Earl Campbell

Large-scale quantum computers have the potential to hold computational capabilities beyond conventional computers for certain problems. However, the physical qubits within a quantum computer are prone to noise and decoherence, which must be corrected in order to perform reliable, fault-tolerant quantum computations. Quantum Error Correction (QEC) provides the path for realizing such computations. QEC continuously generates a continuous stream of data that decoders must process at the rate it is received, which can be as fast as 1 MHz in superconducting quantum computers. A little known fact of QEC is that if the decoder infrastructure cannot keep up, a data backlog problem is encountered and the quantum computer runs exponentially slower. Today's leading approaches to quantum error correction are not scalable as existing decoders typically run slower as the problem size is increased, inevitably hitting the backlog problem. That is: the current leading proposal for fault-tolerant quantum computation is not scalable. Here, we show how to parallelize decoding to achieve almost arbitrary speed, removing this roadblock to scalability. Our parallelization requires some classical feed forward decisions to be delayed, leading to a slow-down of the logical clock speed. However, the slow-down is now only polynomial in code size, averting the exponential slowdown. We numerically demonstrate our parallel decoder for the surface code, showing no noticeable reduction in logical fidelity compared to previous decoders and demonstrating the parallelization speedup.

Abstract We consider simulating quantum systems on digital quantum computers. We show that the performance of quantum simulation can be improved by simultaneously exploiting the commutativity of Hamiltonian, the sparsity of interactions, and the prior knowledge of initial state. We achieve this using Trotterization for a class of correlated electrons that encompasses various physical systems, including the plane-wave-basis electronic structure and the Fermi-Hubbard model. We estimate the simulation error by taking the transition amplitude of nested commutators of Hamiltonian terms within the $\eta$-electron manifold. We develop multiple techniques for bounding the transition amplitude and the expectation of general fermionic operators, which may be of independent interest. We show that it suffices to use $\cO{\frac{n^{5/3}}{\eta^{2/3}}+n^{4/3}\eta^{2/3}}$ gates to simulate electronic structure in the plane-wave basis with $n$ spin orbitals and $\eta$ electrons up to a negligible factor, improving the best previous result in second quantization while outperforming the first-quantized simulation when $\eta=\Om{\sqrt{n}}$. We also obtain an improvement for simulating the Fermi-Hubbard model. We construct concrete examples for which our bounds are almost saturated, giving a nearly tight Trotterization of correlated electrons.

In the stabilizer circuit model of quantum computation, universality requires a resource known as magic. Here, we propose three new ways to quantify the magic of a quantum state using magic monotones, apply the monotones in the characterization of state conversions under stabilizer operations, and connect them with the classical simulation of quantum circuits. We first present a complete theory of these quantifiers for tensor products of single-qubit states, for which the monotones are all equal and all act multiplicatively, constituting the first qubit magic monotones to have this property. We use the monotones to establish several asymptotic and non-asymptotic bounds on state interconversion and distillation rates. We then relate our quantifiers directly to the runtime of classical simulation algorithms, showing that a large amount of magic is a necessary requirement for any quantum speedup. One of our classical simulation algorithms is a quasi-probability simulator with its runtime connected to a generalized notion of negativity, which is exponentially faster than all prior qubit quasi-probability simulation algorithms. We also introduce a new variant of the stabilizer rank simulation algorithm suitable for mixed states, while improving the runtime bounds for this class of simulations. Our work reveals interesting connections between quasi-probability and stabilizer rank simulators, which previously appeared to be unrelated. Generalizing the approach beyond the theory of magic states, we establish methods for the quantitative characterization of classical simulability for more general quantum resources, and use them in the resource theory of quantum coherence to connect the L1-norm of coherence with the simulation of free operations.