HiddenLinearFunction

class HiddenLinearFunction(adjacency_matrix)

Circuit to solve the hidden linear function problem.

The 2D Hidden Linear Function problem is determined by a 2D adjacency matrix A, where only elements that are nearest-neighbor on a grid have non-zero entries. Each row/column corresponds to one binary variable \(x_i\).

The hidden linear function problem is as follows:

Consider the quadratic form

\[q(x) = \sum_{i,j=1}^{n}{x_i x_j} ~(\mathrm{mod}~ 4)\]

and restrict \(q(x)\) onto the nullspace of A. This results in a linear function.

\[2 \sum_{i=1}^{n}{z_i x_i} ~(\mathrm{mod}~ 4) \forall x \in \mathrm{Ker}(A)\]

and the goal is to recover this linear function (equivalently a vector \([z_0, ..., z_{n-1}]\)). There can be multiple solutions.

In [1] it is shown that the present circuit solves this problem on a quantum computer in constant depth, whereas any corresponding solution on a classical computer would require circuits that grow logarithmically with \(n\). Thus this circuit is an example of quantum advantage with shallow circuits.

Reference Circuit:

Reference:

[1] S. Bravyi, D. Gosset, R. Koenig, Quantum Advantage with Shallow Circuits, 2017. arXiv:1704.00690

Create new HLF circuit.

Parameters

adjacency_matrix (Union[List[List[int]], ndarray]) – a symmetric n-by-n list of 0-1 lists. n will be the number of qubits.

Attributes

HiddenLinearFunction.clbits	Returns a list of classical bits in the order that the registers were added.
HiddenLinearFunction.data	Return the circuit data (instructions and context).
HiddenLinearFunction.extension_lib
HiddenLinearFunction.header
HiddenLinearFunction.instances
HiddenLinearFunction.n_qubits	Deprecated, use num_qubits instead.
HiddenLinearFunction.num_clbits	Return number of classical bits.
HiddenLinearFunction.num_parameters	Convenience function to get the number of parameter objects in the circuit.
HiddenLinearFunction.num_qubits	Return number of qubits.
HiddenLinearFunction.parameters	Convenience function to get the parameters defined in the parameter table.
HiddenLinearFunction.prefix
HiddenLinearFunction.qubits	Returns a list of quantum bits in the order that the registers were added.

Methods

HiddenLinearFunction.AND(qr_variables, …)	Build a collective conjunction (AND) circuit in place using mct.
HiddenLinearFunction.OR(qr_variables, …[, …])	Build a collective disjunction (OR) circuit in place using mct.
HiddenLinearFunction.__getitem__(item)	Return indexed operation.
HiddenLinearFunction.__len__()	Return number of operations in circuit.
HiddenLinearFunction.add_register(*regs)	Add registers.
HiddenLinearFunction.append(instruction[, …])	Append one or more instructions to the end of the circuit, modifying the circuit in place.
HiddenLinearFunction.assign_parameters(…)	Assign parameters to new parameters or values.
HiddenLinearFunction.barrier(*qargs)	Apply Barrier.
HiddenLinearFunction.bind_parameters(value_dict)	Assign numeric parameters to values yielding a new circuit.
HiddenLinearFunction.cast(value, _type)	Best effort to cast value to type.
HiddenLinearFunction.cbit_argument_conversion(…)	Converts several classical bit representations (such as indexes, range, etc.) into a list of classical bits.
HiddenLinearFunction.ccx(control_qubit1, …)	Apply CCXGate.
HiddenLinearFunction.ch(control_qubit, …)	Apply CHGate.
HiddenLinearFunction.cls_instances()	Return the current number of instances of this class, useful for auto naming.
HiddenLinearFunction.cls_prefix()	Return the prefix to use for auto naming.
HiddenLinearFunction.cnot(control_qubit, …)	Apply CXGate.
HiddenLinearFunction.combine(rhs)	Append rhs to self if self contains compatible registers.
HiddenLinearFunction.compose(other[, …])	Compose circuit with other circuit or instruction, optionally permuting wires.
HiddenLinearFunction.copy([name])	Copy the circuit.
HiddenLinearFunction.count_ops()	Count each operation kind in the circuit.
HiddenLinearFunction.crx(theta, …[, …])	Apply CRXGate.
HiddenLinearFunction.cry(theta, …[, …])	Apply CRYGate.
HiddenLinearFunction.crz(theta, …[, …])	Apply CRZGate.
HiddenLinearFunction.cswap(control_qubit, …)	Apply CSwapGate.
HiddenLinearFunction.cu1(theta, …[, …])	Apply CU1Gate.
HiddenLinearFunction.cu3(theta, phi, lam, …)	Apply CU3Gate.
HiddenLinearFunction.cx(control_qubit, …)	Apply CXGate.
HiddenLinearFunction.cy(control_qubit, …)	Apply CYGate.
HiddenLinearFunction.cz(control_qubit, …)	Apply CZGate.
HiddenLinearFunction.dcx(qubit1, qubit2)	Apply DCXGate.
HiddenLinearFunction.decompose()	Call a decomposition pass on this circuit, to decompose one level (shallow decompose).
HiddenLinearFunction.depth()	Return circuit depth (i.e., length of critical path).
HiddenLinearFunction.diag_gate(diag, qubit)	Deprecated version of QuantumCircuit.diagonal.
HiddenLinearFunction.diagonal(diag, qubit)	Attach a diagonal gate to a circuit.
HiddenLinearFunction.draw([output, scale, …])	Draw the quantum circuit.
HiddenLinearFunction.extend(rhs)	Append QuantumCircuit to the right hand side if it contains compatible registers.
HiddenLinearFunction.fredkin(control_qubit, …)	Apply CSwapGate.
HiddenLinearFunction.from_qasm_file(path)	Take in a QASM file and generate a QuantumCircuit object.
HiddenLinearFunction.from_qasm_str(qasm_str)	Take in a QASM string and generate a QuantumCircuit object.
HiddenLinearFunction.h(qubit, *[, q])	Apply HGate.
HiddenLinearFunction.hamiltonian(operator, …)	Apply hamiltonian evolution to to qubits.
HiddenLinearFunction.has_register(register)	Test if this circuit has the register r.
HiddenLinearFunction.i(qubit, *[, q])	Apply IGate.
HiddenLinearFunction.id(qubit, *[, q])	Apply IGate.
HiddenLinearFunction.iden(qubit, *[, q])	Deprecated identity gate.
HiddenLinearFunction.initialize(params, qubits)	Apply initialize to circuit.
HiddenLinearFunction.inverse()	Invert this circuit.
HiddenLinearFunction.iso(isometry, q_input, …)	Attach an arbitrary isometry from m to n qubits to a circuit.
HiddenLinearFunction.isometry(isometry, …)	Attach an arbitrary isometry from m to n qubits to a circuit.
HiddenLinearFunction.iswap(qubit1, qubit2)	Apply iSwapGate.
HiddenLinearFunction.mcmt(gate, …[, …])	Apply a multi-control, multi-target using a generic gate.
HiddenLinearFunction.mcrx(theta, q_controls, …)	Apply Multiple-Controlled X rotation gate
HiddenLinearFunction.mcry(theta, q_controls, …)	Apply Multiple-Controlled Y rotation gate
HiddenLinearFunction.mcrz(lam, q_controls, …)	Apply Multiple-Controlled Z rotation gate
HiddenLinearFunction.mct(control_qubits, …)	Apply MCXGate.
HiddenLinearFunction.mcu1(lam, …)	Apply MCU1Gate.
HiddenLinearFunction.mcx(control_qubits, …)	Apply MCXGate.
HiddenLinearFunction.measure(qubit, cbit)	Measure quantum bit into classical bit (tuples).
HiddenLinearFunction.measure_active([inplace])	Adds measurement to all non-idle qubits.
HiddenLinearFunction.measure_all([inplace])	Adds measurement to all qubits.
HiddenLinearFunction.mirror()	Mirror the circuit by reversing the instructions.
HiddenLinearFunction.ms(theta, qubits)	Apply MSGate.
HiddenLinearFunction.num_connected_components([…])	How many non-entangled subcircuits can the circuit be factored to.
HiddenLinearFunction.num_nonlocal_gates()	Return number of non-local gates (i.e.
HiddenLinearFunction.num_tensor_factors()	Computes the number of tensor factors in the unitary (quantum) part of the circuit only.
HiddenLinearFunction.num_unitary_factors()	Computes the number of tensor factors in the unitary (quantum) part of the circuit only.
HiddenLinearFunction.qasm([formatted, filename])	Return OpenQASM string.
HiddenLinearFunction.qbit_argument_conversion(…)	Converts several qubit representations (such as indexes, range, etc.) into a list of qubits.
HiddenLinearFunction.r(theta, phi, qubit, *)	Apply RGate.
HiddenLinearFunction.rcccx(control_qubit1, …)	Apply RC3XGate.
HiddenLinearFunction.rccx(control_qubit1, …)	Apply RCCXGate.
HiddenLinearFunction.remove_final_measurements([…])	Removes final measurement on all qubits if they are present.
HiddenLinearFunction.reset(qubit)	Reset q.
HiddenLinearFunction.rx(theta, qubit, *[, …])	Apply RXGate.
HiddenLinearFunction.rxx(theta, qubit1, qubit2)	Apply RXXGate.
HiddenLinearFunction.ry(theta, qubit, *[, …])	Apply RYGate.
HiddenLinearFunction.ryy(theta, qubit1, qubit2)	Apply RYYGate.
HiddenLinearFunction.rz(phi, qubit, *[, q])	Apply RZGate.
HiddenLinearFunction.rzx(theta, qubit1, qubit2)	Apply RZXGate.
HiddenLinearFunction.rzz(theta, qubit1, qubit2)	Apply RZZGate.
HiddenLinearFunction.s(qubit, *[, q])	Apply SGate.
HiddenLinearFunction.sdg(qubit, *[, q])	Apply SdgGate.
HiddenLinearFunction.size()	Returns total number of gate operations in circuit.
HiddenLinearFunction.snapshot(label[, …])	Take a statevector snapshot of the internal simulator representation.
HiddenLinearFunction.snapshot_density_matrix(label)	Take a density matrix snapshot of simulator state.
HiddenLinearFunction.snapshot_expectation_value(…)	Take a snapshot of expectation value <O> of an Operator.
HiddenLinearFunction.snapshot_probabilities(…)	Take a probability snapshot of the simulator state.
HiddenLinearFunction.snapshot_stabilizer(label)	Take a stabilizer snapshot of the simulator state.
HiddenLinearFunction.snapshot_statevector(label)	Take a statevector snapshot of the simulator state.
HiddenLinearFunction.squ(unitary_matrix, qubit)	Decompose an arbitrary 2*2 unitary into three rotation gates.
HiddenLinearFunction.swap(qubit1, qubit2)	Apply SwapGate.
HiddenLinearFunction.t(qubit, *[, q])	Apply TGate.
HiddenLinearFunction.tdg(qubit, *[, q])	Apply TdgGate.
HiddenLinearFunction.to_gate([parameter_map])	Create a Gate out of this circuit.
HiddenLinearFunction.to_instruction([…])	Create an Instruction out of this circuit.
HiddenLinearFunction.toffoli(control_qubit1, …)	Apply CCXGate.
HiddenLinearFunction.u1(theta, qubit, *[, q])	Apply U1Gate.
HiddenLinearFunction.u2(phi, lam, qubit, *)	Apply U2Gate.
HiddenLinearFunction.u3(theta, phi, lam, …)	Apply U3Gate.
HiddenLinearFunction.uc(gate_list, …[, …])	Attach a uniformly controlled gates (also called multiplexed gates) to a circuit.
HiddenLinearFunction.ucg(angle_list, …[, …])	Deprecated version of uc.
HiddenLinearFunction.ucrx(angle_list, …)	Attach a uniformly controlled (also called multiplexed) Rx rotation gate to a circuit.
HiddenLinearFunction.ucry(angle_list, …)	Attach a uniformly controlled (also called multiplexed) Ry rotation gate to a circuit.
HiddenLinearFunction.ucrz(angle_list, …)	Attach a uniformly controlled (also called multiplexed gates) Rz rotation gate to a circuit.
HiddenLinearFunction.ucx(angle_list, …)	Deprecated version of ucrx.
HiddenLinearFunction.ucy(angle_list, …)	Deprecated version of ucry.
HiddenLinearFunction.ucz(angle_list, …)	Deprecated version of ucrz.
HiddenLinearFunction.unitary(obj, qubits[, …])	Apply unitary gate to q.
HiddenLinearFunction.width()	Return number of qubits plus clbits in circuit.
HiddenLinearFunction.x(qubit, *[, label, …])	Apply XGate.
HiddenLinearFunction.y(qubit, *[, q])	Apply YGate.
HiddenLinearFunction.z(qubit, *[, q])	Apply ZGate.
HiddenLinearFunction.__getitem__(item)	Return indexed operation.
HiddenLinearFunction.__len__()	Return number of operations in circuit.