Abstract: A quantum error correcting code with dynamically generated logical qubits is provided. When viewed as a subsystem code, the code has no logical qubits. Nevertheless, the measurement patterns generate logical qubits, allowing the code to act as a fault-tolerant quantum memory. Each measurement can be a two-qubit Pauli measurement.

Abstract: A quantum computing device is provided, including a logical qubit encoding surface including a plurality of plaquettes. Each plaquette of the plurality of plaquettes may include a plurality of measurement-based qubits. The plurality of measurement-based qubits may include four data qubits and a first ancilla qubit. The first ancilla qubit may be electrically connected to the four data qubits and a second ancilla qubit included in the logical qubit encoding surface.

Abstract: Embodiments of the present disclosure include systems and methods for reducing a sample complexity and a time complexity associated with noise-robust characterization of a quantum device. A plurality of copies of a Gibbs state of the quantum device in thermal equilibrium at a high-temperature. A plurality of estimates for expectation values of the plurality of copies of the Gibbs state. A plurality of cluster derivatives for a plurality of connected clusters of a low-degree Hamiltonian are calculated. A function is inverted on the plurality of estimates based on the plurality of cluster derivatives and a set of Hamiltonian coefficients are estimated for the low-degree Hamiltonian of the quantum device.

Abstract: In some embodiments, one or more unitary-valued functions are generated by a classical computer generating using projectors with a predetermined number of significant bits. A quantum computing device is then configured to implement the one or more unitary-valued functions. In further embodiments, a quantum circuit description for implementing quantum signal processing that decomposes complex-valued periodic functions is generated by a classical computer, wherein the generating further includes representing approximate polynomials in a Fourier series with rational coefficients. A quantum computing device is then configured to implement a quantum circuit defined by the quantum circuit description.

Abstract: A quantum error correcting code with dynamically generated logical qubits is provided. When viewed as a subsystem code, the code has no logical qubits. Nevertheless, the measurement patterns generate logical qubits, allowing the code to act as a fault-tolerant quantum memory. Each measurement can be a two-qubit Pauli measurement.

Abstract: A quantum decoder receives a syndrome from a quantum measurement circuit and performs various decoding operations for processing-efficient fault detection. The decoding operations include generating a decoding graph from the syndrome and growing a cluster around each one of multiple check nodes in the graph that correspond to a non-trivial value in the syndrome. Each cluster includes the check node corresponding to the non-trivial value and a set of neighboring nodes positioned within a distance of d edge-lengths from the check node. Following cluster growth, the decoder determines if, for each cluster, there exists a solution set internal to the cluster that fully explains the non-trivial syndrome bit for the cluster. If so, the decoder identifies and returns at least one solution set that fully explains the set of non-trivial bits in the syndrome.

Abstract: Embodiments of the present disclosure include systems and methods for magic state distillation. A first matrix is generated based on a collection of indices that reference a second matrix. A set of compressed Clifford gates is determined based on the first matrix. The set of compressed Clifford gates is applied to a set of the qubits of a quantum processor. A set of magic states of the quantum processor are obtained as a result of application of the set of compressed Clifford gates. The quantum processor may be configured based on the magic states obtained.

Abstract: A quantum computing system implementing surface code in a measurement circuit may be configured to translate a quantum algorithm including at least one Hadamard gate into an equivalent circuit that lacks a Hadamard gate, the circuit including Hadamard-conjugated Pauli measurements that include joint logical measurements implemented on diagonally-arranged patches of the surface code.

Abstract: A quantum computing system implementing surface code in a measurement circuit may be configured to translate a quantum algorithm including at least one Hadamard gate into an equivalent circuit that lacks a Hadamard gate, the circuit including Hadamard-conjugated Pauli measurements that include joint logical measurements implemented on diagonally-arranged patches of the surface code.

Abstract: Examples are disclosed that relate to, on a quantum computing device, distilling magic states encoded in a [[n,k,d]] block code comprising an outer code. One example provides a method comprising preparing encoded noisy magic states using data qubits, and measuring Clifford stabilizers on the data qubits, thereby applying an inner code. The method further comprises initializing output qubits and initiating a teleportation of distilled magic states derived from the encoded noisy magic states to the output qubits. The method further comprises measuring X-stabilizers on the data qubits, postselecting based on the outcomes, measuring each data qubit destructively utilizing Z-stabilizers, and applying one or more postselection conditions to the data qubits to complete the teleportation of the distilled magic states to the output qubits.

Abstract: A quantum decoder receives a syndrome from a quantum measurement circuit and performs various decoding operations for processing-efficient fault detection. The decoding operations include generating a decoding graph from the syndrome and growing a cluster around each one of multiple check nodes in the graph that correspond to a non-trivial value in the syndrome. Each cluster includes the check node corresponding to the non-trivial value and a set of neighboring nodes positioned within a distance of d edge-lengths from the check node. Following cluster growth, the decoder determines if, for each cluster, there exists a solution set internal to the cluster that fully explains the non-trivial syndrome bit for the cluster. If so, the decoder identifies and returns at least one solution set that fully explains the set of non-trivial bits in the syndrome.

Abstract: Examples are disclosed that relate to, on a quantum computing device, distilling magic states encoded in a [[n,k,d]] block code comprising an outer code. One example provides a method comprising preparing encoded noisy magic states using data qubits, and measuring Clifford stabilizers on the data qubits, thereby applying an inner code. The method further comprises initializing output qubits and initiating a teleportation of distilled magic states derived from the encoded noisy magic states to the output qubits. The method further comprises measuring X-stabilizers on the data qubits, postselecting based on the outcomes, measuring each data qubit destructively utilizing Z-stabilizers, and applying one or more postselection conditions to the data qubits to complete the teleportation of the distilled magic states to the output qubits.

Abstract: Embodiments of the disclosed technology concern a quantum circuit configured to implement a real time evolution unitary of a Hamiltonian in a quantum computing device, wherein a unit time evolution unitary operator is decomposed into overlapping smaller blocks of unitary operators. In some implementations, (a) the size of the overlap is proportional to the logarithm of a number of qubits in the simulated system, (b) the size of the overlap is proportional to the logarithm of a total simulated evolution time, and/or (c) the size of the overlap is proportional to a Lieb-Robinson velocity.

Abstract: Disclosed herein are example embodiments of protocols to distill magic states for T-gates. Particular examples have low space overhead and use an asymptotically optimal number of input magic states to achieve a given target error. The space overhead, defined as the ratio between the physical qubits to the number of output magic states, is asymptotically constant, while both the number of input magic states used per output state and the T-gate depth of the circuit scale linearly in the logarithm of the target error. Unlike other distillation protocols, examples of the disclosed protocol achieve this performance without concatenation and the input magic states are injected at various steps in the circuit rather than all at the start of the circuit. Embodiments of the protocol can be modified to distill magic states for other gates at the third level of the Clifford hierarchy, with the same asymptotic performance.

Abstract: A quantum computing device is provided, including a logical qubit encoding surface including a plurality of plaquettes. Each plaquette of the plurality of plaquettes may include a plurality of measurement-based qubits. The plurality of measurement-based qubits may include four data qubits and a first ancilla qubit. The first ancilla qubit may be electrically connected to the four data qubits and a second ancilla qubit included in the logical qubit encoding surface.

Abstract: This application concerns quantum computing and quantum circuits. For example, among the embodiments disclosed herein are codes and protocols to distill T, controlled-S, and Toffoli (or CCZ) gates for use in croantum circuits. Examples of the disclosed codes use lower overhead for a given target accuracy relative to other distillation techniques. In some embodiments, a magic state distillation protocol is generated for creating magic states in the quantum computing device, wherein the magic state distillation protocol includes (a) Reed-Muller codes, or (b) punctured Reed-Muller codes. The quantum computing device can then configured to implement the magic state distillation protocol.

Abstract: Embodiments of the disclosed technology concern a quantum circuit configured to implement a real time evolution unitary of a Hamiltonian in a quantum computing device, wherein a unit time evolution unitary operator is decomposed into overlapping smaller blocks of unitary operators. In some implementations, (a) the size of the overlap is proportional to the logarithm of a number of qubits in the simulated system, (b) the size of the overlap is proportional to the logarithm of a total simulated evolution time, and/or (c) the size of the overlap is proportional to a Lieb-Robinson velocity.

Abstract: In some embodiments, one or more unitary-valued functions are generated by a classical computer generating using projectors with a predetermined number of significant bits. A quantum computing device is then configured to implement the one or more unitary-valued functions. In further embodiments, a quantum circuit description for implementing quantum signal processing that decomposes complex-valued periodic functions is generated by a classical computer, wherein the generating further includes representing approximate polynomials in a Fourier series with rational coefficients. A quantum computing device is then configured to implement a quantum circuit defined by the quantum circuit description.

Abstract: Disclosed herein are example embodiments of protocols to distill magic states for T-gates. Particular examples have low space overhead and use an asymptotically optimal number of input magic states to achieve a given target error. The space overhead, defined as the ratio between the physical qubits to the number of output magic states, is asymptotically constant, while both the number of input magic states used per output state and the T-gate depth of the circuit scale linearly in the logarithm of the target error. Unlike other distillation protocols, examples of the disclosed protocol achieve this performance without concatenation and the input magic states are injected at various steps in the circuit rather than all at the start of the circuit. Embodiments of the protocol can be modified to distill magic states for other gates at the third level of the Clifford hierarchy, with the same asymptotic performance.

Abstract: Disclosed herein are example embodiments of protocols to distill magic states for T-gates. Particular examples have low space overhead and use an asymptotically optimal number of input magic states to achieve a given target error. The space overhead, defined as the ratio between the physical qubits to the number of output magic states, is asymptotically constant, while both the number of input magic states used per output state and the T-gate depth of the circuit scale linearly in the logarithm of the target error. Unlike other distillation protocols, examples of the disclosed protocol achieve this performance without concatenation and the input magic states are injected at various steps in the circuit rather than all at the start of the circuit. Embodiments of the protocol can be modified to distill magic states for other gates at the third level of the Clifford hierarchy, with the same asymptotic performance.