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Entanglement is a quintessential quantum mechanical phenomenon with no classical equivalent. First discussed by Einstein, Podolsky, and Rosen and formally introduced by Schrödinger in 1935, entanglement has grown from a scientific debate to a radically new resource that sparks a technological revolution. This review focuses on fundamentals and recent advances in entanglement-based quantum information technology (QIT), specifically in photonic systems. Photons are unique quantum information carriers with several advantages, such as their ability to operate at room temperature, their compatibility with existing communication and sensing infrastructures, and the availability of readily accessible optical components. Photons also interface well with other solid-state quantum platforms. We first provide an overview on entanglement, starting with an introduction to its development from a historical perspective followed by the theory for entanglement generation and the associated representative experiments. We then dive into the applications of entanglement-based QIT for sensing, imaging, spectroscopy, data processing, and communication. Before closing, we present an outlook for the architecture of the next-generation entanglement-based QIT and its prospective applications.

 

Abstract The quantum approximate optimization algorithm (QAOA) is an approach for near-term quantum computers to potentially demonstrate computational advantage in solving combinatorial optimization problems. However, the viability of the QAOA depends on how its performance and resource requirements scale with problem size and complexity for realistic hardware implementations. Here, we quantify scaling of the expected resource requirements by synthesizing optimized circuits for hardware architectures with varying levels of connectivity. Assuming noisy gate operations, we estimate the number of measurements needed to sample the output of the idealized QAOA circuit with high probability. We show the number of measurements, and hence total time to solution, grows exponentially in problem size and problem graph degree as well as depth of the QAOA ansatz, gate infidelities, and inverse hardware graph degree. These problems may be alleviated by increasing hardware connectivity or by recently proposed modifications to the QAOA that achieve higher performance with fewer circuit layers. 

The road to computing on quantum devices has been accelerated by the promises that come from using Shor’s algorithm to reduce the complexity of prime factorization. However, this promise hast not yet been realized due to noisy qubits and lack of robust error correction schemes. Here we explore a promising, alternative method for prime factorization that uses well-established techniques from variational imaginary time evolution. We create a Hamiltonian whose ground state encodes the solution to the problem and use variational techniques to evolve a state iteratively towards these prime factors. We show that the number of circuits evaluated in each iteration scales as$$O(n^{5}d)$$$O\left(n^{5}d\right)$, wherenis the bit-length of the number to be factorized anddis the depth of the circuit. We use a single layer of entangling gates to factorize 36 numbers represented using 7, 8, and 9-qubit Hamiltonians. We also verify the method’s performance by implementing it on the IBMQ Lima hardware to factorize 55, 65, 77 and 91 which are greater than the largest number (21) to have been factorized on IBMQ hardware.

 

We develop a global variable substitution method that reduces n-variable monomials in combinatorial optimization problems to equivalent instances with monomials in fewer variables. We apply this technique to 3-SAT and analyze the optimal quantum unitary circuit depth needed to solve the reduced problem using the quantum approximate optimization algorithm. For benchmark 3-SAT problems, we find that the upper bound of the unitary circuit depth is smaller when the problem is formulated as a product and uses the substitution method to decompose gates than when the problem is written in the linear formulation, which requires no decomposition. 

Quantum chemistry is a key application area for noisy‐intermediate scale quantum (NISQ) devices, and therefore serves as an important benchmark for current and future quantum computer performance. Previous benchmarks in this field have focused on variational methods for computing ground and excited states of various molecules, including a benchmarking suite focused on the performance of computing ground states for alkali‐hydrides under an array of error mitigation methods. State‐of‐the‐art methods to reach chemical accuracy in hybrid quantum‐classical electronic structure calculations of alkali hydride molecules on NISQ devices from IBM are outlined here. It is demonstrated how to extend the reach of variational eigensolvers with symmetry preserving Ansätze. Next, it is outlined how to use quantum imaginary time evolution and Lanczos as a complementary method to variational techniques, highlighting the advantages of each approach. Finally, a new error mitigation method is demonstrated which uses systematic error cancellation via hidden inverse gate constructions, improving the performance of typical variational algorithms. These results show that electronic structure calculations have advanced rapidly, to routine chemical accuracy for simple molecules, from their inception on quantum computers a few short years ago, and they point to further rapid progress to larger molecules as the power of NISQ devices grows.