Reducing the Depth of Quantum Circuits Using Additional Circuit Lines

Abstract

Abstract. The synthesis of Boolean functions, as they are found in many quantum algorithms, is usually conducted in two steps. First, the function is realized in terms of a reversible circuit followed by a mapping into a corresponding quantum realization. During this process, the number of lines and the quantum costs of the resulting circuits have mainly been considered as optimization objectives thus far. However, beyond that also the depth of a quantum circuit is vital. Although first synthesis approaches that consider depth have recently been introduced, the majority of design methods did not consider this metric. In this paper, we introduce an optimization approach aiming for the reduction of depth in the process of mapping a reversible circuit into a quantum circuit. For this purpose, we present an improved (local) mapping of single gates as well as a (global) optimization scheme considering the whole circuit. In both cases, we incorporate the idea of exploiting additional circuit lines which are used in order to split a chain of serial gates. Our optimization techniques enable a concurrent application of gates which significantly reduces the depth of the circuit. Experiments show that reductions of approx. 40% on average can be achieved when following this scheme.

Qubit-efficient entanglement spectroscopy using qubit resets

“…Since effective depth reduces to standard depth for circuits which do not use resets, the effective depth of HT is T sp + Θ(nk) and the effective depth of TCT is T sp + O (1). For the qubit-efficient variants of HT, the ancilla qubit leads to effective depths the same as their depths, Θ(n × (T sp + k)), which asymptotically matches that of HT when T sp is small.…”

“…It is designed to obfuscate the long time for which the ancilla qubit in the qe-HT must be kept coherent. This naive measure would rate this circuit as Θ(k), and with further changes this could be made O (1). Clearly though, information stored in the ancilla is just as exposed to thermal noise in this new circuit as in the other qubitefficient circuits.…”

“…While some approaches help for specific applications [5,19,37,40] or for individual circuits [39], there are few general techniques for (re)designing low-depth quantum algorithms. One technique is to trade shorter circuit depth for increased circuit width [1,9,50], i.e. use more qubits, but those qubits may still be unavailable or unacceptably noisy.…”

“…, n max [29,49]. 1 These algorithms compute Tr (ρ n A ) using O(n) copies of the state |ψ [29,50]. The standard algorithm is an extension of the Swap Test [11,25] by [29] which we call the Entanglement Spectroscopy Hadamard Test (HT) (Fig.…”

Quantum Circuit Optimization by Hadamard Gate Reduction

“…There are many existing methods targeting the optimization of reversible circuits for either reducing the number of lines [21], number of gates [20], depth [22], or quantum cost [23]. We are interested in techniques that lead to lower quantum cost.…”