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We extend the circuit model of quantum comuptation so that the wiring between gates is soft-coded within registers inside the gates. The addresses in these registers can be manipulated and put into superpositions. This aims at capturing indefinite causal orders, as well as making their geometrical layout explicit. We show how to implement the quantum switch and the polarizing beam splitter within our model. One difficulty is that the names used as addresses should not matter beyond the wiring they describe, i.e. the evolution should commute with renamings. Yet, the evolution may act nontrivially on these names. Our main technical contribution is a full characterization of such nameblind matrices.
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We generalize quantum circuits for the Toffoli gate presented by Selinger and Jones for functionally controlled NOT gates, i.e., $X$ gates controlled by arbitrary $n$-variable Boolean functions. Our constructions target the gate set consisting of Clifford gates and single qubit rotations by arbitrary angles. Our constructions use the Walsh-Hadamard spectrum of Boolean functions and build on the work by Schuch and Siewert and Welch et al. We present quantum circuits for the case where the target qubit is in an arbitrary state as well as the special case where the target is in a known state. Additionally, we present constructions that require no auxiliary qubits and constructions that have a rotation depth of 1.
Parallel operations in conventional computing have proven to be an essential tool for efficient and practical computation, and the story is not different for quantum computing. Indeed, there exists a large body of works that study advantages of parallel implementations of quantum gates for efficient quantum circuit implementations. Here, we focus on the recently invented efficient, arbitrary, simultaneously entangling (EASE) gates, available on a trapped-ion quantum computer. Leveraging its flexibility in selecting arbitrary pairs of qubits to be coupled with any degrees of entanglement, all in parallel, we show a $n$-qubit Clifford circuit can be implemented using $6log(n)$ EASE gates, a $n$-qubit multiply-controlled NOT gate can be implemented using $3n/2$ EASE gates, and a $n$-qubit permutation can be implemented using six EASE gates. We discuss their implications to near-term quantum chemistry simulations and the state of the art pattern matching algorithm. Given Clifford + multiply-controlled NOT gates form a universal gate set for quantum computing, our results imply efficient quantum computation by EASE gates, in general.
Efficiently entangling pairs of qubits is essential to fully harness the power of quantum computing. Here, we devise an exact protocol that simultaneously entangles arbitrary pairs of qubits on a trapped-ion quantum computer. The protocol requires classical computational resources polynomial in the system size, and very little overhead in the quantum control compared to a single-pair case. We demonstrate an exponential improvement in both classical and quantum resources over the current state of the art. We implement the protocol on a software-defined trapped-ion quantum computer, where we reconfigure the quantum computer architecture on demand. Together with the all-to-all connectivity available in trapped-ion quantum computers, our results establish that trapped ions are a prime candidate for a scalable quantum computing platform with minimal quantum latency.
Quantum computing is currently limited by the cost of two-qubit entangling operations. In order to scale up quantum processors and achieve a quantum advantage, it is crucial to economize on the power requirement of two-qubit gates, make them robust to drift in experimental parameters, and shorten the gate times. In this paper, we present two methods, one exact and one approximate, to construct optimal pulses for entangling gates on a pair of ions within a trapped ion chain, one of the leading quantum computing architectures. Our methods are direct, non-iterative, and linear, and can construct gate-steering pulses requiring less power than the standard method by more than an order of magnitude in some parameter regimes. The power savings may generally be traded for reduced gate time and greater qubit connectivity. Additionally, our methods provide increased robustness to mode drift. We illustrate these trade-offs on a trapped-ion quantum computer.
Current quantum computers are especially error prone and require high levels of optimization to reduce operation counts and maximize the probability the compiled program will succeed. These computers only support operations decomposed into one- and two-qubit gates and only two-qubit gates between physically connected pairs of qubits. Typical compilers first decompose operations, then route data to connected qubits. We propose a new compiler structure, Orchestrated Trios, that first decomposes to the three-qubit Toffoli, routes the inputs of the higher-level Toffoli operations to groups of nearby qubits, then finishes decomposition to hardware-supported gates. This significantly reduces communication overhead by giving the routing pass access to the higher-level structure of the circuit instead of discarding it. A second benefit is the ability to now select an architecture-tuned Toffoli decomposition such as the 8-CNOT Toffoli for the specific hardware qubits now known after the routing pass. We perform real experiments on IBM Johannesburg showing an average 35% decrease in two-qubit gate count and 23% increase in success rate of a single Toffoli over Qiskit. We additionally compile many near-term benchmark algorithms showing an average 344% increase in (or 4.44x) simulated success rate on the Johannesburg architecture and compare with other architecture types.
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