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Register a new userScheduling of Operations in Quantum Compiler
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When scheduling quantum operations, a shorter overall execution time of the resulting schedule yields a better throughput and higher fidelity output. In this paper, we demonstrate that quantum operation scheduling can be interpreted as a special type of job-shop problem. On this basis, we provide its formulation as Constraint Programming while taking into account commutation between quantum operations. We show that this formulation improves the overall execution time of the resulting schedules in practice through experiments with a real quantum compiler and quantum circuits from two common benchmark sets.
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A quantum computer consists of a set of quantum bits upon which operations called gates are applied to perform computations. In order to perform quantum algorithms, physicists would like to design arbitrary gates to apply to quantum bits. However, the physical limitations of the quantum computing device restrict the set of gates that physicists are able to apply. Thus, they must compose a sequence of gates from the permitted gate set, which approximates the gate they wish to apply - a process called quantum compiling. Austin Fowler proposes a method that finds optimal gate sequences in exponential time, but which is tractable for common problems. In this paper, I present several optimizations to this algorithm. While my optimizations do not improve its overall exponential behavior, they improve its empirical performance by one to two orders of magnitude.
I derive a tight bound between the quality of estimating the state of a single copy of a $d$-level system, and the degree the initial state has to be altered in course of this procedure. This result provides a complete analytical description of the quantum mechanical trade-off between the information gain and the quantum state disturbance expressed in terms of mean fidelities. I also discuss consequences of this bound for quantum teleportation using nonmaximally entangled states.
Quantum error correction is vital for implementing universal quantum computing. A key component is the encoding circuit that maps a product state of physical qubits into the encoded multipartite entangled logical state. Known methods are typically not optimal either in terms of the circuit depth (and therefore the error burden) or the specifics of the target platform, i.e. the native gates and topology of a system. This work introduces a variational compiler for efficiently finding the encoding circuit of general quantum error correcting codes with given quantum hardware. Focusing on the noisy intermediate scale quantum regime, we show how to systematically compile the circuit following an optimising process seeking to minimise the number of noisy operations that are allowed by the noisy quantum hardware or to obtain the highest fidelity of the encoded state with noisy gates. We demonstrate our method by deriving novel encoders for logic states of the five qubit code and the seven qubit Steane code. We describe ways to augment the discovered circuits with error detection. Our method is applicable quite generally for compiling the encoding circuits of quantum error correcting codes.
We prove a general limitation in quantum information that unifies the impossibility principles such as no-cloning and no-anticloning. Further, we show that for an unknown qubit one cannot design a universal Hadamard gate for creating equal superposition of the original and its complement state. Surprisingly, we find that Hadamard transformations exist for an unknown qubit chosen either from the polar or equatorial great circles. Also, we show that for an unknown qubit one cannot design a universal unitary gate for creating unequal superpositions of the original and its complement state. We discuss why it is impossible to design a controlled-NOT gate for two unknown qubits and discuss the implications of these limitations.
We study the possibility for a global unitary applied on an arbitrary number of qubits to be decomposed in a sequential unitary procedure, where an ancillary system is allowed to interact only once with each qubit. We prove that sequential unitary decompositions are in general impossible for genuine entangling operations, even with an infinite-dimensional ancilla, being the controlled-NOT gate a paradigmatic example. Nevertheless, we find particular nontrivial operations in quantum information that can be performed in a sequential unitary manner, as is the case of quantum error correction and quantum cloning.
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