Microsoft Technology Licensing, LLC

Michael Edward Beverland

Nicolas Guillaume Delfosse

Jeongwan Haah

Vadym Kliuchnikov

Maxime Tremblay

Rui Chao

Alexander Vaschillo

Christopher Anand Pattison

Adam Edward Paetznick

Marcus Palmer Da Silva

Vivien Londe

Christopher Chamberland

Dmitry Vasilevsky

Eddie Schoute

A computing system including one or more processing devices configured to receive a stabilizer channel sequence of three or more stabilizer channels and respective fault sets. The one or more processing devices compute a lower-bound channel distance of the stabilizer channel sequence at least in part by computing lower-bound channel distances of compositions of adjacent pairs of stabilizer channels. For a stabilizer channel and a plurality of partition timestep counts, computing the lower-bound channel distance further includes receiving an indication of whether there exists a partition of the fault set of that stabilizer channel that has that partition timestep count and for which the stabilizer channel is time-local. Computing the lower-bound channel distance further includes selecting a lowest value among the lower-bound channel distances of the compositions and each of the partition timestep counts that has a time-locality-satisfying partition. The one or more processing devices output the lower-bound channel distance.

Lower-bounding distance of stabilizer channel sequence

A computing system including one or more processing devices configured to identify one or more severe hook faults in a stabilizer channel. Identifying the severe hook faults includes receiving a circuit channel check matrix, the columns of which indicate values of checks associated with elementary faults of the stabilizer channel. Identifying the severe hook faults further includes receiving a phenomenological channel check matrix as a sub-matrix of the circuit channel check matrix, receiving a logical effect matrix, and receiving a weight vector that indicates probability weights of the elementary faults. Based at least in part on the circuit channel check matrix, the logical effect matrix, the phenomenological channel check matrix, and the weight vector, identifying the severe hook faults further includes computing column indices of columns of the circuit channel check matrix that correspond to the severe hook faults. The processing devices output an indication of the severe hook faults.

Identifying severe hook faults of stabilizer channel

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.

Logical qubit encoding surface

A quantum measurement circuit implements a hypergraph product code (HPG). A syndrome can be extracted from the circuit by preparing a readout qubit of the quantum measurement circuit in a known state, preparing a row-based measurement gadget, and preparing a column-based measurement gadget in the quantum measurement circuit. The row-based measurement gadget entangles the readout qubit with a first subset of the target set of data qubits in a same row of the quantum measurement circuit as the readout qubit, and the column based gadget entangles the readout qubit with a second subset of the target set of data qubits in a same column of the quantum measurement circuit as the readout qubit. The syndrome is extracted by measuring the readout qubit to extract the parity of the target set of data qubits.

Short-depth syndrome extraction circuits in 2D quantum architectures for hypergraph product codes

A computing system including a processor configured to receive a stabilizer circuit specification of a stabilizer circuit that includes one or more elementary operations. The elementary operations are each selected from the group consisting of an allocation of one or more qubits in a stabilizer state, an allocation of one or more random classical bits, a Clifford unitary, a Pauli unitary conditional on respective parities of measurement outcomes and/or respective parities of the random classical bits, a joint multi-qubit Pauli measurement, and a destructive one-qubit Pauli measurement. The processor is further configured to compute a standardized stabilizer instrument specification of a stabilizer instrument based at least in part on the stabilizer circuit specification. The standardized stabilizer instrument specification includes an input Clifford unitary, an output Clifford unitary, and a plurality of bit matrices. The processor is further configured to store the standardized stabilizer instrument specification in memory.

Stabilizer instrument specification for stabilizer circuit

A method for performing long-range multi-qubit measurements in a quantum circuit utilizes a graph that maps qubits of the quantum circuit to nodes that are connected to one another by edges. The method provides for identifying sets of the nodes on the graph corresponding to sets of qubits targeted by multi-qubit operations in a quantum algorithm and for defining a group of edge-disjoint paths connecting the nodes of each set. The group of edge-disjoint paths is defined such that no two of the paths in the group share an edge. The method further provides for performing a set of operations to entangle the qubits corresponding to the to the identified set of nodes that are included in each path in the group and for performing the set of multi-qubit operations on the entangled sets of the qubits.

Edge-disjoint paths for long-range multi-qubit operations in quantum circuit

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.

Union-find decoder for LDPC codes

A quantum computing system computes soft information quantifying an effect of soft noise on multiple rounds of a syndrome measurement that is output by a quantum measurement circuit. The soft noise arises due to imperfections in a readout device that introduce variability in repeated measurements of ancilla qubits and is distinct from quantum noise arising from bit-flips in data qubits that are indirectly measured by the ancilla qubits. The quantum computing system applying decoding logic to identify fault locations within the quantum measurement circuit based on the computed soft information.

Quantum error correction with realistic measurement data

A disclosed methodology for syndrome extraction in a quantum measurement circuit includes generating a graph representing a code implemented by the quantum measurement circuit. The graph includes bit nodes corresponding to data qubits in the quantum measurement circuit, check nodes corresponding to syndrome qubits in the quantum measurement circuit, and edges between the bit nodes and check nodes that are each associated with a stabilizer measurement provided by the code. The methodology provides for assigning each of the different edges in the graph to a select one of 'G' number of different edge types and performing at least G-number of temporally-separated rounds of qubit operations that each enact concurrent multi-qubit operations on endpoints of a subset of the edges assigned to a same one of the G different edge types.

Short-depth syndrome extraction circuits for Calderbank Shor Steane (CSS) stabilizer codes

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.

Joint logical measurements on diagonal patches of surface code

Fault-tolerant error correction (EC) is desirable for performing large quantum computations. In this disclosure, example fault-tolerant EC protocols are disclosed that use flag circuits, which signal when errors resulting from &#x3c5; faults have weight greater than &#x3c5;. Also disclosed are general constructions for these circuits (also referred to as flag qubits) for measuring arbitrary weight stabilizers. The example flag EC protocol is applicable to stabilizer codes of arbitrary distance that satisfy a set of conditions and uses fewer qubits than other schemes, such as Shor, Steane and Knill error correction. Also disclosed are examples of infinite code families that satisfy these conditions and analyze the behaviour of distance-three and -five examples numerically. Using fewer resources than Shor EC, the example flag EC protocols can be used in low-overhead fault-tolerant EC protocols using large low density parity check quantum codes.

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Michael Edward Beverland