Advanced Features Tutorial

This tutorial covers advanced simulation techniques in ATLAS-Q including circuit cutting, PEPS for 2D systems, Clifford circuit simulation, distributed computing, noise modeling, and custom optimization strategies for research and production use.

Prerequisites

Before starting this tutorial, you should:

• Have completed basic MPS tutorials (see MPS Basics)

• Understand variational algorithms (see VQE Tutorial, QAOA Tutorial)

• Be familiar with multi-GPU or multi-node computing concepts

• Know tensor network basics and entanglement structure

• Have experience with Python profiling and performance analysis

Learning Objectives

By the end of this tutorial, you will be able to:

1. Use circuit cutting to simulate large circuits with limited resources

2. Apply PEPS to efficiently simulate 2D quantum systems

3. Leverage stabilizer backend for fast Clifford circuit simulation

4. Deploy distributed MPS across multiple GPUs or compute nodes

5. Model realistic quantum noise with custom channels

6. Implement constrained and multi-objective optimization

7. Profile simulations to identify performance bottlenecks

8. Troubleshoot advanced simulation issues

Part 1: Circuit Cutting and Distribution

What is Circuit Cutting?

Circuit cutting decomposes large quantum circuits into smaller subcircuits that fit on available hardware or simulation resources. This trades circuit depth for classical post-processing: instead of simulating one large circuit, we simulate many small circuits and combine results.

For a circuit with \(n\) qubits cut into \(k\) partitions, the overhead is exponential in the number of cuts \(c\): typically \(O(4^c)\) subcircuits. This is worthwhile when \(n\) is too large but \(c\) is small.

Why Cut Circuits?

Circuit cutting is valuable when:

• Full circuit exceeds memory or qubit capacity

• Circuit has sparse connectivity (natural cutting points)

• Simulating on distributed hardware without direct qubit communication

• Prototyping algorithms before full-scale hardware is available

The technique is particularly effective for modular circuits where subsystems have limited entanglement.

Implementing Circuit Cutting

from atlas_q.circuit_cutting import CircuitCutter, CuttingConfig
from atlas_q.adaptive_mps import AdaptiveMPS
import torch

# Define a large circuit (30 qubits)
def build_large_circuit():
    """Circuit too large for direct simulation."""
    gates = []

    # Layer 1: Local Hadamards
    for i in range(30):
        gates.append(('H', [i], []))

    # Layer 2: Nearest-neighbor CNOTs (creates entanglement)
    for i in range(29):
        gates.append(('CNOT', [i, i+1], []))

    # Layer 3: More local rotations
    for i in range(30):
        gates.append(('RZ', [i], [0.5]))

    # Sparse long-range gates (cutting targets)
    gates.append(('CNOT', [0, 15], []))
    gates.append(('CNOT', [14, 29], []))

    return gates

# Configure circuit cutter
config = CuttingConfig(
    max_partition_size=10,  # Each partition ≤ 10 qubits
    max_cuts=2,             # Allow up to 2 cuts
    optimization='min_cuts' # Minimize number of cuts
)

cutter = CircuitCutter(config)

# Partition the circuit
gates = build_large_circuit()
partitions, cut_locations = cutter.partition_circuit(gates, n_partitions=3)

print(f"Original circuit: 30 qubits, {len(gates)} gates")
print(f"Partitioned into {len(partitions)} subcircuits with {len(cut_locations)} cuts")

for i, part in enumerate(partitions):
    print(f"  Partition {i}: {part.n_qubits} qubits, {len(part.gates)} gates")

# Simulate each partition independently
results = []
for i, partition in enumerate(partitions):
    mps = AdaptiveMPS(num_qubits=partition.n_qubits, bond_dim=32, device='cuda')

    for gate_name, qubits, params in partition.gates:
        if gate_name == 'H':
            H = torch.tensor([[1, 1], [1, -1]], dtype=torch.complex64, device='cuda') / torch.sqrt(torch.tensor(2.0))
            mps.apply_single_qubit_gate(qubits[0], H)
        elif gate_name == 'CNOT':
            mps.apply_cnot(qubits[0], qubits[1])
        # ... other gates ...

    results.append(mps)

# Combine results (classical post-processing)
final_result = cutter.reconstruct(results, cut_locations)
print(f"Final expectation value: {final_result:.8f}")

Adaptive Cutting Strategies

# Different cutting strategies for different circuit structures
strategies = ['min_cuts', 'balanced_size', 'min_entanglement']

for strategy in strategies:
    config = CuttingConfig(
        max_partition_size=12,
        max_cuts=3,
        optimization=strategy
    )
    cutter = CircuitCutter(config)
    partitions, cuts = cutter.partition_circuit(gates, n_partitions=3)

    overhead = 4 ** len(cuts)  # Classical overhead
    print(f"{strategy:20s}: {len(cuts)} cuts, overhead = {overhead}x")

Part 2: PEPS for 2D Systems

Projected Entangled Pair States

PEPS generalize MPS to 2D lattices. Instead of a 1D chain of tensors, PEPS arrange tensors on a 2D grid where each tensor connects to 4 neighbors (up, down, left, right). This captures area-law entanglement scaling natural to 2D systems.

PEPS are ideal for:

• 2D materials and spin models

• Quantum error correction codes (surface code)

• Shallow circuits on 2D architectures

Implementing 2D Simulations

from atlas_q.peps import PatchPEPS

# Simulate 4×4 qubit grid
patch = PatchPEPS(
    patch_size=4,
    bond_dim=8,
    device='cuda'
)

# Apply 2D circuit
# Coordinates are (row, col)
gates_2d = [
    # Layer 1: Hadamards on all qubits
    *[('H', [(i, j)], []) for i in range(4) for j in range(4)],

    # Layer 2: Horizontal CNOTs
    *[('CZ', [(i, j), (i, j+1)], []) for i in range(4) for j in range(3)],

    # Layer 3: Vertical CNOTs
    *[('CZ', [(i, j), (i+1, j)], []) for i in range(3) for j in range(4)]
]

# Apply gates
for gate_name, qubits, params in gates_2d:
    if gate_name == 'H':
        patch.apply_single_site_gate(qubits[0], 'H')
    elif gate_name == 'CZ':
        patch.apply_two_site_gate(qubits[0], qubits[1], 'CZ')

# Measure observable
magnetization = patch.measure_magnetization()
print(f"Total magnetization: {magnetization:.6f}")

# Sample final state
bitstring_2d = patch.sample()
print(f"Sample configuration:\n{bitstring_2d}")

Surface Code Simulation

# Simulate distance-3 surface code (5×5 qubits)
def surface_code_stabilizers(distance=3):
    """Generate stabilizer measurements for surface code."""
    size = 2 * distance - 1
    patch = PatchPEPS(patch_size=size, bond_dim=16, device='cuda')

    # Initialize |+⟩ state
    for i in range(size):
        for j in range(size):
            patch.apply_single_site_gate((i, j), 'H')

    # Apply stabilizer measurements
    # X-stabilizers (plaquettes)
    for i in range(0, size-1, 2):
        for j in range(1, size-1, 2):
            qubits = [(i, j), (i+1, j), (i, j-1), (i, j+1)]
            syndrome_x = patch.measure_stabilizer(qubits, pauli_type='X')

    # Z-stabilizers (vertices)
    for i in range(1, size-1, 2):
        for j in range(0, size-1, 2):
            qubits = [(i, j), (i, j+1), (i-1, j), (i+1, j)]
            syndrome_z = patch.measure_stabilizer(qubits, pauli_type='Z')

    return patch

# Run surface code
patch_sc = surface_code_stabilizers(distance=3)
error_rate = patch_sc.estimate_logical_error_rate()
print(f"Logical error rate: {error_rate:.4e}")

Part 3: Stabilizer Backend

Clifford Circuits and Stabilizers

The stabilizer formalism provides exponentially faster simulation for Clifford circuits (gates: H, S, CNOT, CZ). The Gottesman-Knill theorem states Clifford circuits can be simulated efficiently classically using stabilizer tableaux.

Stabilizer simulation is \(O(n^2)\) per gate for \(n\) qubits, compared to \(O(2^n)\) for full statevector simulation. This enables simulation of 1000+ qubit Clifford circuits.

Fast Clifford Simulation

from atlas_q.stabilizer_backend import StabilizerSimulator

# Simulate large Clifford circuit
sim = StabilizerSimulator(n_qubits=200)

# Apply Clifford gates
for i in range(200):
    sim.h(i)

for i in range(199):
    sim.cnot(i, i+1)

for i in range(0, 200, 2):
    sim.s(i)

# Measure in Z basis
outcomes = []
for i in range(200):
    outcome = sim.measure(i)
    outcomes.append(outcome)

print(f"Measurement outcomes (first 20): {outcomes[:20]}")

# Check stabilizers
stabilizers = sim.get_stabilizers()
print(f"Number of independent stabilizers: {len(stabilizers)}")

Use Cases

Stabilizer backend is ideal for:

1. Quantum error correction: Simulate encoding/decoding circuits

2. Circuit verification: Check if circuit is Clifford

3. Magic state distillation: Clifford part of fault-tolerant protocols

4. Debugging: Fast validation before expensive full simulation

# Verify circuit is Clifford before full simulation
def is_clifford_circuit(gates):
    """Check if gate sequence contains only Clifford gates."""
    clifford_gates = {'H', 'S', 'CNOT', 'CZ', 'X', 'Y', 'Z'}
    return all(gate[0] in clifford_gates for gate in gates)

# Example workflow
gates = [('H', [0], []), ('CNOT', [0, 1], []), ('S', [1], [])]

if is_clifford_circuit(gates):
    # Use fast stabilizer simulation
    sim = StabilizerSimulator(n_qubits=10)
    for gate_name, qubits, _ in gates:
        if gate_name == 'H':
            sim.h(qubits[0])
        elif gate_name == 'CNOT':
            sim.cnot(qubits[0], qubits[1])
        elif gate_name == 'S':
            sim.s(qubits[0])
    print("Used fast Clifford simulation")
else:
    # Use full MPS simulation
    mps = AdaptiveMPS(num_qubits=10, bond_dim=32, device='cuda')
    # ... apply gates ...
    print("Used full MPS simulation")

Part 4: Distributed MPS

Multi-GPU and Multi-Node Parallelism

Distributed MPS partitions tensors across multiple devices to overcome single-device memory limits and accelerate computation through parallelism.

Two distribution strategies:

• Bond-parallel: Split along bond dimension, useful for large χ

• Qubit-parallel: Split along qubit index, useful for many qubits

from atlas_q.distributed_mps import DistributedMPS, DistributedConfig

# Bond-parallel distribution (4 GPUs)
config_bond = DistributedConfig(
    mode='bond_parallel',
    world_size=4,           # Use 4 devices
    backend='nccl',         # NCCL for GPU communication
    compression=True        # Compress communications
)

mps_bond = DistributedMPS(
    num_qubits=50,
    bond_dim=256,          # 256 split across 4 GPUs = 64 per GPU
    config=config_bond
)

print(f"Bond dimension per device: {256 // 4}")

# Qubit-parallel distribution
config_qubit = DistributedConfig(
    mode='qubit_parallel',
    world_size=4
)

mps_qubit = DistributedMPS(
    num_qubits=200,        # 200 qubits split across 4 GPUs = 50 per GPU
    bond_dim=64,
    config=config_qubit
)

print(f"Qubits per device: {200 // 4}")

Communication Patterns

import time

# Apply gates and measure communication overhead
mps = DistributedMPS(num_qubits=100, bond_dim=128, config=config_bond)

# Local gates (no communication)
start = time.time()
for i in range(100):
    mps.apply_local_gate(i, 'H')
t_local = time.time() - start

# Two-qubit gates (require communication if qubits on different devices)
start = time.time()
for i in range(99):
    mps.apply_cnot(i, i+1)
t_two_qubit = time.time() - start

# Expectation values (global communication for reduction)
start = time.time()
energy = mps.expectation(H)
t_expectation = time.time() - start

print(f"Local gates: {t_local:.3f}s")
print(f"Two-qubit gates: {t_two_qubit:.3f}s (includes communication)")
print(f"Expectation value: {t_expectation:.3f}s (includes reduction)")

Scaling Analysis

# Benchmark scaling with number of devices
world_sizes = [1, 2, 4, 8]
times = []

for ws in world_sizes:
    config = DistributedConfig(mode='bond_parallel', world_size=ws)
    mps = DistributedMPS(num_qubits=100, bond_dim=256, config=config)

    # Benchmark gate application
    start = time.time()
    for _ in range(1000):
        mps.apply_cnot(50, 51)  # Central qubits
    elapsed = time.time() - start

    times.append(elapsed)
    speedup = times[0] / elapsed if ws > 1 else 1.0
    efficiency = speedup / ws

    print(f"World size {ws}: {elapsed:.2f}s, speedup {speedup:.2f}x, efficiency {efficiency:.2%}")

# Expected output:
# World size 1: 5.23s, speedup 1.00x, efficiency 100%
# World size 2: 2.87s, speedup 1.82x, efficiency 91%
# World size 4: 1.65s, speedup 3.17x, efficiency 79%
# World size 8: 1.12s, speedup 4.67x, efficiency 58%

Part 5: Noise Models

Depolarizing Noise

Depolarizing channels model uniform errors: with probability \(p\), apply random Pauli (X, Y, Z):

\[\mathcal{E}(\rho) = (1-p)\rho + \frac{p}{3}(X\rho X + Y\rho Y + Z\rho Z)\]

from atlas_q.noise_models import NoiseModel

# Depolarizing noise for single and two-qubit gates
noise = NoiseModel.depolarizing(
    p1q=0.001,   # 0.1% error rate for single-qubit gates
    p2q=0.01,    # 1% error rate for two-qubit gates
    device='cuda'
)

# Apply noisy gates to MPS
mps = AdaptiveMPS(num_qubits=20, bond_dim=64, device='cuda')
mps.set_noise_model(noise)

# Gates are now automatically noisy
H = torch.tensor([[1, 1], [1, -1]], dtype=torch.complex64, device='cuda') / torch.sqrt(torch.tensor(2.0))
mps.apply_single_qubit_gate(0, H)  # Applied with 0.1% depolarizing noise
mps.apply_cnot(0, 1)               # Applied with 1% depolarizing noise

# Measure fidelity degradation
ideal_mps = AdaptiveMPS(num_qubits=20, bond_dim=64, device='cuda')
ideal_mps.apply_single_qubit_gate(0, H)
ideal_mps.apply_cnot(0, 1)

fidelity = mps.fidelity(ideal_mps)
print(f"State fidelity after noisy gates: {fidelity:.6f}")

Amplitude and Phase Damping

Model T1 and T2 decoherence:

# Amplitude damping (T1 decay, energy relaxation)
noise_t1 = NoiseModel.amplitude_damping(
    gamma=0.01,  # Decay rate
    device='cuda'
)

# Phase damping (T2 decay, dephasing)
noise_t2 = NoiseModel.phase_damping(
    lambda_=0.005,  # Dephasing rate
    device='cuda'
)

# Combined T1 and T2
noise_t1t2 = NoiseModel.t1_t2_noise(
    t1=50e-6,   # T1 time (seconds)
    t2=30e-6,   # T2 time (seconds)
    gate_time=50e-9,  # Gate duration (nanoseconds)
    device='cuda'
)

# Apply to simulation
mps.set_noise_model(noise_t1t2)

Custom Noise Channels

Define arbitrary noise channels:

import torch

# Custom noise: preferential X errors
def x_biased_noise(p_x=0.01, p_y=0.001, p_z=0.001):
    """Noise biased toward X errors."""
    def channel(rho):
        X = torch.tensor([[0, 1], [1, 0]], dtype=torch.complex64)
        Y = torch.tensor([[0, -1j], [1j, 0]], dtype=torch.complex64)
        Z = torch.tensor([[1, 0], [0, -1]], dtype=torch.complex64)

        p_total = p_x + p_y + p_z
        return (1 - p_total) * rho + p_x * (X @ rho @ X) + p_y * (Y @ rho @ Y) + p_z * (Z @ rho @ Z)

    return NoiseModel.from_kraus_operators(
        [torch.sqrt(torch.tensor(1 - p_x - p_y - p_z)) * torch.eye(2),
         torch.sqrt(torch.tensor(p_x)) * X,
         torch.sqrt(torch.tensor(p_y)) * Y,
         torch.sqrt(torch.tensor(p_z)) * Z],
        device='cuda'
    )

noise_biased = x_biased_noise(p_x=0.02, p_y=0.001, p_z=0.001)
mps.set_noise_model(noise_biased)

Part 6: Advanced Optimization Techniques

Constrained Optimization

Optimize VQE subject to constraints:

from atlas_q.vqe_qaoa import VQE, VQEConfig
from atlas_q.mpo_ops import MPOBuilder

# Problem Hamiltonian
H = MPOBuilder.heisenberg_hamiltonian(n_sites=12, Jx=1.0, Jy=1.0, Jz=1.0, device='cuda')

# Constraint: total spin Sz must be zero
Sz_total = MPOBuilder.total_spin_z(n_sites=12, device='cuda')

# Configure constrained VQE
config = VQEConfig(
    ansatz='hardware_efficient',
    n_layers=4,
    max_iter=200,
    optimizer='SLSQP',  # Supports constraints
    constraints=[
        {'type': 'eq', 'fun': lambda params: Sz_total.expectation(params)}
    ],
    device='cuda'
)

vqe = VQE(H, config)
energy, params = vqe.optimize()

print(f"Constrained energy: {energy:.8f}")
print(f"Sz constraint violation: {abs(Sz_total.expectation(params)):.2e}")

Multi-Objective VQE

Optimize multiple objectives simultaneously:

# Objectives: minimize energy AND maximize entanglement
H1 = MPOBuilder.heisenberg_hamiltonian(n_sites=10, Jx=1.0, Jy=1.0, Jz=1.0, device='cuda')
H2_entanglement = MPOBuilder.entanglement_hamiltonian(n_sites=10, device='cuda')

def multi_objective_loss(params, weights=[0.8, 0.2]):
    """Weighted combination of objectives."""
    E1 = vqe_obj1.energy(params)
    E2 = -vqe_obj2.entanglement(params)  # Maximize entanglement = minimize negative
    return weights[0] * E1 + weights[1] * E2

config = VQEConfig(
    ansatz='hardware_efficient',
    n_layers=3,
    max_iter=200,
    custom_loss=multi_objective_loss,
    device='cuda'
)

vqe_multi = VQE(H1, config)
energy, params = vqe_multi.optimize()

print(f"Energy: {H1.expectation(params):.6f}")
print(f"Entanglement: {-H2_entanglement.expectation(params):.6f}")

Adaptive Circuits

Dynamically adjust circuit structure during optimization:

# Start with shallow circuit, add layers if not converged
for n_layers in range(1, 10):
    config = VQEConfig(
        ansatz='hardware_efficient',
        n_layers=n_layers,
        max_iter=100,
        tol=1e-6,
        device='cuda'
    )

    vqe = VQE(H, config)
    energy, params = vqe.optimize()

    # Check convergence
    gradient_norm = vqe.get_history()['gradient_norms'][-1]

    print(f"Layers {n_layers}: E = {energy:.8f}, grad_norm = {gradient_norm:.2e}")

    if gradient_norm < 1e-6:
        print(f"Converged with {n_layers} layers")
        break

Part 7: Performance Profiling

Timing Analysis

Identify computational bottlenecks:

import time
from atlas_q.diagnostics import MPSStatistics

mps = AdaptiveMPS(num_qubits=30, bond_dim=64, device='cuda')
stats = MPSStatistics()

# Time gate operations
H = torch.tensor([[1, 1], [1, -1]], dtype=torch.complex64, device='cuda') / torch.sqrt(torch.tensor(2.0))

start = time.time()
for i in range(30):
    mps.apply_single_qubit_gate(i, H)
t_single = time.time() - start

start = time.time()
for i in range(29):
    mps.apply_cnot(i, i+1)
t_two_qubit = time.time() - start

start = time.time()
for i in range(30):
    mps.canonicalize(center=i)
t_canonicalize = time.time() - start

print(f"Single-qubit gates: {t_single*1000:.1f} ms ({t_single/30*1000:.2f} ms per gate)")
print(f"Two-qubit gates: {t_two_qubit*1000:.1f} ms ({t_two_qubit/29*1000:.2f} ms per gate)")
print(f"Canonicalization: {t_canonicalize*1000:.1f} ms ({t_canonicalize/30*1000:.2f} ms per site)")

# Use stats summary
summary = mps.stats_summary()
print(f"\nTotal operations: {summary['total_operations']}")
print(f"Total time: {summary['total_time_ms']:.1f} ms")
print(f"Average operation time: {summary['total_time_ms']/summary['total_operations']:.3f} ms")

Memory Profiling

Track memory usage:

import torch.cuda

# Monitor GPU memory
def profile_memory(func, *args, **kwargs):
    """Profile GPU memory usage of function."""
    torch.cuda.reset_peak_memory_stats()
    torch.cuda.synchronize()

    initial_mem = torch.cuda.memory_allocated() / 1024**3  # GB

    result = func(*args, **kwargs)

    torch.cuda.synchronize()
    final_mem = torch.cuda.memory_allocated() / 1024**3
    peak_mem = torch.cuda.max_memory_allocated() / 1024**3

    print(f"Initial memory: {initial_mem:.2f} GB")
    print(f"Final memory: {final_mem:.2f} GB")
    print(f"Peak memory: {peak_mem:.2f} GB")
    print(f"Delta: {final_mem - initial_mem:.2f} GB")

    return result

# Profile VQE optimization
def run_vqe():
    H = MPOBuilder.heisenberg_hamiltonian(n_sites=20, Jx=1.0, Jy=1.0, Jz=1.0, device='cuda')
    config = VQEConfig(ansatz='hardware_efficient', n_layers=3, max_iter=50, device='cuda')
    vqe = VQE(H, config)
    return vqe.optimize()

energy, params = profile_memory(run_vqe)

Bottleneck Identification

Use profiling to find slow operations:

import cProfile
import pstats

# Profile VQE run
profiler = cProfile.Profile()
profiler.enable()

H = MPOBuilder.heisenberg_hamiltonian(n_sites=15, Jx=1.0, Jy=1.0, Jz=1.0, device='cuda')
config = VQEConfig(ansatz='hardware_efficient', n_layers=3, max_iter=30, device='cuda')
vqe = VQE(H, config)
energy, params = vqe.optimize()

profiler.disable()

# Print stats
stats = pstats.Stats(profiler)
stats.sort_stats('cumulative')
stats.print_stats(20)  # Top 20 functions

# Expected bottlenecks:
# - apply_two_site_gate (most time in entangling gates)
# - svd (truncation overhead)
# - expectation (Hamiltonian evaluation)

Part 8: Troubleshooting

Problem: Out of Memory Errors

Symptoms: CUDA out of memory, allocation failures

Solutions:

1. Reduce bond dimension:

   mps = AdaptiveMPS(num_qubits=30, bond_dim=32, device='cuda')  # Instead of 128
   

2. Use CPU for large systems:

   mps = AdaptiveMPS(num_qubits=50, bond_dim=64, device='cpu')
   

3. Enable distributed mode:

   config = DistributedConfig(mode='bond_parallel', world_size=2)
   mps = DistributedMPS(num_qubits=50, bond_dim=128, config=config)
   

Problem: Distributed Simulation Hangs

Symptoms: Process stuck, no progress, timeouts

Solutions:

1. Check communication backend:

   config = DistributedConfig(
       mode='qubit_parallel',
       world_size=4,
       backend='nccl',  # Try 'gloo' if NCCL fails
       timeout=300      # Increase timeout
   )
   

2. Verify device placement:

   # Ensure each process uses different GPU
   import os
   local_rank = int(os.environ.get('LOCAL_RANK', 0))
   torch.cuda.set_device(local_rank)
   

3. Enable debug logging:

   import logging
   logging.basicConfig(level=logging.DEBUG)
   # Watch for communication deadlocks
   

Problem: Noise Simulation is Too Slow

Symptoms: Noisy simulation 100× slower than ideal

Solutions:

1. Increase truncation tolerance for noisy states:

   mps = AdaptiveMPS(
       num_qubits=20,
       bond_dim=64,
       truncation_threshold=1e-4,  # Less strict for noisy states
       device='cuda'
   )
   

2. Use approximate noise models:

   # Depolarizing instead of full Kraus
   noise = NoiseModel.depolarizing(p1q=0.001, p2q=0.01, device='cuda')
   

3. Apply noise only to critical gates:

   # Apply noise selectively
   mps.apply_cnot(0, 1, noise=True)   # Noisy two-qubit gate
   mps.apply_single_qubit_gate(0, H, noise=False)  # Ideal single-qubit gate
   

Problem: Circuit Cutting Overhead Too High

Symptoms: 1000× overhead, impractical runtimes

Solutions:

1. Minimize cuts:

   config = CuttingConfig(
       max_cuts=2,  # Strict limit
       optimization='min_cuts'
   )
   

2. Restructure circuit to reduce entanglement:

   # Reorder gates to localize interactions
   # Use SWAP networks to bring interacting qubits together
   

3. Use hybrid simulation:

   # Cut only hard-to-simulate parts
   # Simulate easy parts with full MPS
   

Summary

This tutorial covered advanced ATLAS-Q features:

✓ Circuit cutting to partition large circuits with controlled overhead ✓ PEPS for efficient simulation of 2D quantum systems ✓ Stabilizer backend for fast Clifford circuit simulation ✓ Distributed MPS for multi-GPU and multi-node scaling ✓ Noise models including depolarizing, amplitude damping, and custom channels ✓ Constrained and multi-objective optimization for VQE ✓ Performance profiling to identify and resolve bottlenecks ✓ Troubleshooting techniques for advanced simulation challenges

These techniques enable research-grade simulations of complex quantum systems beyond basic MPS capabilities.

Next Steps

• MPS Basics - Review MPS fundamentals

• VQE Tutorial - Apply advanced techniques to VQE

• How to Optimize Performance - Deep dive into performance tuning

• Design Decisions - Understand architectural choices

Practice Exercises

1. Cut a 50-qubit circuit into 5 partitions and measure overhead vs accuracy trade-off

2. Simulate a 6×6 surface code using PEPS and estimate logical error rate

3. Benchmark stabilizer vs full MPS simulation for random Clifford circuits up to 500 qubits

4. Implement distributed VQE across 4 GPUs and measure scaling efficiency

5. Design a custom noise model for specific hardware and validate against experimental data

See Also

• Circuit Cutting - Circuit cutting API

• PEPS (2D Tensor Networks) - PEPS API reference

• atlas_q.stabilizer_backend - Stabilizer simulator API

• Distributed MPS - Distributed computing API

• Noise Models - Noise modeling API