence of correlated noise. On the other hand, phase fli…
We describe a versatile toolbox for the quantum simulation of many-body lattice models, capable of exploring the combined effects of background Abelian and non-Abelian gauge fields, bond and site disorder, and strong on-site interactions. We show how to control the quantum dynamics of particles trapped in lattice potentials by the photon-assisted tunneling induced by periodic drivings. This scheme is general enough to be applied to either bosons or fermions with the additional advantage of being non-perturbative. It finds an ideal application in microfabricated ion trap arrays, where the quant…
It is easy to show coincidence of the entanglement-assisted classical capacity and the Holevo capacity for any c-q channel between finite dimensional quantum systems. In this paper we prove the converse assertion: coincidence of the above-mentioned capacities of a quantum channel implies that the $χ$-essential part of this channel is a c-q channel (the $χ$-essential part is a restriction of a channel obtained by discarding all input states useless for transmission of classical information). The above observations are generalized to infinite dimensional quantum channels with linear constraints …
Non-Gaussian operations on two mode squeezed vacuum states (TMSV) in continuous variable measurement device independent quantum key distribution (CV-MDI-QKD) protocols have been shown to effectively increase the total transmission distances drastically. In this paper we show that photon subtraction on a two mode squeezed coherent (PSTMSC) state can further improve the transmission distances remarkably. To that end we also provide a generalized covariance matrix corresponding to PSTMSC, which has not been attempted before. We show that coherence, defined as the amount of displacement of vacuum …
We provide a general framework to describe cooling of a micromechanical oscillator to its quantum ground state by means of radiation-pressure coupling with a driven optical cavity. We apply it to two experimentally realized schemes, back-action cooling via a detuned cavity and cold-damping quantum-feedback cooling, and we determine the ultimate quantum limits of both schemes for the full parameter range of a stable cavity. While both allow to reach the oscillator's quantum ground state, we find that back-action cooling is more efficient in the good cavity limit, i.e. when the cavity bandwidth …
In one-way quantum computation (1WQC) model, universal quantum computations are performed using measurements to designated qubits in a highly entangled state. The choices of bases for these measurements as well as the structure of the entanglements specify a quantum algorithm. As scalable and reliable quantum computers have not been implemented yet, quantum computation simulators are the only widely available tools to design and test quantum algorithms. However, simulating the quantum computations on a standard classical computer in most cases requires exponential memory and time. In this pape…
We introduce two generalizations of Kochen-Specker (KS) sets: projective KS sets and generalized KS sets. We then use projective KS sets to characterize all graphs for which the chromatic number is strictly larger than the quantum chromatic number. Here, the quantum chromatic number is defined via a nonlocal game based on graph coloring. We further show that from any graph with separation between these two quantities, one can construct a classical channel for which entanglement assistance increases the one-shot zero-error capacity. As an example, we exhibit a new family of classical channels w…
Quantum networks provide a platform for astronomical interferometers capable of imaging faint stellar objects. In a recent work [arXiv:1809.01659], we presented a protocol that circumvents transmission losses with efficient use of quantum resources and modest quantum memories. Here we analyze a number of extensions to that scheme. We show that it can be operated as a truly broadband interferometer and generalized to multiple sites in the array. We also analyze how imaging based on the quantum Fourier transform provides improved signal-to-noise ratio compared to classical processing. Finally, w…
Environment-assisted quantum transport (ENAQT) is a unique situation where environmental noise can, counterintuitively, enhance the transport of an open quantum system. In this paper, we investigate how the presence of a one-dimensional single-particle mobility edge can generate strong ENAQT. For this purpose, we study the energy current of a generalized Aubry-André-Harper (AAH) tight binding model coupled at its edges to spin baths of differing temperature and dephasing noise along the system. We find that the ENAQT increases by orders of magnitude and depends on the number of localized eigen…
We introduce and study the task of assisted coherence distillation. This task arises naturally in bipartite systems where both parties work together to generate the maximal possible coherence on one of the subsystems. Only incoherent operations are allowed on the target system while general local quantum operations are permitted on the other, an operational paradigm that we call local quantum-incoherent operations and classical communication (LQICC). We show that the asymptotic rate of assisted coherence distillation for pure states is equal to the coherence of assistance, an analog of the ent…
