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Quantum simulation of strongly correlated systems is potentially the most feasible useful application of near-term quantum computers. Minimizing quantum computational resources is crucial to achieving this goal. A promising class of algorithms for this purpose consists of variational quantum eigensolvers (VQEs). Among these, problem-tailored versions such as ADAPT-VQE that build variational ansätze step by step from a predefined operator pool perform particularly well in terms of circuit depths and variational parameter counts. However, this improved performance comes at the expense of an additional measurement overhead compared to standard VQEs. Here, we show that this overhead can be reduced to an amount that grows only linearly with the number$n$of qubits, instead of quartically as in the original ADAPT-VQE. We do this by proving that operator pools of size$2n-2$can represent any state in Hilbert space if chosen appropriately. We prove that this is the minimal size of such complete pools, discuss their algebraic properties, and present necessary and sufficient conditions for their completeness that allow us to find such pools efficiently. We further show that, if the simulated problem possesses symmetries, then complete pools can fail to yield convergent results, unless the pool is chosen to obey certain symmetry rules. We demonstrate the performance of such symmetry-adapted complete pools by using them in classical simulations of ADAPT-VQE for several strongly correlated molecules. Our findings are relevant for any VQE that uses an ansatz based on Pauli strings.

 

By encoding logical qubits into specific types of photonic graph states, one can realize quantum repeaters that enable fast entanglement distribution rates approaching classical communication. However, the generation of these photonic graph states requires a formidable resource overhead using traditional approaches based on linear optics. Overcoming this challenge, a number of new schemes have been proposed that employ quantum emitters to deterministically generate photonic graph states. Although these schemes have the potential to significantly reduce the resource cost, a systematic comparison of the repeater performance among different encodings and different generation schemes is lacking. Here, we quantitatively analyze the performance of quantum repeaters based on two different graph states, i.e. the tree graph states and the repeater graph states. For both states, we compare the performance between two generation schemes, one based on a single quantum emitter coupled to ancillary matter qubits, and one based on a single quantum emitter coupled to a delayed feedback. We identify the numerically optimal scheme at different system parameters. Our analysis provides a clear guideline on the selection of the generation scheme for graph-state-based quantum repeaters, and lays out the parameter requirements for future experimental realizations of different schemes. 

Abstract Multi-photon entangled graph states are a fundamental resource in quantum communication networks, distributed quantum computing, and sensing. These states can in principle be created deterministically from quantum emitters such as optically active quantum dots or defects, atomic systems, or superconducting qubits. However, finding efficient schemes to produce such states has been a long-standing challenge. Here, we present an algorithm that, given a desired multi-photon graph state, determines the minimum number of quantum emitters and precise operation sequences that can produce it. The algorithm itself and the resulting operation sequence both scale polynomially in the size of the photonic graph state, allowing one to obtain efficient schemes to generate graph states containing hundreds or thousands of photons. 

We present a new hybrid quantum algorithm to estimate molecular excited and charged states on near-term quantum computers following any VQE-based ground state estimation.

 

Abstract The transfer of information between quantum systems is essential for quantum communication and computation. In quantum computers, high connectivity between qubits can improve the efficiency of algorithms, assist in error correction, and enable high-fidelity readout. However, as with all quantum gates, operations to transfer information between qubits can suffer from errors associated with spurious interactions and disorder between qubits, among other things. Here, we harness interactions and disorder between qubits to improve a swap operation for spin eigenstates in semiconductor gate-defined quantum-dot spins. We use a system of four electron spins, which we configure as two exchange-coupled singlet–triplet qubits. Our approach, which relies on the physics underlying discrete time crystals, enhances the quality factor of spin-eigenstate swaps by up to an order of magnitude. Our results show how interactions and disorder in multi-qubit systems can stabilize non-trivial quantum operations and suggest potential uses for non-equilibrium quantum phenomena, like time crystals, in quantum information processing applications. Our results also confirm the long-predicted emergence of effective Ising interactions between exchange-coupled singlet–triplet qubits.