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Quantum computers are currently accessible through a cloud-based platform that allows users to run their programs on a suite of quantum hardware. As the quantum computing ecosystem grows in popularity and utility, it is reasonable to expect…
Running quantum circuits on quantum computers does not always generate "clean" results, unlike on a simulator, as noise plays a significant role in any quantum device. To explore this, we experimented with the Quantum Approximate…
Traffic optimization on roads is a highly complex problem, with one important aspect being minimization of traffic congestion. By mapping to an Ising formulation of the traffic congestion problem, we benchmark solutions obtained from the…
We compare the performance of a quantum local algorithm to a similar classical counterpart on a well-established combinatorial optimization problem LocalMaxCut. We show that a popular quantum algorithm first discovered by Farhi, Goldstone,…
Recent progress in the development of quantum technologies has enabled the direct investigation of dynamics of increasingly complex quantum many-body systems. This motivates the study of the complexity of classical algorithms for this…
The quantum approximate optimization algorithm (QAOA) has emerged as a promising candidate for demonstrating quantum advantage on noisy intermediate-scale quantum (NISQ) devices. While various QAOA parameterization schemes exist, ranging…
Recently, there has been much interest in the efficient preparation of complex quantum states using low-depth quantum circuits, such as Quantum Approximate Optimization Algorithm (QAOA). While it has been numerically shown that such…
This paper studies the application of the Quantum Approximate Optimization Algorithm (QAOA) to spin-glass models with random multi-body couplings in the limit of a large number of spins. We show that for such mixed-spin models the…
This paper discusses a classical simulation to compute the partition function (or free energy) of generic one-dimensional quantum many-body systems. Many numerical methods have previously been developed to approximately solve…
Quantum computers may provide good solutions to combinatorial optimization problems by leveraging the Quantum Approximate Optimization Algorithm (QAOA). The QAOA is often presented as an algorithm for noisy hardware. However, hardware…
The Quantum Approximate Optimization Algorithm (QAOA) requires considered optimization problems to be translated into a compatible format. A popular transformation step in this pipeline involves the quadratization of higher-order binary…
Quantum Approximate Optimisation (QAOA) is the most studied gate based variational quantum algorithm today. We train QAOA one layer at a time to maximize overlap with an $n$ qubit target state. Doing so we discovered that such training…
We implement two Quantum Approximate Optimisation Algorithm (QAOA) variants for a battery revenue optimisation problem, equivalent to the weakly NP-hard Knapsack Problem. Both approaches investigate how to tackle constrained problems with…
Combinatorial optimization is one of the fields where near term quantum devices are being utilized with hybrid quantum-classical algorithms to demonstrate potentially practical applications of quantum computing. One of the most well studied…
Noise on near-term quantum devices will inevitably limit the performance of Quantum Approximate Optimization Algorithm (QAOA). One significant consequence is that the performance of QAOA may fail to monotonically improve with depth. In…
The quantum approximate optimization algorithm (QAOA) transforms a simple many-qubit wavefunction into one which encodes a solution to a difficult classical optimization problem. It does this by optimizing the schedule according to which…
Clifford gates are a winsome class of quantum operations combining mathematical elegance with physical significance. The Gottesman-Knill theorem asserts that Clifford computations can be classically efficiently simulated but this is true…
We introduce a relax-and-round approach embedding the quantum approximate optimization algorithm (QAOA) with $p\geq 1$ layers. We show for many problems, including Sherrington-Kirkpatrick spin glasses, that at $p=1$, it is as accurate as…
The Quantum Approximate Optimization Algorithm can be applied to search problems on graphs with a cost function that is a sum of terms corresponding to the edges. When conjugating an edge term, the QAOA unitary at depth p produces an…
The Quantum Approximate Optimization Algorithm (QAOA) is a powerful tool in solving various combinatorial problems such as Maximum Satisfiability and Maximum Cut. Hard computational problems, however, require deep circuits that place high…