International Business Machines Corporation

Ionq, Inc.

University System of Maryland

Duke University

Dmitri Maslov

Sergey Bravyi

Jay Michael Gambetta

Yunseong Nam

Andrew W Cross

Christopher R Monroe

Ali Javadiabhari

Norbert M Linke

Caroline Figgatt

Shelly-Erika Garion

Kevin A Landsman

Daiwei Zhu

Aaron Ostrander

Shaohan Hu

Andrew Childs

Neil Julien Ross

Yuan Su

Marco Pistoia

Jungsang Kim

Paul Kristan Temme

Ewout Van Den Berg

Joseph Latone

Kenneth Brown

Ruslan Shaydulin

Ken Brown

Systems and techniques that facilitate improved single-shot error mitigation for Clifford circuits are provided. For a Clifford circuit, various embodiments described herein can facilitate two-sided or one-sided Pauli checks. In various aspects, left-side Pauli operators of two-sided Pauli checks can be selected randomly without replacement, and right-side Pauli operators of two-sided Pauli checks can be identified via commutation identities respectively relating the Clifford circuit to the left-side Pauli operators. In various instances, Pauli operators of one-sided Pauli checks can be selected via commutation identities respectively relating the Clifford circuit to Z-type Paulis selected randomly without replacement. For either two-sided or one-sided Pauli checks, various embodiments described herein can involve implementation of interleaved SWAP gates, which can allow such two-sided or one-sided Pauli checks to be performed on linear nearest neighbor coupling topologies.

Single-shot error mitigation for Clifford circuits

Systems and techniques that facilitate efficient synthesis of optimal multi-qubit Clifford circuits are provided. In various embodiments, a system can receive as input a number n representing a quantity of qubits. In various instances, the system can generate, via a cost-invariant reduction function, as output a library of different n-qubit canonical representatives that respectively correspond to different cost-invariant equivalence classes of n-qubit Clifford group elements. In various embodiments, a system can receive as input a first Clifford group element. In various aspects, the system can search a database of canonical representatives, wherein different canonical representatives in the database respectively correspond to different cost-invariant equivalence classes of Clifford group elements. In various cases, the system can identify based on the search a second Clifford group element that implements the first Clifford group element and that has a lower entangling-gate cost than the first Clifford group element.

Efficient synthesis of optimal multi-qubit Clifford circuits

The disclosure describes various aspects related to enabling effective multi-qubit operations, and more specifically, to techniques for enabling parallel multi-qubit operations on a universal ion trap quantum computer. In an aspect, a method of performing quantum operations in an ion trap quantum computer or trapped-ion quantum system includes implementing at least two parallel gates of a quantum circuit, each of the at least two parallel gates is a multi-qubit gate, each of the at least two parallel gates is implemented using a different set of ions of a plurality of ions in a ion trap, and the plurality of ions includes four or more ions. The method further includes simultaneously performing operations on the at least two parallel gates as part of the quantum operations. A trapped-ion quantum system and a computer-readable storage medium corresponding to the method described above are also disclosed.

Parallel multi-qubit operations on a universal ion trap quantum computer

Systems and techniques that facilitate partitioned template matching and/or symbolic peephole optimization are provided. In various embodiments, a system can comprise a template component, which can perform template matching on a Clifford circuit associated with a set of qubits. In various aspects, the system can comprise a partition component, which can partition, prior to the template matching, the Clifford circuit into a computation stage, a Pauli stage, and a SWAP stage. In various instances, the template matching can be performed on the computation stage. In various embodiments, the system can comprise a symbolic component, which can select a subset of qubits from the set of qubits, rewrite at least one entangling gate in the computation stage such that a target of the at least one entangling gate is in the subset of qubits, and replace the at least one rewired entangling gate with a symbolic Pauli gate. In various cases, the symbolic Pauli gate can be a Pauli gate that is controlled by a symbolic variable. In various aspects, the system can comprise a peephole component, which can perform peephole optimization on the subset of qubits with the symbolic Pauli gate by implementing a dynamic programming algorithm.

Partitioned template matching and symbolic peephole optimization

A repository is configured in a hybrid data processing environment comprising a classical computing system and a quantum computing system, to hold a plurality of quantum circuit components (QCC(s)). A degree of difficulty in simulating the received QCC in the classical computing system is transformed into a classical hardness score. A degree of difficulty in implementing the received QCC in the quantum computing system is transformed into a quantum hardness score. A first parameter in a metadata data structure associated with the received QCC is populated with the classical hardness score. A second parameter in the metadata data structure associated with the received QCC is populated with the quantum hardness score. The received QCC is transformed into a library element by at least augmenting the received QCC with the metadata data structure. The library element is added to the repository.

Providing reusable quantum circuit components as a curated service

Systems, computer-implemented methods, and computer program products to facilitate synthesis of a quantum circuit are provided. According to an embodiment, a system can comprise a memory that stores computer executable components and a processor that executes the computer executable components stored in the memory. The computer executable components can comprise a circuit generation component that generates, iteratively, quantum circuits from 1 to N two-qubit gates, wherein at least one or more iterations (1, 2, . . . , N) adds a single two-qubit gate to circuits from a previous iteration based on using added single 2-qubit gates that represent operations distinct from previous operations relative to previous iterations. The computer executable components can further comprise a circuit identification component that identifies, from the quantum circuits, a desired circuit that matches a quantum circuit representation.

Synthesis of a quantum circuit

Techniques for enhancing quantum circuit execution in a quantum service are presented. Database component stores compiled unitaries associated with quantum functions. Unitary management component (UMC) determines whether to compile a unitary associated with a quantum function for storage in the database component based on a composite quality score associated with the unitary and a threshold composite quality score associated with the quantum function, wherein the threshold score can be, or can be based on, a composite quality score of a compiled unitary that performs the same quantum function or a compiled unitary that performs a different quantum function. UMC determines the composite quality score based on a group of factors comprising frequency of utilizing the quantum function or equivalent quantum function or computation, age of the quantum function or computation, difficulty level of compiling a unitary, quantum circuit quality, or error associated with experimental execution of the quantum function.

Enhanced quantum circuit execution in a quantum service

The disclosure describes various aspects of techniques for optimal fault-tolerant implementations of controlled-Zgates and Heisenberg interactions. Improvements in the implementation of the controlled-Zgate can be made by using a clean ancilla and in-circuit measurement. Various examples are described that depend on whether the implementation is with or without measurement and feedforward. The implementation of the Heisenberg interaction can leverage the improved controlled-Zgate implementation. These implementations can cut down significantly the implementation costs associated with fault-tolerant quantum computing systems.

Optimal fault-tolerant implementations of Heisenberg interactions and controlled-Zgates

A method of generating a randomized benchmarking protocol includes providing a randomly generated plurality of Hadamard gates; applying the Hadamard gates to a plurality of qubits; and generating randomly a plurality of Hadamard-free Clifford circuits. Each of the plurality of Hadamard-free Clifford circuits is generated by at least randomly generating a uniformly distributed phase (P) gate, and randomly generating a uniformly distributed linear Boolean invertible matrix of conditional NOT (CNOT) gate, and combining the P and CNOT gates to form each of the plurality of Hadamard-free Clifford circuits. The method also includes combining each of the plurality of Hadamard-free Clifford circuits with corresponding each of the plurality of Hadamard gates to form a sequence of alternating Hadamard-free Clifford-Hadamard pairs circuit to form the randomized benchmarking protocol; and measuring noise in a quantum mechanical processor using the randomized benchmarking protocol.

Randomized benchmarking by exploiting the structure of the clifford group

Systems, computer-implemented methods, and computer program products to facilitate synthesis of a quantum circuit are provided. According to an embodiment, a system can comprise a memory that stores computer executable components and a processor that executes the computer executable components stored in the memory. The computer executable components can comprise a circuit generation component that generates, iteratively, quantum circuits from 1 to N two-qubit gates, wherein at least one or more iterations (, . . . , N) adds a single two-qubit gate to circuits from a previous iteration based on using added single 2-qubit gates that represent operations distinct from previous operations relative to previous iterations. The computer executable components can further comprise a circuit identification component that identifies, from the quantum circuits, a desired circuit that matches a quantum circuit representation.

The disclosure describes the implementation of automated techniques for optimizing quantum circuits of the size and type expected in quantum computations that outperform classical computers. The disclosure shows how to handle continuous gate parameters and report a collection of fast algorithms capable of optimizing large-scale-scale quantum circuits. For the suite of benchmarks considered, the techniques described obtain substantial reductions in gate counts. In particular, the techniques in this disclosure provide better optimization in significantly less time than previous approaches, while making minimal structural changes so as to preserve the basic layout of the underlying quantum algorithms. The results provided by these techniques help bridge the gap between computations that can be run on existing quantum computing hardware and more advanced computations that are more challenging to implement in quantum computing hardware but are the ones that are expected to outperform what can be achieved with classical computers.

Automated optimization of large-scale quantum circuits with continuous parameters

A method of generating a random uniformly distributed Clifford unitary circuit (C) includes: generating a random Hadamard (H) gate; drawing a plurality of qubits from a probability distribution of qubits; applying the random H gate to the plurality of qubits drawn from the probability distribution; and generating randomly a first Hadamard-free Clifford circuit (F1) and a second Hadamard-free Clifford circuit (F2). The first and second Hadamard-free Clifford circuits is generated by at least randomly generating a uniformly distributed phase (P) gate, and randomly generating a uniformly distributed linear Boolean invertible conditional NOT (CNOT) gate, and combining the P and CNOT gates to form the first and second Hadamard-free Clifford circuits. The method further includes combining the generated first Hadamard-free circuit (F1) and the second Hadamard-free Clifford circuit (F2) with the generated random Hadamard (H) gate to form the random uniformly distributed Clifford unitary circuit (C).

Efficient synthesis of a random uniformly distributed Clifford unitary

The disclosure describes various aspects of techniques for using global interactions in efficient quantum circuit constructions. More specifically, this disclosure describes ways to use a global entangling operator to efficiently implement circuitry common to a selection of important quantum algorithms. The circuits may be constructed with global Ising entangling gates (e.g., global M&#xf8;lmer-S&#xf8;renson gates or GMS gates) and arbitrary addressable single-qubit gates. Examples of the types of circuits that can be implemented include stabilizer circuits, Toffoli-4 gates, Toffoli-n gates, quantum Fourier transformation (QTF) circuits, and quantum Fourier adder (QFA) circuits. In certain instances, the use of global operations can substantially improve the entangling gate count.

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New Canaan, CT, United States of America

Dmitri Maslov