ABSTRACT We present a non-deterministic circuit decomposition technique for approximating an arbi... more ABSTRACT We present a non-deterministic circuit decomposition technique for approximating an arbitrary single-qubit unitary to within distance $\epsilon$ that requires significantly fewer non-Clifford gates than deterministic decomposition techniques. We develop "Repeat-Until-Success" (RUS) circuits and characterize unitaries that can be exactly represented as an RUS circuit. Our RUS circuits operate by conditioning on a given measurement outcome and using only a small number of non-Clifford gates and ancilla qubits. We construct an algorithm based on RUS circuits that approximates an arbitrary single-qubit $Z$-axis rotation to within distance $\epsilon$, where the number of $T$ gates scales as $1.3\log(1/\epsilon) - 2.79$, an improvement of roughly three-fold over state-of-the-art techniques. We then extend our algorithm and show that a scaling of $2.4\log_2(1/\epsilon) - 3.3$ can be achieved for arbitrary unitaries and a small range of $\epsilon$, which is roughly twice as good as optimal deterministic decomposition methods.
ABSTRACT The fragile nature of quantum information limits our ability to construct large quantiti... more ABSTRACT The fragile nature of quantum information limits our ability to construct large quantities of quantum bits suitable for quantum computing. An important goal, therefore, is to minimize the amount of resources required to implement quantum algorithms, many of which are serial in nature and leave large numbers of qubits idle much of the time unless compression techniques are used. Furthermore, quantum error-correcting codes, which are required to reduce the effects of noise, introduce additional resource overhead. We consider a strategy for quantum circuit optimization based on topological deformation in the surface code, one of the best performing and most practical quantum error-correcting codes. Specifically, we examine the problem of minimizing computation time on a two-dimensional qubit lattice of arbitrary, but fixed dimension, and propose two algorithms for doing so.
ABSTRACT We present a non-deterministic circuit decomposition technique for approximating an arbi... more ABSTRACT We present a non-deterministic circuit decomposition technique for approximating an arbitrary single-qubit unitary to within distance $\epsilon$ that requires significantly fewer non-Clifford gates than deterministic decomposition techniques. We develop "Repeat-Until-Success" (RUS) circuits and characterize unitaries that can be exactly represented as an RUS circuit. Our RUS circuits operate by conditioning on a given measurement outcome and using only a small number of non-Clifford gates and ancilla qubits. We construct an algorithm based on RUS circuits that approximates an arbitrary single-qubit $Z$-axis rotation to within distance $\epsilon$, where the number of $T$ gates scales as $1.3\log(1/\epsilon) - 2.79$, an improvement of roughly three-fold over state-of-the-art techniques. We then extend our algorithm and show that a scaling of $2.4\log_2(1/\epsilon) - 3.3$ can be achieved for arbitrary unitaries and a small range of $\epsilon$, which is roughly twice as good as optimal deterministic decomposition methods.
ABSTRACT The fragile nature of quantum information limits our ability to construct large quantiti... more ABSTRACT The fragile nature of quantum information limits our ability to construct large quantities of quantum bits suitable for quantum computing. An important goal, therefore, is to minimize the amount of resources required to implement quantum algorithms, many of which are serial in nature and leave large numbers of qubits idle much of the time unless compression techniques are used. Furthermore, quantum error-correcting codes, which are required to reduce the effects of noise, introduce additional resource overhead. We consider a strategy for quantum circuit optimization based on topological deformation in the surface code, one of the best performing and most practical quantum error-correcting codes. Specifically, we examine the problem of minimizing computation time on a two-dimensional qubit lattice of arbitrary, but fixed dimension, and propose two algorithms for doing so.
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